# subscribed links TSV file
author	wikipedia
item	Mathematics	http://en.wikipedia.org/wiki/Mathematics	Mathematics is the discipline that deals with concepts such as quantity, structure, space and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement and the study of the shapes and motions of physical objects. Mathematicians explore these and related concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.Mathematics is used throughout the world in many fields, including science, engineering, medicine and economics. These fields both inspire and make use of new discoveries in mathematics. New mathematics is also created for its own sake, without any particular application in view, a common practice in the branch known as pure mathematics.The word "mathematics" is often abbreviated math in the <a href="/wiki/No
item	Additional logarithm topics	http://en.wikipedia.org/wiki/Additional_logarithm_topics	In mathematics, a logarithm is the inverse operation of an exponent.
item	Additively closed	http://en.wikipedia.org/wiki/Additively_closed	In mathematics, a set S is said to be additively closed if adding any two elements of S together always produces another element of S. Equivalently, S is additively closed if and only if it is closed under addition.[edit]
item	Areas of mathematics	http://en.wikipedia.org/wiki/Areas_of_mathematics	The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way.
item	Australian Mathematical Society	http://en.wikipedia.org/wiki/Australian_Mathematical_Society	Australian Mathematical Society, founded in 1956, is the national society of the mathematics profession in Australia.
item	Baire set	http://en.wikipedia.org/wiki/Baire_set	In mathematics, Baire set may mean:set having the property of BaireBaire set (general topology), an element of the smallest sigma-algebra containing all compact Gδ sets.This is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Baire_set"			Categories: Disambiguation | Mathematics																Views						 Article				 Discussion				 <li id="ca-edit
item	Bathtub curve	http://en.wikipedia.org/wiki/Bathtub_curve	The bathtub curve is widely used in reliability engineering, although the general concept is also applicable to humans (example of use: actuarial work). It describes a particular form of the hazard function which comprises three parts:The first part is a decreasing failure rate, known as early failures or infant mortality.The second part is a constant failure rate, known as random failures.The third part is an increasing failure rate, known as wear-out failures.
item	Boolean-valued function	http://en.wikipedia.org/wiki/Boolean-valued_function	A boolean-valued function, in some usages a predicate or a proposition, is a function of the type , where X is an arbitrary set, where  is a generic 2-element set, typically , and where the latter is frequently interpreted for logical applications as .
item	Brahmagupta interpolation formula	http://en.wikipedia.org/wiki/Brahmagupta_interpolation_formula	In trigonometry, the Brahmagupta interpolation formula is a special case of the Newton-Stirling interpolation formula, which calculates the values of sine at different intervals. The formula was developed by Brahmagupta in 665, which was later expanded by Newton and Stirling around a thousand years later to develop the more general Newton-Stirling interpolation formula.
item	Calculation	http://en.wikipedia.org/wiki/Calculation	A calculation is a deliberate process for transforming one or more inputs into one or more results.
item	Calculus	http://en.wikipedia.org/wiki/Calculus	Calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, a fact delivered conclusively by the fundamental theorem of calculus.Examples of typical differential calculus problems include:finding the acceleration and velocity of a free-falling body at a particular moment.finding the optimal number of units a company should produce to maximize their profit.Examples of integral calculus problems include:finding areas and volumesfinding the amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressurefinding the amount of parking lot plowed by a snowplow of g
item	Closure %28mathematics%29	http://en.wikipedia.org/wiki/Closure_%28mathematics%29	In mathematics, a set is said to be closed under some operation if the operation on members of the set produces a member of the set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 7 are both natural numbers, but 3 − 7 is not.
item	Cognitive science of mathematics	http://en.wikipedia.org/wiki/Cognitive_science_of_mathematics	The cognitive science of mathematics is the study of mathematical ideas using the techniques of cognitive science. Specifically, it is the search for foundations of mathematics in human cognition.
item	Common logarithm	http://en.wikipedia.org/wiki/Common_logarithm	In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm, named after its base. It is indicated by log10(x), or sometimes Log(x) with a capital L (however, this notation is ambiguous since it can also mean the complex natural logarithmic multi-valued function). On calculators it is usually "log", but mathematicians usually mean natural logarithm rather than common logarithm when they write "log".
item	Compactly generated	http://en.wikipedia.org/wiki/Compactly_generated	In mathematics, compactly generated can refer to:compactly generated groupcompactly generated spaceThis is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Compactly_generated"			Categories: Disambiguation | Mathematics																Views						 Article				 Discussion				 Edit this page				 <li id="ca-hist
item	Connectedness	http://en.wikipedia.org/wiki/Connectedness	In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected. When a disconnected object can be split naturally into connected pieces, each piece is usually called a component (or connected component).
item	Contact process %28mathematics%29	http://en.wikipedia.org/wiki/Contact_process_%28mathematics%29	The contact process is an example of interacting particle systems. It is a continuous time Markov process with state space {0,1}S, where S is a finite or countable graph, usually Zd. The process is usually interpreted as a model for the spread of an infection: if the state of the process at a given time is η, then a site x in S is "infected" if η(x) = 1 and healthy if η(x) = 0. Infected sites become healthy at a constant rate, while healthy sites become infected at a rate proportional to the number infected neighbors. One can generalize the state space to , such is called the multitype contact process. It represents a model when more than one type of infection is competing for space.
item	Cost-weighted activity index	http://en.wikipedia.org/wiki/Cost-weighted_activity_index	A cost-weighted activity index is a technique for measuring the changes in the output of an organisation over time. It is used particularly for Government departments and other bodies that do not operate in a market, hence normal means of measuring output cannot be used.
item	Cycle graph %28disambiguation%29	http://en.wikipedia.org/wiki/Cycle_graph_%28disambiguation%29	A cycle graph or cyclic graph is a connected, 2-regular graph.
item	Decimal representation	http://en.wikipedia.org/wiki/Decimal_representation	A decimal representation of a non-negative real number r is an expression of the form
item	Disjunctive sequence	http://en.wikipedia.org/wiki/Disjunctive_sequence	A disjunctive sequence is an infinite sequence (over a finite alphabet of characters) in which every finite string appears as a substring. For instance, the binary Champernowne sequence
item	Epigraph	http://en.wikipedia.org/wiki/Epigraph	The word epigraph has several meanings, depending on the context.[edit]ArcheologyIn archeology, an epigraph refers to a (usually) signed inscription on structures and coins. See epigraphy.[edit]LiteratureIn literature, an epigraph is a quotation that is placed at the start of a work or section that expresses in some succinct way an aspect or theme of what is to follow.The epigraph may serve as a banner, to link the work to a wider literary canon, either to invite comparison or to enlist a conventional context. The long quotation from Dante's Inferno that prefaces T. S. Eliot's 'The Love Song of J. Alfred Prufrock' is part of a speech by one of the damned souls in Dante's Hell. Linking it to the monologue which forms Eliot's poem adds a comment and a dimension to Prufrock's confession. The epigraph to Eliot's "Gerontion" is a quotation from Shakespeare's Measure for Measure.The epigraphs to
item	Erd%C5%91s number	http://en.wikipedia.org/wiki/Erd%C5%91s_number	The Erdős number, honouring the late Hungarian mathematician Paul Erdős, one of the most prolific writers of mathematical papers, is a way of describing the "collaborative distance", in regard to mathematical papers, between an author and Erdős.Contents1 Definition2 Impact3 See also4 References5 External links
item	Exceptional object	http://en.wikipedia.org/wiki/Exceptional_object	Many branches of mathematics study objects of a certain type and prove a theorem that classifies these objects. A common theme is that the classification results in a number of series of objects as well as a finite number of exceptions that don't fit into any series. These are known as 'exceptional objects'. Frequently these objects play an important role in the subject and surprisingly, the exceptional objects in one branch of mathematics are often related to the exceptional objects in others.Contents1 Regular Polyhedra2 Finite Simple Groups3 Division Algebras4 Simple Lie Groups5 Unimodular Lattices6 Codes7 Block designs8 References
item	Exponential smoothing	http://en.wikipedia.org/wiki/Exponential_smoothing	This forecasting technique in its basic form (simple exponential smoothing) should only be used for non seasonal time series showing no systematic trend, both of these chosen series visibly exhibit at least one of these phenomenon, but it is not fair to say it is of little use as these effects can be measured and removed to produce a stationary series. Given a non seasonal time series with no systematic trend (which is what I hope to reduce these series to), it is considered natural to take as an estimate of Xn+1 a weighted sum of the past observations,
item	Factorization	http://en.wikipedia.org/wiki/Factorization	In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5; and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, we obtain a product of simpler things.
item	Fatilary calculus	http://en.wikipedia.org/wiki/Fatilary_calculus	Fatilary calculus (sv: fatilarkalkyl), the topic discussed in the fake disputation of Rickard Wilson 1955 at Chalmers University of Technology, Gothenburg, Sweden.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Fatilary_calculus"			Categories: <a href
item	Formula	http://en.wikipedia.org/wiki/Formula	In mathematics and in the sciences, a formula (plural: formulae, formulæ or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. One of many famous formulae is Albert Einstein's E=mc² (see special relativity).
item	Foundations of mathematics	http://en.wikipedia.org/wiki/Foundations_of_mathematics	Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathematics is however also a central question of the philosophy of mathematics: On what ultimate basis can mathematical statements be called true?
item	Function space	http://en.wikipedia.org/wiki/Function_space	In mathematics, a function space is a set of functions of a given kind from a set X to a set Y. It is called a space because in many applications, it is a topological space or a vector space or both. Function spaces appear in various areas of mathematics:in set theory, the power set of a set X may be identified with the set of all functions from X to {0,1};, denoted 2X. More generally, the set of functions X → Y is denoted YX.in linear algebra the set of all linear transformations from a vector space V to another one, W, over the same field, is itself a vector space;in functional analysis the same is seen for continuous linear transformations, including topologies on the vector spaces in the above, and many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and Banach spaces.in <a href="/wiki/Functional_analysis" title="Functional analysis"
item	GRE Mathematics Test	http://en.wikipedia.org/wiki/GRE_Mathematics_Test	The GRE subject test in mathematics is designed to assess a candidate's potential for graduate study in the field of mathematics. It contains questions from many fields of mathematics but focuses on calculus and algebra (linear and abstract). The test also contains questions that focus on a broad variety of topics typically encountered in undergraduate mathematics, such as topology, number theory, probability, statistics, and mathematical logic.Retrieved from "http://en.wikipedia.org/wiki/GRE_Mathematics_Test"			Categories: Mathematics | Standardized tests																Views						 Article				 Discussion				 Edit this page				 <a h
item	Gesellschaft f%C3%BCr Angewandte Mathematik und Mechanik	http://en.wikipedia.org/wiki/Gesellschaft_f%C3%BCr_Angewandte_Mathematik_und_Mechanik	Gesellschaft für Angewandte Mathematik und Mechanik ("Society of Applied Mathematics and Mechanics"), often referred to by the acronym GAMM, is a German society for the promotion of science, founded in 1922 by the physicist Ludwig Prandtl and the mathematician Richard von Mises.
item	Group theory	http://en.wikipedia.org/wiki/Group_theory	Group theory is that branch of mathematics concerned with the study of groups. It has several applications in physics and chemistry. Please refer to the glossary of group theory for the definitions of terms used throughout group theory. See also the list of group theory topics.
item	Higher-order function	http://en.wikipedia.org/wiki/Higher-order_function	In mathematics and computer science, higher-order functions are functions which do at least one of the following:take one or more functions as an inputoutput a function
item	Index %28mathematics%29	http://en.wikipedia.org/wiki/Index_%28mathematics%29	The word index is used in variety of senses in mathematics.In perhaps the most frequent sense, an index is a superscript or subscript to a symbol. Superscript indices are often, but not always, used to indicate powers. Subscript indices are usually used to label a set or sequence of variables. See also index set and indexed family.The index of a subgroup is the number of its left cosets (which is equal to the number of its right cosets).The index of a Fredholm operator is the dimension of its kernel minus the dimension of its cokernel.The index of a real quadratic form Q is defined (but not always consistently) as p − q where Q can be written as a difference of p squared linear terms and q squared linear terms.The index of a vector field v at an isolated zero is the degree of the map<img class='tex' src="http://upload.wikimedia.org/math/c/f/e/cfe01f5f2d336c2b78dc498279c5a713.png" alt="x^a \mapsto \frac{v^a(x)}{\sqrt{\sum_b(v^b(x))^2}}" /
item	Infinity	http://en.wikipedia.org/wiki/Infinity	The word infinity comes from the Latin infinitas or "unboundedness". It refers to several distinct concepts which arise in theology, philosophy, mathematics and everyday life. Popular or colloquial usage of the term often does not accord with its more technical meanings.
item	Intercept	http://en.wikipedia.org/wiki/Intercept	In telecommunication, the term intercept has the following meanings:
item	Intransitivity	http://en.wikipedia.org/wiki/Intransitivity	Intransitivity is a scenario in which weighing several options produces a "loop" of preference.
item	List of basic mathematical topics	http://en.wikipedia.org/wiki/List_of_basic_mathematical_topics	
item	List of formulae involving %CF%80	http://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80	The following is a list of formulae involving the mathematical constant pi:Contents1 Classical geometry2 Analysis2.1 Integrals2.2 Infinite series2.3 Infinite products2.4 Miscellaneous3 Approximations4 References
item	Math rock	http://en.wikipedia.org/wiki/Math_rock	Math rock is a style of rock music that emerged in the late 1980s. It is characterised by complex, atypical rhythmic structures, stop/start dynamics and angular, dissonant riffs.Contents1 Characteristics2 Development2.1 Midwestern groups2.2 Pittsburgh groups2.3 San Diego groups2.4 Japanese groups2.5 D.C. area groups2.6 The Louisville sound2.7 Vanguarda Paulista3 <span class="
item	Mathematical joke	http://en.wikipedia.org/wiki/Mathematical_joke	A mathematical joke is a form of professional humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor. The humor may come from a pun or double meaning of a mathematical term, or on a non-mathematician's misunderstanding of a mathematical concept. Such jokes are frequently inaccessible to those without a mathematical bent.Contents1 Pun-based jokes2 'Mathematical pun' based jokes3 Mathematical reasoning4 Mathematicians5 Non-mathematicians6 Non-mathematical mathematical jokes7 See also8 External links
item	Mathematical sociology	http://en.wikipedia.org/wiki/Mathematical_sociology	Mathematical sociology is the usage of mathematics to construct social theories. Generally in sociology, the connection between mathematics and sociology is confined to problems of data analysis; employing statistical models. Many sociological theories are strong in intuitive content, but weak from a formal point of view. In mathematical sociology, the preferred style is encapsulated in the phrase "constructing a mathematical model." This means making specified assumptions about some mathematical objects and providing an empirical interpretation for the ideas. It also means deducing properties of the model and comparing these with relevant empirical data.Contents1 Some influential early work2 A few further developments3 Texts and journals4 Cited books and articles5 See also6 External links
item	Mathematician manqu%C3%A9	http://en.wikipedia.org/wiki/Mathematician_manqu%C3%A9	Mathematician manqué is an unrequited or unaccomplished lover of mathematics. This condition is common among philosophers, apparently in response to the inscription above the door of Plato's Academy, let no one devoid of geometry enter here, ἀγεωμέτρητος μηδεὶς εἰσίτω. (Quoted in Elias' commentary on Aristotle's Categories.)
item	Mathematics Subject Classification	http://en.wikipedia.org/wiki/Mathematics_Subject_Classification	The Mathematics Subject Classification (MSC) is a numerical classification scheme formulated by the American Mathematical Society.
item	Mathematics as a language	http://en.wikipedia.org/wiki/Mathematics_as_a_language	The central question involved in discussing mathematics as a language can be stated as follows&#160;:What do we mean when we talk about the language of mathematics&#160;? To what extent does mathematics meet generally accepted criteria of being a language&#160;?
item	Model selection	http://en.wikipedia.org/wiki/Model_selection	Model selection is the task of selecting a mathematical model from a set of potential models, given evidence. There are many model selection methods, including Akaike information criterion (AIC), Bayesian information criteria (BIC), Deviance information criterion (DIC), various Linear regression methods, Minimum description length (MDL), Minimum Message Length (MML), and many more.
item	Multigrade operator	http://en.wikipedia.org/wiki/Multigrade_operator	In logic and mathematics, a multigrade operator Ω is a parametric operator with parameter k in the set N of non-negative integers.
item	Network calculus	http://en.wikipedia.org/wiki/Network_calculus	Network calculus is theoretical framework for analysing performance guarantees in computer networks. As traffic flows through a network it is subject to constraints imposed by the system components, for example:link capacitytraffic shapers (leaky buckets)congestion controlbackground traffic
item	Nonlinearity	http://en.wikipedia.org/wiki/Nonlinearity	In mathematics, nonlinear systems represent systems whose behavior is not expressible as a sum of the behaviors of its descriptors. In particular, the behavior of nonlinear systems is not subject to the principle of superposition, as linear systems are. Crudely, a nonlinear system is one whose behavior is not simply the sum of its parts or their multiples.
item	Object of the mind	http://en.wikipedia.org/wiki/Object_of_the_mind	An object of the mind is an object which exists in the imagination, but can only be represented or modeled in the real world. Some such objects are mathematical abstractions, literary concepts, or fictional scenarios.Contents1 Mathematical objects2 Logical sequences2.1 False antecedent2.2 False consequent3 Philosophy of mind4 Invented sources5 Convenient fictions6 Pseudoscience7 Self-reference</spa
item	Orbital momentum vector	http://en.wikipedia.org/wiki/Orbital_momentum_vector	The orbital momentum vector may be used as a term in orbital mechanics to calculate anything from eccentricity to both radial and tangential velocity and accelerations. It is derived from a constant of integration.
item	Parametric operator	http://en.wikipedia.org/wiki/Parametric_operator	In logic and mathematics, a parametric operator  with parameter  in the parametric set  is a indexed family of operators  with index  in the index set .[edit]
item	Pendent	http://en.wikipedia.org/wiki/Pendent	Relating to the concave triangular segments composing the structure of a dome, something pendent may be viewed as any member of a support system (i.e: a section of a dome; or, organically, a parent/guardian in a nuclear family).
item	Perfect power	http://en.wikipedia.org/wiki/Perfect_power	In mathematics, a perfect power is a number that can be expressed as a power of any positive, whole number. More formally, n is a perfect power if there exist natural numbers m &gt; 1, and k &gt; 1 such that mk = n. In this case, n may be called a perfect kth power. If k=2 or k=3, then n would be called a perfect square or perfect cube, respectively.
item	Pi culture	http://en.wikipedia.org/wiki/Pi_culture	There is an entire field of humorous yet serious study that involves the use of mnemonic techniques to remember the digits of π, which is known as piphilology. For example, part of the school cheer of MIT is: "Cosine, secant, tangent, sine! 3 point 1 4 1 5 9!" See Pi mnemonics for more examples.
item	Pointwise	http://en.wikipedia.org/wiki/Pointwise	In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An example is pointwise convergence of functions — a sequence of functions
item	Progression %28mathematics%29	http://en.wikipedia.org/wiki/Progression_%28mathematics%29	Progression, in mathematics, may refer to:Arithmetic progressionGeometric progressionThis is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Progression_%28mathematics%29"			Categories: Disambiguation | Mathematics																Views						 Article				 Discussion				 Edit this page				 <li id="ca-history
item	Proportionality %28mathematics%29	http://en.wikipedia.org/wiki/Proportionality_%28mathematics%29	In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.Contents1 Definition2 Examples3 Properties4 Inverse proportionality5 Exponential and logarithmic proportionality6 Experimental determination7 See also
item	Quantity	http://en.wikipedia.org/wiki/Quantity	Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things like as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum.
item	Quantum mechanics	http://en.wikipedia.org/wiki/Quantum_mechanics	Quantum mechanics is a fundamental branch of theoretical physics that replaces classical mechanics and classical electromagnetism at the atomic and subatomic levels. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle physics, and nuclear physics. Along with general relativity, quantum mechanics is one of the pillars of modern physics.Contents1 Introduction2 Description of the theory2.1 Quantum mechanical effects<a href="#Mathematic
item	Safe sex makespan	http://en.wikipedia.org/wiki/Safe_sex_makespan	The safe sex makespan problem is used in operations research as an example that the cheapest capital cost often leads to dramatic increase in operational time, but that the shortest operational time need not be given by the most expensive capital cost.
item	Sir Edmund Whittaker Memorial Prize	http://en.wikipedia.org/wiki/Sir_Edmund_Whittaker_Memorial_Prize	The Sir Edmund Whittaker Memorial Prize is awarded every four years by the Edinburgh Mathematical Society to an outstanding young mathematician having a specified connection with Scotland. Past notable winners have included Gavin Brown.[edit]
item	Mathematical structure	http://en.wikipedia.org/wiki/Mathematical_structure	In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.
item	Superstructure	http://en.wikipedia.org/wiki/Superstructure	A superstructure is an extension of an existing structure or baseline. This term is applied to both physical structures (building, ship) or to conceptual structures (social science). The word itself is a combination of super (Latin for above, in addition) and structure (also from Latin meaning to build, to heap up).Contents1 Engineering concept2 Mathematical concept3 Social sciences concept4 Marxist concept5 See also6 References
item	System equivalence	http://en.wikipedia.org/wiki/System_equivalence	System equivalence is the notion that a parameter of one system behaves the same way as another of a different system.
item	The Unreasonable Effectiveness of Mathematics in the Natural Sciences	http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences	The Unreasonable Effectiveness of Mathematics in the Natural Sciences, published by the physicist Eugene Wigner in 1960, argues that the capacity of mathematics to successfully predict events in physics cannot be a coincidence, but must reflect some larger, deeper or simpler truth in both.Contents1 The miracle of mathematics in the natural sciences2 The deep connection between science and mathematics3 See also4 References
item	Theoretical physics	http://en.wikipedia.org/wiki/Theoretical_physics	Theoretical physics employs mathematical models and abstractions, as opposed to experimental processes, in an attempt to understand Nature. Central to it is mathematical physics 1, though other conceptual techniques are also used. The goal is to rationalize, explain and predict physical phenomena. The advancement of science depends in general on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. For example, while developing special relativity, Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson-Morley experiment on Earth's drift through a luminiferous ether. On the other hand, Einstein was awarded the <a href="/wiki/Nobel_Prize" title="Nob
item	Types of relations	http://en.wikipedia.org/wiki/Types_of_relations	In logic and mathematics generally, and in the theory of relations specifically, relations fall into various types according to their specific properties, often as expressed in the axioms or definitions that they satisfy. An enumeration of the most important of these types of relations is carried out the remainder of the article.[edit]
item	University of Chicago School Mathematics Project	http://en.wikipedia.org/wiki/University_of_Chicago_School_Mathematics_Project	The University of Chicago School Mathematics Project (UCSMP) was founded in 1983 at the University of Chicago with the aim of upgrading mathematics education in elementary and secondary schools throughout the United States. The UCSMP has created a curriculum for students from kindergarten through twelfth grade that emphasizes reading, problem-solving, everyday applications, and the use of calculators, computers, and other technologies. An estimated 3.5 to 4 million students in elementary and secondary schools in every state and virtually every major urban area are now using UCSMP materials[1].Contents1 Secondary education materials1.1 Transition Mathematics (Year 1)1.2 Algebra (Year 2)1.3 Geometry (Year 3)1.4 Advanced Algebra (Year 4)<
item	Vedic mathematics	http://en.wikipedia.org/wiki/Vedic_mathematics	Vedic mathematics is a system of mental calculation developed by Shri Bharati Krishna Tirthaji in the middle 20th century which he claimed he had based on a appendix of Atharvaveda, an ancient text of the Indian teachings known as the Vedas. He stated that these sutras only appeared in his personal copy of the appendix, which he later lost, and not in the generally known appendices; his general editor noted that the style of language of the sutras "point to their discovery by Shri Swamiji himself".
item	Vertical %28angles%29	http://en.wikipedia.org/wiki/Vertical_%28angles%29	A pair of angles are said to be vertical if they share the same vertex and are bounded by the same pair of lines but are opposite to each other. If a pair of angles are vertical, then they are (congruent). More precisely, if two lines AB and CD intersect at E, and E is between A and B, and E is between C and D, then angle AEC is vertical to angle BED, and angle AED is vertical to angle BEC.
item	List of mathematics articles	http://en.wikipedia.org/wiki/List_of_mathematics_articles	This list of mathematics articles collects pointers to articles related to mathematics. Everything related to mathematics, even quite remotely, should be listed here -- including, for example, the list of mathematicians. The process of creating topical lists is ongoing; almost all links on topical lists should also appear in the main alphabetical listing. These lists are necessarily neither complete nor up-to-date — if you see an article that should be listed but is not (or one that shouldn't be here but is), please do update the page accordingly.List of mathematics articles0-9 A B C D E F G H I J <a 
item	List of mathematics lists	http://en.wikipedia.org/wiki/List_of_mathematics_lists	This article attempts to list all lists collecting articles about mathematics in Wikipedia. Some of these lists link to hundreds of articles; some link only to a few. The extremely long list of mathematics articles contains all mathematical articles in alphabetical order. This article brings together the same content organised in a manner better suited to browsing.
item	List of abstract algebra topics	http://en.wikipedia.org/wiki/List_of_abstract_algebra_topics	This is a list of abstract algebra topics, by Wikipedia page. See also:list of commutative algebra topicslist of group theory topicslist of homological algebra topicslist of linear algebra topicsglossary of field theoryglossary of group theoryglossary of ring theoryglossary of tensor theoryContents1 Basic language2 Semigroups and monoids3 Group theory4 Ring theory5 Field theory6</span
item	List of African-American mathematicians	http://en.wikipedia.org/wiki/List_of_African-American_mathematicians	This is a list of articles on African-American mathematicians.Benjamin BannekerDavid BlackwellElbert Frank CoxKelly MillerClarence F. StephensJ. Ernest Wilkins, Jr.This list is incomplete; you can help by expanding it.[edit]
item	List of algebraic coding theory topics	http://en.wikipedia.org/wiki/List_of_algebraic_coding_theory_topics	This is a list of algebraic coding theory topics.Dual codeError-correcting codeEnumerator polynomialGilbert-Varshamov boundBinary Golay codeGoppa codeHamming boundHamming codeHamming distanceHamming weightHat problemLinear codeMcWilliams identityParity bitPerfect codeReed-Solomon codeSingleton boundSyndrome decodingTanner graphRetrieved from "http://en.wikipedi
item	List of algebraic geometry topics	http://en.wikipedia.org/wiki/List_of_algebraic_geometry_topics	This is a list of algebraic geometry topics, by Wikipedia page.Contents1 Classical topics in projective geometry2 Algebraic curves3 Algebraic surfaces4 Algebraic geometry: classical approach5 Complex manifolds6 Algebraic groups7 Contemporary foundations7.1 Commutative algebra7.2 Sheaf theory7.3 Schemes7.4 Category theory8 Alg
item	List of algebraic number theory topics	http://en.wikipedia.org/wiki/List_of_algebraic_number_theory_topics	This is a list of algebraic number theory topics, by Wikipedia page.Gaussian integer, Gaussian rationalQuadratic fieldAlgebraic number fieldDedekind domainGlobal fieldIdeal class groupClass number problem for imaginary quadratic fieldsStark-Heegner theoremHeegner numberAnkeny-Artin-Chowla congruenceRoot of unityGaussian period, Gauss sumChowla-Mordell theoremCyclotomic fieldStickelberger's theoremKronecker-Weber theoremHerbrand-Ribet theorem
item	List of algebraic surfaces	http://en.wikipedia.org/wiki/List_of_algebraic_surfaces	This is a list of named (classes of) algebraic surfaces. It also contains a few non-algebraic complex surfaces. The notation κ stands for the Kodaira dimension, which divides surfaces into four coarse classes.Contents1 Algebraic surfaces2 See also3 References4 External links
item	List of algebraic topology topics	http://en.wikipedia.org/wiki/List_of_algebraic_topology_topics	This is a list of algebraic topology topics, by Wikipedia page. See also: list of general topology topics.Topological propertyContents1 Homology (mathematics)2 Homotopy theory3 Further developments4 Homological algebra5 History
item	List of algorithm general topics	http://en.wikipedia.org/wiki/List_of_algorithm_general_topics	This is a list of algorithm general topics, by Wikipedia page.Analysis of algorithmsAnt colony algorithmApproximation algorithmBest and worst casesBig O notationCombinatorial searchCompetitive analysisComputability theoryComputational complexity theoryEmbarrassingly parallel problemEmergent algorithmEvolutionary algorithmFast Fourier transformGenetic algorithmGraph exploration algorithmHeuristicHill climbingImplementationLas Vegas al
item	List of algorithms	http://en.wikipedia.org/wiki/List_of_algorithms	The following is a list of the algorithms described in Wikipedia. See also the list of data structures, list of algorithm general topics and list of terms relating to algorithms and data structures.
item	List of amateur mathematicians	http://en.wikipedia.org/wiki/List_of_amateur_mathematicians	This is a list of people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics.Ahmes (scribe)Robert Ammann (programmer and postal worker)Rev. Thomas Bayes (Presbyterian minister)Harlan J. Brothers (teacher and inventor)Sir James Cockle (judge)Martin Demaine (goldsmith and glass artist)Britney Gallivan (high school student)James A. Garfield (politician)Hermann Grassmann (school teacher)Kurt Heegner (high school teacher)F. H. Jackson (navy chaplain)Alfred Bray Kempe (lawyer)Kathleen Ollerenshaw (politician)Panini (linguist)Pingala (musician)Marjorie Rice (homemaker)Gast
item	List of axioms	http://en.wikipedia.org/wiki/List_of_axioms	This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.Contents1 Zermelo-Frankel axioms2 Axiom of choice2.1 Equivalents of AC2.2 Weaker than AC2.3 Alternates incompatible with AC3 Other axioms of mathematical logic4 Geometry5 Other axioms
item	List of Boolean algebra topics	http://en.wikipedia.org/wiki/List_of_Boolean_algebra_topics	
item	List of calculus topics	http://en.wikipedia.org/wiki/List_of_calculus_topics	This is a list of calculus topics.Note: the ordering of topics in sections is a suggestion to students.Contents1 Before calculus (pre calculus)2 Limits3 Differential calculus4 Integral calculus5 Special functions and numbers6 Numerical integration7 Lists and tables8 Multivariable9 Series10 History11 Nonstandard calculus
item	List of Cambridge mathematicians	http://en.wikipedia.org/wiki/List_of_Cambridge_mathematicians	A list of mathematicians, past and present, with associations with the University of Cambridge.John Couch Adams, fellow of St. John's College, Cambridge 1843-1852; fellow of Pembroke College, Cambridge 1853-1892; Lowndean Professor of Astronomy and Geometry 1859-1891Michael Atiyah, fellow of Trinity College, Cambridge 1954-1957; fellow of Pembroke College, Cambridge 1958-1961; Master of Trinity College, Cambridge 1990-1997Charles Babbage, Lucasian Professor of Mathematics 1828-1839Alan Baker, fellow of Trinity College, Cambridge 1964-Isaac Barrow, fellow of Trinity College, CambridgeRichard Ewen BorcherdsJ. W. S. Cassels, fellow of
item	List of mathematics categories	http://en.wikipedia.org/wiki/List_of_mathematics_categories	[edit]Mathematics categoriesThe contents of these categories will be automatically added to the list of mathematics articles.[edit]0–93-manifolds -- 4-dimensional geometry -- 4-manifolds --[edit]AAbel Prize -- Abelian group theory -- Abelian varieties -- Abstract algebra -- Adjoint functors -- Affine geometry -- Algebra -- <
item	List of category theory topics	http://en.wikipedia.org/wiki/List_of_category_theory_topics	This is a list of category theory topics, by Wikipedia page.Contents1 Specific categories2 Objects3 Morphisms4 Functors5 Limits6 Additive structure7 Monoidal category8 Cartesian closed category9 Structure (category theory)10 Topoi, Toposes
item	List of chaotic maps	http://en.wikipedia.org/wiki/List_of_chaotic_maps	In mathematics, a chaotic map is a map that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
item	List of circle topics	http://en.wikipedia.org/wiki/List_of_circle_topics	This list of circle topics is not intended for metaphorical circles, but rather for topics related to the geometric shape. Thus, for example, a link to inner circle does not belong here.Contents1 Geometry2 Geography3 Artifacts4 Glyphs and symbols5 See also
item	List of mathematical topics in classical mechanics	http://en.wikipedia.org/wiki/List_of_mathematical_topics_in_classical_mechanics	This is a list of mathematical topics in classical mechanics, by Wikipedia page. See also list of variational topics, correspondence principle.Contents1 Newtonian physics2 Conservation laws3 Law of universal gravitation4 Hamiltonian mechanics5 Lagrangian mechanics
item	List of cohomology theories	http://en.wikipedia.org/wiki/List_of_cohomology_theories	This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at the end of this article.Contents1 Notation2 Ordinary homology theories2.1 Homology and cohomology with integer coefficients.2.2 Homology and cohomology with rational (or real or complex) coefficients.2.3 Homology and cohomology with mod p coefficients.3 K-theories3.1 Real K-theory<span class="toc
item	List of combinatorial computational geometry topics	http://en.wikipedia.org/wiki/List_of_combinatorial_computational_geometry_topics	List of combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects as discrete entities and hence the methods of their solution are mostly theories and algorithms of combinatorial character.
item	List of combinatorics topics	http://en.wikipedia.org/wiki/List_of_combinatorics_topics	This is a list of combinatorics topics.
item	List of commutative algebra topics	http://en.wikipedia.org/wiki/List_of_commutative_algebra_topics	This is a list of commutative algebra topics, by Wikipedia page.commutative ringring ideal, maximal ideal, prime idealring homomorphismring monomorphismring epimorphismring isomorphismquotient ringintegral domainalgebraic number fieldfield of fractionsproduct of ringsBoolean algebrazero divisornilpotent, reduced ringannihilatorprincipal ideal domainunique factorization domainDedekind domain<a href="/wiki/Fra
item	List of mathematics competitions	http://en.wikipedia.org/wiki/List_of_mathematics_competitions	Mathematics competitions or mathematical olympiads are competitive events where participants write a mathematics test. These tests may require multiple choice or numeric answers, or a detailed written solution or proof. In the United States, usually only competitions where the participants write a full proof are called Mathematical Olympiads.Contents1 International mathematics competitions2 Regional mathematics competitions3 National mathematics competitions3.1 Argentina3.2 Australia3.3 Austria3.4 Belgium3.5 Brazil3.6 Canada3.7 China3.8 Cyprus<li class="tocleve
item	List of complex analysis topics	http://en.wikipedia.org/wiki/List_of_complex_analysis_topics	This is a list of complex analysis topics, by Wikipedia page.Contents1 Local theory2 Growth3 Contour integrals4 Special functions5 Riemann surfaces6 Other7 Several complex variables8 History (needs work)
item	List of complexity classes	http://en.wikipedia.org/wiki/List_of_complexity_classes	This is a list of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics.
item	List of computability and complexity topics	http://en.wikipedia.org/wiki/List_of_computability_and_complexity_topics	This is a list of computability and complexity topics, by Wikipedia page.
item	List of computer algebra systems	http://en.wikipedia.org/wiki/List_of_computer_algebra_systems	The following is a list of computer algebra systems.Contents1 General purpose1.1 Proprietary1.2 Free / open source software2 Algebraic geometry, polynomial computations3 Graph theory4 Algebra, group theory5 Number theory6 Calculator algebra systems7 Educational8 See also9 External links
item	List of computer graphics and descriptive geometry topics	http://en.wikipedia.org/wiki/List_of_computer_graphics_and_descriptive_geometry_topics	This is a list of computer graphics and descriptive geometry topics, by Wikipedia page.2D computer graphics2D geometric model3D computer graphics3D projectionAlpha compositingAnisotropic filteringAnti-aliasingAxis-aligned bounding boxAxonometric projectionBézier curveBézier surfaceBicubic interpolationBilinear interpolationBinary space partitioningBitmap graphics editorBounding volumeBresenham's line algorithmBump mapping<a href=
item	List of conjectures	http://en.wikipedia.org/wiki/List_of_conjectures	This is a list of mathematical conjectures, by Wikipedia page. They are divided into four sections, according to their status in 2006.
item	List of convexity topics	http://en.wikipedia.org/wiki/List_of_convexity_topics	This is a list of convexity topics, by Wikipedia page.Alpha blendingBarycentric coordinatesBohr-Mollerup theoremBond convexityCarathéodory's theorem (convex hull)Choquet theoryClosed convex functionConcavityConvexConvex analysisConvex combinationConvex and ConcaveConvex conjugateConvex functionConvex geometryConvex hullConvex lensEpigraphExtreme pointFenchel conjugateFenchel's inequality<a href="/wiki/Fixed_point_theorems_in_infinite-dimensi
item	List of coordinate charts	http://en.wikipedia.org/wiki/List_of_coordinate_charts	This article attempts to conveniently list articles on some of the most useful coordinate charts in some of the most useful examples of Riemannian manifolds.
item	List of cryptography topics	http://en.wikipedia.org/wiki/List_of_cryptography_topics	This page aims to alphabetically list articles that are primarily related to cryptography. There is a categorised and (somewhat) annotated list of the same articles in subject groupings at Topics in cryptography; it will probably be more useful to those attempting to make some sense of the field. This page is intended to be useful to those monitoring Wikipedia's coverage of the subject (e.g. for editing or maintenance purposes) by providing an easy way to track changes in the indexed articles by clicking on "Related changes" in the sidebar or the link below:Recent changes in articles about cryptographyThis list does not necessarily include all cryptography-related articles in the Wikipedia, though there is a concerted effort to keep it so. Nevertheless, if you see an article that should be here, but isn't (or one that shouldn't be here but is), please do update the list accordingly.Note 1: This page is also being made somewhat redundant by the new category system. See Category:Cryptography and its subcategories.Note 2: The purpose of the hidden talk page links to each page in this list is so also the talk pages become visible in the related/recent changes.[edit]See alsoTopics in cryptography — an analytical list of articles and terms.<
item	User:Matt Crypto/tmp	http://en.wikipedia.org/wiki/User:Matt_Crypto/tmp	This page aims to alphabetically list articles that are primarily related to cryptography. There is a categorised and (somewhat) annotated list of the same articles in subject groupings at Topics in cryptography; it will probably be more useful to those attempting to make some sense of the field. This page is intended to be useful to those monitoring Wikipedia's coverage of the subject (e.g. for editing or maintenance purposes) by providing an easy way to track changes in the indexed articles by clicking on "Related changes" in the sidebar or the link below:Recent changes in articles about cryptographyThis list does not necessarily include all cryptography-related articles in the Wikipedia, though there is a concerted effort to keep it so. Nevertheless, if you see an article that should be here, but isn't (or one that shouldn't be here but is), please do update the list accordingly.Note 1: This page is also being made somewhat redundant by the new category system. See Category:Cryptography and its subcategories.Note 2: The purpose of the hidden talk page links to each page in this list is so also the talk pages become visible in the related/recent changes.[edit]See alsoTopics in cryptography — an analytical list of articles and terms.<a h
item	List of terms based on the word cube	http://en.wikipedia.org/wiki/List_of_terms_based_on_the_word_cube	ShapesCube itselfCuboctahedronCuboidHypercube (tesseract)RhombicuboctahedronSnub cubeTruncated cube[edit]
item	List of curve topics	http://en.wikipedia.org/wiki/List_of_curve_topics	This is a list of curve topics in mathematics, by Wikipedia page. See also curve, list of curves, and list of differential geometry topics.acnodealgebraic curvearcasymptoteasymptotic curveBarbier's theorembarycentric[1]Bézier curveBezout's theoremBirch and Swinnerton-Dyer conjecturecausticCesàro equationchord (geometry)cissoidcircumference<a href="/wiki/Closed_timelike_curve" title="Closed timeli
item	List of curves	http://en.wikipedia.org/wiki/List_of_curves	This is a list of curves, by Wikipedia page. See also list of curve topics.
item	Table of derivatives	http://en.wikipedia.org/wiki/Table_of_derivatives	The primary operation in differential calculus is finding a derivative. This table lists derivatives of many functions. In the following, f and g are differentiable functions from the real numbers, and c is a real number. These formulas are sufficient to differentiate any elementary function.Contents1 Rules for differentiation of general functions2 Derivatives of simple functions3 Derivatives of exponential and logarithmic functions4 Derivatives of trigonometric functions5 Derivatives of hyperbolic functions
item	List of differential geometry topics	http://en.wikipedia.org/wiki/List_of_differential_geometry_topics	This is a list of differential geometry topics, by Wikipedia page. See also glossary of differential and metric geometry, list of Lie group topics.Contents1 Differential geometry of curves2 Differential geometry of surfaces3 Calculus on manifolds4 Differential topology5 Fiber bundles6 Riemannian geometry7 Variant structures8 Curvature9 Other
item	List of basic discrete mathematics topics	http://en.wikipedia.org/wiki/List_of_basic_discrete_mathematics_topics	This is a list of basic discrete mathematics topics, by Wikipedia page. Included here is much of the standard mathematical language, used in university-level courses and routinely in research papers. This is not, however, intended as a complete glossary of mathematical terms; just a selection of typical terms of art that may be encountered.Contents1 Sets2 Functions3 Operations4 Arithmetic5 Elementary algebra6 Mathematical relations7 Mathematical phraseology8 Combinatorics9 Probability10 Propositional logic<li class="t
item	Table of divisors	http://en.wikipedia.org/wiki/Table_of_divisors	The tables below list all of the divisors of the numbers 1 to 1000.
item	List of dynamical systems and differential equations topics	http://en.wikipedia.org/wiki/List_of_dynamical_systems_and_differential_equations_topics	This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations.Contents1 Dynamical systems, in general2 Abstract dynamical systems3 Dynamical systems, examples4 Complex dynamics5 Ordinary differential equations: general6 Linear differential equations7 Mechanics8 Functions defined via an ODE9 Rotating systems</
item	List of special functions and eponyms	http://en.wikipedia.org/wiki/List_of_special_functions_and_eponyms	This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential operators of the theory (but not intended to include every mathematical eponym). Named symmetric functions, and more general special polynomials, are included.Contents1 Niels Abel2 Sir George Biddell Airy3 Waleed Al-Salam (1926-1996)4 C. T. Anger5 Kazuhiko Aomoto6 Paul Emile Appell (1855-1930)7 Richard Askey8 E. T. Bell<span clas
item	List of equations	http://en.wikipedia.org/wiki/List_of_equations	This is a list of equations, by Wikipedia page. See also list of equations in classical mechanics, list of relativistic equations, equation solving, theory of equations.[edit]
item	List of topics named after Leonhard Euler	http://en.wikipedia.org/wiki/List_of_topics_named_after_Leonhard_Euler	In mathematics and physics, there are a large number of topics named in honour of Leonhard Euler. Many of these topics involve a function, formula or identity, often ambiguously called Euler's formula, Euler's function, or Euler's identity. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. Physicists and mathematicians often jest that often times a discovery or theorem is named after the "first person after Euler to discover it".[edit]
item	List of mathematical examples	http://en.wikipedia.org/wiki/List_of_mathematical_examples	This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a general theorem, could perhaps be considered an "example"). The discussion page for list of mathematical topics has some comments on this. Eventually this page may have its own discussion page. This page links to itself in order that edits to this page will be included among related changes when the user clicks on that button.
item	List of exceptional set concepts	http://en.wikipedia.org/wiki/List_of_exceptional_set_concepts	This is a list of exceptional set concepts. In mathematics, and in particular in mathematical analysis, it is very useful to be able to characterise subsets of a given set X as 'small', in some definite sense, or 'large' if their complement in X is small. There are numerous concepts that have been introduced to study 'small' or 'exceptional' subsets. In the case of sets of natural numbers, it is possible to define more than one concept of 'density', for example. See also list of properties of sets of reals.Almost allAlmost alwaysAlmost everywhereAlmost neverAlmost surelyAnalytic capacityClosed unbounded setCofinal (mathematics)CofiniteDense subsetIP set2-largeLarge set (Ramsey theory)<a href="/wiki/Meagre_set" title
item	List of exponential topics	http://en.wikipedia.org/wiki/List_of_exponential_topics	This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics.Bacterial growthCell growthBarometric formula Basic infection number Beer-Lambert law Characterizations of the exponential function Catenary Compound interest Elimination half-life Euler's identity <a href="/wiki/E_%
item	List of factorial and binomial topics	http://en.wikipedia.org/wiki/List_of_factorial_and_binomial_topics	This is a list of factorial and binomial topics in mathematics, by Wikipedia page. See also binomial (disambiguation).Alternating factorialAntichainBeta functionBinomial coefficientBinomial distributionBinomial seriesBinomial theorem, Pascal's triangleBinomial transformBinomial typeCarlson's theoremCatalan numberCombinationDe Polignac's formulaDifference operatorDifference polynomialsDigamma functionErdős-Ko-Rado theoremEuler-Masche
item	List of finite simple groups	http://en.wikipedia.org/wiki/List_of_finite_simple_groups	In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type (including the Tits group, which strictly speaking is not of Lie type), or one of 26 sporadic groups.
item	List of first-order theories	http://en.wikipedia.org/wiki/List_of_first-order_theories	In mathematical logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model theory and some of their properties.Contents1 Preliminaries2 Pure identity theories3 Equivalence relations4 Orders5 Graphs6 Boolean algebras7 Groups8 Rings and fields9 Arithmetic10 Set theories11 See also<span class="tocn
item	List of Fourier analysis topics	http://en.wikipedia.org/wiki/List_of_Fourier_analysis_topics	This is an alphabetical list of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis and representation theory topics.Almost periodic functionAutocorrelationAutocovarianceBanach algebraBessel functionCompact groupContinuous Fourier transformConvergence of Fourier seriesConvolutionConvolution theoremCosine transformDFT matrixDini testDirichlet kernelDirichlet problemDiscrete Fourier transform<a href="/wiki/Discrete_Hartley_
item	List of Fourier-related transforms	http://en.wikipedia.org/wiki/List_of_Fourier-related_transforms	This is a list of linear transformations of functions related to the Fourier transform. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component.Applied to functions of continuous arguments, Fourier-related transforms include:Two-sided Laplace transform, a generalization of the continuous Fourier transformMellin transform, another closely related integral transformLaplace transformContinuous Fourier transform (often, just Fourier transform or FT), with special cases:Cosine transform and sine transform (for functions of even/odd symmetry)<a href="/wiki/Fourier_series" ti
item	List of fractal topics	http://en.wikipedia.org/wiki/List_of_fractal_topics	This is a list of fractal topics, by Wikipedia page, See also list of dynamical systems and differential equations topics.1/f noiseApollonian gasketAttractorBox-counting dimensionCantor distributionCantor dustCantor functionCantor setCantor spaceChaos theoryCoastlineConstructal theoryDevil's staircaseDimensionDimension theoryDragon curveFatou setFractal antennaFractal artFractal compression<a href="/wiki/Fractal_flame" title="Fractal flame
item	List of fractals by Hausdorff dimension	http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension	A fractal is a geometric object whose Hausdorff dimension (δ) strictly exceeds its topological dimension. Presented here is a list of fractals ordered by increasing Hausdorff dimension, with the purpose of visualizing what it means for a fractal to have a low or a high dimension.δ&#160;=&#160;0.6309Cantor set1.26Hénon attractorThe canonical Hénon map (with parameters a&#160;=&#160;1.4 and b&#160;=&#160;0.3) has Hausdorff dimension δ&#160;=&#160;1.261&#160;±&#160;0.003. Different parameters yield different δ values.1.2619Koch curve<img src="http://upload.wikimedia.org/wikipedia/commons/t
item	List of functional analysis topics	http://en.wikipedia.org/wiki/List_of_functional_analysis_topics	This is a list of functional analysis topics, by Wikipedia page.Contents1 Hilbert space2 Functional analysis, classic results3 Operator theory4 Banach space examples5 Real and complex algebras6 Topological vector spaces7 Amenability8 Wavelets9 Quantum theory10 Probability11 Non-linear12 History
item	List of mathematical functions	http://en.wikipedia.org/wiki/List_of_mathematical_functions	In mathematics, several functions or groups of functions are important enough to deserve their own names. This is a listing of pointers to those articles which explain these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics. A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations. See also orthogonal polynomial.Contents1 Elementary functions1.1 Algebraic functions1.2 Elementary transcendental functions2 Special functions<a
item	List of topics named after Carl Friedrich Gauss	http://en.wikipedia.org/wiki/List_of_topics_named_after_Carl_Friedrich_Gauss	Carl Friedrich Gauss (1777 - 1855) is the eponym of all of the topics listed below.[edit]
item	List of general topology topics	http://en.wikipedia.org/wiki/List_of_general_topology_topics	This is a list of general topology topics, by Wikipedia page. See also:topology glossarylist of geometric topology topicslist of algebraic topology topicsContents1 Basic concepts2 Limits3 Topological properties3.1 Compactness and countability3.2 Connectedness3.3 Separation axioms4 Topological constructions5 Examples6 Uniform spaces7 <span class
item	List of examples in general topology	http://en.wikipedia.org/wiki/List_of_examples_in_general_topology	This is a list of useful examples in general topology, a field of mathematics.Alexandrov topologyCantor spaceCo-kappa topologyCocountable topologyCofinite topologyCompact-open topologyCompactificationDiscrete topologyDouble-pointed cofinite topologyExtended real number lineHawaiian earringHilbert cubeLakes of WadaLong lineOrder topologyLexicographical/dictionary orderOrdinal number topologyReal lineOverlapping interval topology<a href="/wiki/Moore_plane" title="
item	List of geometers	http://en.wikipedia.org/wiki/List_of_geometers	A geometer is a mathematician whose area of study is geometry. Some important geometers and their main fields of work are:[edit]
item	List of geometric shapes	http://en.wikipedia.org/wiki/List_of_geometric_shapes	This is a list of geometric shapes.Contents1 Generally composed of straight line segments2 Curved2.1 Not composed of circular arcs3 See also
item	List of geometric topology topics	http://en.wikipedia.org/wiki/List_of_geometric_topology_topics	This is a list of geometric topology topics, by Wikipedia page.Contents1 Knot theory2 Surfaces3 Three-manifolds4 Manifolds in general
item	List of geometry topics	http://en.wikipedia.org/wiki/List_of_geometry_topics	This is list of geometry topics, by Wikipedia page.Geometric shape covers standard terms for plane shapesList of mathematical shapes covers all dimensionsList of differential geometry topicsList of geometersSee also list of curves, list of curve topics.Contents1 Types, methodologies, and terminologies of geometry2 Euclidean geometry, foundations2.1 Euclidean plane geometry2.2 3-dimensional Euclidean geometry (solid geometry)2.3 n-dimensional Euclidean geometry3 Non-Euclidean geometry
item	List of graph theory topics	http://en.wikipedia.org/wiki/List_of_graph_theory_topics	This is a list of graph theory topics, by Wikipedia page.
item	List of graphical methods	http://en.wikipedia.org/wiki/List_of_graphical_methods	This is a list of graphical methods with a mathematical basis. See also list of computer graphics and descriptive geometry topics.Contents1 Simple displays2 Set theory3 Descriptive geometry4 Engineering drawing5 Software design6 Cartography7 Natural sciences8 Physical sciences9 Business methods10 Conceptual analysis11 Statistics12 <span class="toct
item	List of group theory topics	http://en.wikipedia.org/wiki/List_of_group_theory_topics	This is a list of group theory topics, by Wikipedia page, to provide an overview of the topic and to allow those interested to use the "Related changes" feature to keep abreast of edits in this area.
item	List of small groups	http://en.wikipedia.org/wiki/List_of_small_groups	The following list in mathematics contains the finite groups of small order up to group isomorphism.
item	List of harmonic analysis and representation theory topics	http://en.wikipedia.org/wiki/List_of_harmonic_analysis_and_representation_theory_topics	This is a list of harmonic analysis and representation theory topics, by Wikipedia page. See also list of Fourier analysis topics and list of Fourier-related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical analysis, mathematical physics and engineering.Contents1 Fourier analysis1.1 Fourier series1.2 Fourier transform2 Topological groups3 Representation theory4 Representations of Lie groups<a href="#F
item	List of mathematics history topics	http://en.wikipedia.org/wiki/List_of_mathematics_history_topics	This is a list of mathematics history topics, by Wikipedia page. See also list of mathematicians, timeline of mathematics, history of mathematics, list of publications in mathematics.
item	List of homological algebra topics	http://en.wikipedia.org/wiki/List_of_homological_algebra_topics	This is a list of homological algebra topics, by Wikipedia page.[edit]
item	List of hypergeometric identities	http://en.wikipedia.org/wiki/List_of_hypergeometric_identities	In mathematics, the hypergeometric series is involved in a number of classical hypergeometric function identities. This article provides an incomplete listing of some of these, referred to as Bailey's list, in reference to W. N. Bailey.
item	List of mathematical identities	http://en.wikipedia.org/wiki/List_of_mathematical_identities	This page lists identities in the sense of mathematics, that is, identically true relations holding in algebra or between special functions.Cassini's identityDifference of two squaresBézout's identityEuler's identityVandermonde's identityBrahmagupta-Fibonacci identityEuler's four-square identityFibonacci's identityMcWilliams identity[edit]
item	List of Indian mathematicians	http://en.wikipedia.org/wiki/List_of_Indian_mathematicians	The chronology of Indian mathematics spans from the Indus valley civilization and the Vedas to Modern times.
item	List of inequalities	http://en.wikipedia.org/wiki/List_of_inequalities	This page lists Wikipedia articles about named mathematical inequalities.[edit]
item	List of information theory topics	http://en.wikipedia.org/wiki/List_of_information_theory_topics	This is a list of information theory topics, by Wikipedia page.A Mathematical Theory of Communicationalgorithmic information theoryarithmetic encodingchannel capacityCommunication Theory of Secrecy Systemsconditional entropyconditional quantum entropyconfusion and diffusioncross entropydata compressionentropy encodingFisher informationHick's lawHirchman uncertaintyHuffman encodinginformation bottleneck methodinformation entropyinformation theoretic security
item	Table of integrals	http://en.wikipedia.org/wiki/Table_of_integrals	Integration is one of the two basic operations in calculus and since it, unlike differentiation, is non-trivial, tables of known integrals are often useful. This page lists some of the most common antiderivatives; a more complete list can be found in the list of integrals.
item	Lists of integrals	http://en.wikipedia.org/wiki/Lists_of_integrals	See the following pages for lists of integrals:List of integrals of rational functionsList of integrals of irrational functionsList of integrals of trigonometric functionsList of integrals of inverse trigonometric functionsList of integrals of hyperbolic functionsList of integrals of arc hyperbolic functionsList of integrals of exponential functionsList of integrals of logarithmic functionsAlso see table of integrals for the most common integral functions.Contents1 Other lists of integrals2 References<
item	List of integrals of arc functions	http://en.wikipedia.org/wiki/List_of_integrals_of_arc_functions	The following is a list of integrals (antiderivative formulas) for integrands that contain inverse trigonometric functions (also know as “arc functions”). For a complete list of integral formulas, see the Table of Integrals and the List of Integrals.
item	List of integrals of arc hyperbolic functions	http://en.wikipedia.org/wiki/List_of_integrals_of_arc_hyperbolic_functions	The following is a list of integrals (antiderivative functions) of arc hyperbolic functions. For a complete list of integral functions, please see table of integrals and list of integrals.<img class='tex' src="http://upload.wikimedia.org/math/b/6/8/b68dd2d4f02d5913b734873e20a80bc9.png" alt="\int\mathrm{arcsch}\,\frac{x}{c}\,dx = x\,\mathrm{arcsch}\,\frac{x}{c} + c\,\ln\,\frac{x + \sqrt{x^2
item	List of integrals of exponential functions	http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions	The following is a list of integrals (antiderivative functions) of exponential functions. For a complete list of Integral functions, please see table of integrals and list of integrals.<img class='tex' src="http://uplo
item	List of integrals of hyperbolic functions	http://en.wikipedia.org/wiki/List_of_integrals_of_hyperbolic_functions	The following is a list of integrals (antiderivative functions) of hyperbolic functions. For a complete list of Integral functions, please see table of integrals and list of integrals.also: als
item	List of integrals of irrational functions	http://en.wikipedia.org/wiki/List_of_integrals_of_irrational_functions	The following is a list of integrals (antiderivative functions) of irrational functions. For a complete list of integral functions, please see table of integrals and list of integrals.[edit]
item	List of integrals of logarithmic functions	http://en.wikipedia.org/wiki/List_of_integrals_of_logarithmic_functions	The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, please see table of integrals and list of integrals.
item	List of integrals of rational functions	http://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions	The following is a list of integrals (antiderivative functions) of rational functions. For a more complete list of integrals, please see table of integrals and list of integrals.
item	List of integrals of trigonometric functions	http://en.wikipedia.org/wiki/List_of_integrals_of_trigonometric_functions	The following is a list of integrals (antiderivative functions) of trigonometric functions. For a complete list of Integral functions, please see table of integrals and list of integrals. See also: trigonometric integral
item	List of integration and measure theory topics	http://en.wikipedia.org/wiki/List_of_integration_and_measure_theory_topics	This is a list of integration and measure theory topics, by Wikipedia page.Contents1 Intuitive foundations2 Riemann integral3 Improper integrals4 Measure theory and the Lebesgue integral5 Extensions6 Integral equations7 Integral transforms8 Integral geometry9 Other10 See also
item	Karp%27s 21 NP-complete problems	http://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems	One of the most important results of computational complexity theory was Stephen Cook's 1971 paper that demonstrated the first NP-complete problem, the boolean satisfiability problem. In 1972, Richard Karp took this idea a leap forward with his landmark paper, "Reducibility Among Combinatorial Problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for their intractability, were all NP-complete.
item	List of knot theory topics	http://en.wikipedia.org/wiki/List_of_knot_theory_topics	This list contains articles related to the mathematical theory of knots, links, and braids.
item	List of mathematical knots and links	http://en.wikipedia.org/wiki/List_of_mathematical_knots_and_links	This article contains a list of mathematical knots and links. See also list of knots, list of geometric topology topics.[edit]
item	List of large cardinal properties	http://en.wikipedia.org/wiki/List_of_large_cardinal_properties	This page is a list of some types of cardinals; it is arranged roughly in order of the consistency strength of the axiom asserting the existence of cardinals with the given property. Existence of a cardinal number κ of a given type implies the existence of cardinals of most of the types listed above that type, and for most listed cardinal descriptions φ of lesser consistency strength, V(κ) satisfies "there are unboundedly many cardinals satisfying φ"."Small" cardinals: 0, 1, 2, ..., ,..., , ... (see Aleph number)weakly and strongly inaccessible cardinals, α-inaccessible cardinals, and hyper inaccessible cardinalsweakly and strongly Mahlo cardinals, α-Mahlo cardinals, and hyper Mahlo cardinals.weakly compact cardinals (same as Π11-indescribable cardinals)Πmn-indescribable cardinals, totally indescribable cardinalsunfoldable cardinals and λ-u
item	List of lemmas	http://en.wikipedia.org/wiki/List_of_lemmas	This is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs), by Wikipedia page. See also list of theorems and list of conjectures.Summation by parts Abel's lemmaArtin-Rees lemma (commutative algebra)Borel's lemma (partial differential equations)Borel-Cantelli lemma (probability theory)Burnside's lemmaCovering lemmaDehn's lemma (geometric topology)Diagonalization lemmaDickson's lemma (combinatorics)Euclid's lemmaFatou's lemma<a href="/wiki/Subadditive_function" tit
item	List of letters used in mathematics and science	http://en.wikipedia.org/wiki/List_of_letters_used_in_mathematics_and_science	Some common conventions:Intensive quantities in physics are usually denoted with minuscules, while extensive are denoted with capital letters.Most symbols are written in italics.Vectors are bold.Sets of numbers are blackboard bold.[bearbeiden]
item	List of Lie group topics	http://en.wikipedia.org/wiki/List_of_Lie_group_topics	This is a list of Lie group topics, by Wikipedia page.Contents1 Examples2 Lie algebras3 Foundational results4 Semisimple theory5 Representation theory6 Applications6.1 Physical theories6.2 Geometry6.3 Discrete groups6.4 Algebraic groups7 Special functions7.1 Automorphic forms8 Peop
item	Table of Lie groups	http://en.wikipedia.org/wiki/Table_of_Lie_groups	This article gives a table of some common Lie groups and their associated Lie algebras.
item	List of simple Lie groups	http://en.wikipedia.org/wiki/List_of_simple_Lie_groups	In mathematics, the simple Lie groups were classified by Élie Cartan. The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces. See also the table of Lie groups for a smaller list of groups that commonly occur in theoretical physics.Contents1 Simple Lie groups2 Simple Lie algebras3 Symmetric spaces4 Hermitean symmetric spaces5 Notation6 The list of simple Lie groups6.1 R (Abelian)6.2 An (n �
item	Table of limits	http://en.wikipedia.org/wiki/Table_of_limits	This is a table of limits for common functions. Note that a and b are constants with respect to x.Contents1 Limits for general functions2 Simple functions3 Logarithmic and exponential functions4 Trigonometric functions5 Near infinities
item	List of linear algebra topics	http://en.wikipedia.org/wiki/List_of_linear_algebra_topics	This is a list of linear algebra topics, by Wikipedia page. See alsolist of matricesglossary of matrix theoryglossary of tensor theory.Contents1 Linear equations2 Matrices3 Matrix decompositions4 Computations5 Vectors6 Vector spaces7 Multilinear algebra8 Affine space9 Projective space
item	List of Muslim mathematicians	http://en.wikipedia.org/wiki/List_of_Muslim_mathematicians	A Muslim mathematician is a person that professes Islam and engaged in the mathematicians aspect of Islamic science.[edit]
item	List of canonical coordinate transformations	http://en.wikipedia.org/wiki/List_of_canonical_coordinate_transformations	This is a list of canonical coordinate transformations.Contents1 2-Dimensional1.1 To Cartesian coordinates from polar coordinates1.2 To polar coordinates from Cartesian coordinates2 3-Dimensional2.1 To Cartesian coordinates2.1.1 From spherical coordinates2.1.2 From cylindrical coordinates2.2 To Spherical coordinates2.2.1 From Cartesian coordinates2.2.2 From cylindrical coordinates2.3 To cylindrical coordina
item	List of integrals of inverse trigonometric functions	http://en.wikipedia.org/wiki/List_of_integrals_of_inverse_trigonometric_functions	Substitution or other forms of algebraic manipulation are used to arrive at integrals listed in the table.
item	List of notable textbooks in statistical mechanics	http://en.wikipedia.org/wiki/List_of_notable_textbooks_in_statistical_mechanics	A list of notable textbooks in statistical mechanics, arranged by date.[edit]
item	List of logarithm topics	http://en.wikipedia.org/wiki/List_of_logarithm_topics	This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics.Acoustic powerantilogarithmApparent magnitudeBelBenford's lawBinary logarithmBode plotHenry BriggsCologarithmCommon logarithmDiscrete logarithme (mathematical constant)El Gamal discrete log cryptosystemHarmonic series (mathematics)Iterated logarithmLaw of the iterated logarithmLinear form in logarithmsLinearithmic<a href="/wiki/List_of_integrals_of_logarit
item	List of topics in logic	http://en.wikipedia.org/wiki/List_of_topics_in_logic	This is a list of topics in logic.Contents1 Alphabetical list1.1 A1.2 B1.3 C1.4 D1.5 E1.6 F1.7 G1.8 H1.9 I1.10 J1.11 K1.12 L1.13 M1.14 N1.15 O
item	List of mathematical logic topics	http://en.wikipedia.org/wiki/List_of_mathematical_logic_topics	This is a list of mathematical logic topics, by Wikipedia page.
item	List of logicians	http://en.wikipedia.org/wiki/List_of_logicians	A logician is a person, such as a philosopher or mathematician, whose topic of scholarly study is logic. The famous logicians are listed below in English alphabetical transliteration order (by surname).
item	List of manifolds	http://en.wikipedia.org/wiki/List_of_manifolds	This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For types of manifold by additional structure (e.g. Riemannian manifolds with a metric) see Category:Structures on manifolds.[edit]
item	List of Mathematical Societies	http://en.wikipedia.org/wiki/List_of_Mathematical_Societies	This is a list of Mathematical Societies by country.[edit]
item	List of mathematicians	http://en.wikipedia.org/wiki/List_of_mathematicians	The famous mathematicians are listed below in English alphabetical transliteration order (by surname).
item	List of mathematics articles %280-9%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%280-9%29	[edit]0∫  -- ?:  -- ×  -- −0 (number)  -- −1 (number)  -- −40 (number)  -- 0 (number)  -- 1-factorable  -- 1 (number)  -- 10 (number)  -- 100 (number)  -- 1000 (number)  -- <a href="/wiki/10000_%28number%29" tit
item	List of mathematics articles %28A%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28A%29	[edit]AA Beautiful Mind  -- A Beautiful Mind (book)  -- A Beautiful Mind (film)  -- A Course of Pure Mathematics  -- A derivation of the discrete Fourier transform  -- A group  -- A Mathematical Theory of Communication  -- A Mathematician's Apology <a href="/wiki/Talk:A_Mathematician%27s_Apology" title="Talk:A Mathematician's
item	List of mathematics articles %28B%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28B%29	[edit]B(B, N) pair  -- B-spline  -- Ba space  -- Baby Monster group  -- Baby-step giant-step  -- Babylonian mathematics  -- Babylonian numerals  -- Bach language  -- Bach tensor  -- Bach's algorithm  -- Ba
item	List of mathematics articles %28A-C%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28A-C%29	[edit]AA Beautiful Mind  -- A Beautiful Mind (book)  -- A Beautiful Mind (film)  -- A Course of Pure Mathematics  -- A derivation of the discrete Fourier transform  -- A group  -- A Mathematical Theory of Communication  -- A Mathematician's Apology <a href="/wiki/Talk:A_Mathematician%27s_Apology" title="Talk:
item	List of mathematics articles %28C%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28C%29	[edit]CC closed subgroup  -- C normal subgroup  -- C-semiring  -- C-symmetry  -- C0-semigroup  -- CA group  -- Cabal (set theory)  -- Cabibbo-Kobayashi-Maskawa matrix  -- Cabri 3D  -- <a href="/wiki/Cabri_Geometry" title="Cabri
item	List of mathematics articles %28D%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28D%29	[edit]DD-module  -- D-separation  -- D'Alembert operator  -- D'Alembert's formula  -- D'Alembert's principle  -- Damerau-Levenshtein distance  -- Damping  -- Damping ratio  -- Dandelin spheres  -- Daniell integral <a href="/
item	List of mathematics articles %28E%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28E%29	[edit]EE (mathematical constant)  -- E6 (mathematics)  -- E7½ (Lie algebra)  -- E7 (mathematics)  -- E8 (mathematics)  -- Ear curve  -- Early stopping  -- Earnshaw's theorem  -- Eastern Arabic numerals <a href="/w/index.php?title=Talk:Eastern_Arabic_numerals&amp;action=edit" class="new" title="Talk
item	List of mathematics articles %28D-F%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28D-F%29	[edit]DD-module  -- D-separation  -- D'Alembert operator  -- D'Alembert's formula  -- D'Alembert's principle  -- Damerau-Levenshtein distance  -- Damping  -- Damping ratio  -- Dandelin spheres  -- Daniell integr
item	List of mathematics articles %28F%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28F%29	[edit]FF-algebra  -- F. and M. Riesz theorem  -- F-coalgebra  -- F-distribution  -- F-sigma set  -- F-space  -- F-test  -- F-theory  -- F1 Score  -- F4 (mathematics)  -- Faà di Bruno's formula <a href="/w/index.php?title=Talk:Fa%C3%
item	List of mathematics articles %28G%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28G%29	[edit]GG-delta set  -- G-structure  -- G-test  -- G2 manifold  -- G2 (mathematics)  -- Gabor filter  -- Gabriel's Horn  -- Galerkin method  -- Galilean transformation  -- Galileo's paradox  -- Gall-Peters projection  -- <
item	List of mathematics articles %28H%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28H%29	[edit]HH-cobordism  -- H-index  -- H-principle  -- H-space  -- H-theorem  -- Haag's theorem  -- Haar measure  -- Haar wavelet  -- Hackenbush  -- Hadamard matrix  -- Hadamard three-circle theorem </a
item	List of mathematics articles %28G-I%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28G-I%29	[edit]GG-delta set  -- G-structure  -- G-test  -- G2 manifold  -- G2 (mathematics)  -- Gabor filter  -- Gabriel's Horn  -- Galerkin method  -- Galilean transformation  -- Galileo's paradox  -- Gall-Peters projection <a href="/wiki/Talk:Gall-Peters_projection" title="Talk:Gall-Peters proj
item	List of mathematics articles %28I%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28I%29	[edit]IaIA automorphism  -- Iban number  -- IBGE  -- Icosagon  -- Icosahedral symmetry  -- Icosahedron  -- Icosidodecadodecahedron  -- Icosidodecahedron  -- Icositruncated dodecadodecahedron  -- Ideal class group  -- <
item	List of mathematics articles %28J%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28J%29	[edit]JJ-homomorphism  -- J integral  -- J-invariant  -- Jaccard index  -- Jackson network  -- Jackson's theorem  -- Jacobi field  -- Jacobi identity  -- Jacobi method  -- Jacobi polynomials  -- Jacobi sum <a h
item	List of mathematics articles %28K%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28K%29	[edit]KK-ary tree  -- K-core  -- K-edge-connected graph  -- K-function  -- K group  -- K-homology  -- K-loop  -- K-means algorithm  -- K-minimum spanning tree  -- K-theory  -- K-theory (physic
item	List of mathematics articles %28J-L%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28J-L%29	[edit]JJ-homomorphism  -- J integral  -- J-invariant  -- Jaccard index  -- Jackson network  -- Jackson's theorem  -- Jacobi field  -- Jacobi identity  -- Jacobi method  -- Jacobi polynomials  -- Ja
item	List of mathematics articles %28L%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28L%29	[edit]LL (complexity)  -- L-function  -- L game  -- L-notation  -- L-system  -- La Géométrie  -- Labeled graph  -- Labelled enumeration theorem  -- Lacunary value  -- Lag operator  -- Lagged Fibon
item	List of mathematics articles %28M%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28M%29	[edit]MM group  -- M-theory  -- Mac Lane's planarity criterion  -- Machin-like formula  -- Mackey topology  -- MacTutor History of Mathematics archive  -- Magic constant  -- Magic cube  -- Magic cube classes  -- Magic hexagon <
item	List of mathematics articles %28N%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28N%29	[edit]NN-body problem  -- N-category  -- N-cube  -- N-dimensional space  -- N-huge cardinal  -- N-Mahlo cardinal  -- N-monoid  -- N-puzzle  -- N-skeleton  -- Nabla symbol  -- Nachbin's theorem <a href="/wiki/Talk:Nachbin%27s_theorem" tit
item	List of mathematics articles %28M-O%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28M-O%29	[edit]MM group  -- M-theory  -- Mac Lane's planarity criterion  -- Machin-like formula  -- Mackey topology  -- MacTutor History of Mathematics archive  -- Magic constant  -- Magic cube  -- Magic cube classes  -- Ma
item	List of mathematics articles %28O%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28O%29	[edit]OO-minimality  -- Oban number  -- Obelus  -- Object of the mind  -- Object theory  -- Oblate  -- Oblate spheroidal coordinates  -- Oblique reflection  -- Observability  -- Observability Gramian <a href="/w/index.php?title=Talk:Observability_Gramian&amp;action=edit" class="new" title="Talk:Observability 
item	List of mathematics articles %28P%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28P%29	[edit]PP-adic analysis  -- P-adic division algorithm  -- P-adic number  -- P-complete  -- P (complexity)  -- P-group  -- P²-irreducible  -- P-value  -- P-vector  -- P-y method  -- Pacific Journal of Mathematics <a href="/w/index.php?title=Talk:Pacific_Jo
item	List of mathematics articles %28Q%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28Q%29	[edit]QQ-analog  -- Q-derivative  -- Q-difference polynomial  -- Q-exponential  -- Q factor  -- Q-Q plot  -- Q-series  -- Q-statistic  -- Q-systems  -- Q test  -- Q-theta function <a href="/w/index.php?title=Talk:Q-theta_function&amp;action=edit" c
item	List of mathematics articles %28P-R%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28P-R%29	[edit]PP-adic analysis  -- P-adic division algorithm  -- P-adic number  -- P-complete  -- P (complexity)  -- P-group  -- P²-irreducible  -- P-value  -- P-vector  -- P-y method  -- Pacific Journal of Mathematics <a href="/w/index.php?titl
item	List of mathematics articles %28R%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28R%29	[edit]RabRabbit sequence  -- Rabdology  -- Rabin automaton  -- Rabinovich-Fabrikant equations  -- Racetrack (game)  -- Racks and quandles  -- Rademacher distribution  -- Rader's FFT algorithm  -- Radial basis function <a href="/wiki/Talk
item	List of mathematics articles %28S%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28S%29	[edit]SS-duality  -- S-m-n theorem  -- S matrix  -- S-number  -- S plane  -- SA subgroup  -- Saccheri quadrilateral  -- Sacred geometry  -- Saddle-node bifurcation  -- Saddle point  -- Sadleirian Chair  -- <a hr
item	List of mathematics articles %28T%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28T%29	[edit]TT-design  -- T-duality  -- T group  -- T-integration  -- T-norm  -- T-schema  -- T-Square (fractal)  -- T-symmetry  -- T1 space  -- Table of bases  -- Table of Clebsch-Gordan coefficients <a href="/w/index.php?title=Talk:Table_of_Clebsch-Gordan_coefficients&amp;action=edit" class="new" title="Talk:Table of Clebsch-Gordan coefficients"
item	List of mathematics articles %28S-U%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28S-U%29	[edit]SS-duality  -- S-m-n theorem  -- S matrix  -- S-number  -- S plane  -- SA subgroup  -- Saccheri quadrilateral  -- Sacred geometry  -- Saddle-node bifurcation  -- Saddle point  -- Sadleirian Chair <a href="/w/index.php?title=Talk:Sadleirian_Chair&amp;action=edit" class="new" title="Talk:Sadleirian Cha
item	List of mathematics articles %28U%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28U%29	[edit]UU-duality  -- Uban number  -- UCT Mathematics Competition  -- Ulam spiral  -- Ultrafilter  -- Ultrafilter lemma  -- Ultrafinitism  -- Ultrametric space  -- Ultraparallel theorem  -- Ultrapower  -- Ultraproduct</a
item	List of mathematics articles %28V%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28V%29	[edit]VacVacuous truth  -- Valenzetti  -- Valuation (mathematics)  -- Valuation ring  -- Value at risk  -- Value distribution theory of holomorphic functions  -- Value (mathematics)  -- Vampire number  -- Van Aubel's theorem  -- Van Deemter's equation<
item	List of mathematics articles %28W%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28W%29	[edit]WadWadge hierarchy  -- Wagstaff prime  -- Wald test  -- Wald-Wolfowitz runs test  -- Wald's equation  -- WalkSAT  -- Wall-Sun-Sun prime  -- Wallis product  -- Wallpaper group  -- Walsh code  -- Walsh function <a href="/
item	List of mathematics articles %28X%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28X%29	[edit]XX-Y-Z matrix  -- Xiaolin Wu's line algorithm  --Retrieved from "http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28X%29"			Category: Mathematics-related lists																Views						 Article				 Discussion				 Edit this page				 History				<div class="port
item	List of mathematics articles %28Y%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28Y%29	[edit]YY-Δ transform  -- Y-homeomorphism  -- Y-intercept  -- Yang-Baxter equation  -- Yang–Mills existence and mass gap  -- Yarrow algorithm  -- Yates' correction for continuity  -- Yaw angle  -- Yellow Pig's Day  -- <a href
item	List of mathematics articles %28V-Z%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28V-Z%29	List of mathematics articles0-9 A B C D E F G H I J K L M N O P <a href="/wiki/List_of_mathematic
item	List of mathematics articles %28Z%29	http://en.wikipedia.org/wiki/List_of_mathematics_articles_%28Z%29	[edit]ZZ-factor  -- Z function  -- Z notation  -- Z-order (curve)  -- Z-test  -- Z-transform  -- Z-value  -- ZAMM — Journal of Applied Mathematics &amp; Mechanics  -- Zarankiewicz problem  -- Zariski geometry <a href="/w/index.php?title=Talk:Zariski_geometry&amp;action=edit" cla
item	List of matrices	http://en.wikipedia.org/wiki/List_of_matrices	Listed below are some important classes of matrices used in mathematics:(0,1)-matrix or binary matrix — a matrix with all elements either 0 or 1.Adjacency matrix — a square matrix used to represent the connectivity of a graph.Alternating sign matrix — a generalization of permutation matrices that arises from Dodgson condensation.Anti-diagonal matrix — a square matrix with all entries off the anti-diagonal equal to zero.Anti-Hermitian matrix — another name for a skew-Hermitian matrix.Anti-symmetric matrix — another name for a skew-symmetric matrix.Band matrix — a square matrix with all entries off a diagonally bordered "band" equal to zero.Bézout matrix — a tool for efficient location of polynomial zerosBlock diagonal matrix — a block matrix with entries only on the diagonal.Block matrix — a matrix partitioned in sub-matrices called blocks.<a href="/wiki/Cartan
item	List of mathematics-based methods	http://en.wikipedia.org/wiki/List_of_mathematics-based_methods	This is a list of mathematics-based methods, by Wikipedia page.
item	List of multivariable calculus topics	http://en.wikipedia.org/wiki/List_of_multivariable_calculus_topics	This is a list of multivariable calculus topics, by Wikipedia page. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics.Closed and exact differential formsContact (mathematics)Contour integralContour lineCritical pointCurlCurrent (mathematics)CurvatureCurvilinear coordinatesD'Alembertian operatorDelDifferential formDifferential operatorDirectional derivativeDivergenceDivergence theoremD
item	List of NP-complete problems	http://en.wikipedia.org/wiki/List_of_NP-complete_problems	Here are some of the more commonly known problems that are NP-complete when expressed as decision problems. This list is in no way comprehensive. Most of the problems in this list are taken from Garey and Johnson's seminal book Computers and Intractability: A Guide to the Theory of NP-Completeness, and are here presented in the same order and organization.Contents1 Graph theory1.1 Covering and partitioning1.2 Subgraphs and supergraphs1.3 Vertex ordering1.4 Iso- and other morphisms1.5 Miscellaneous2 Network design2.1 Spanning trees2.2 Cuts and connectivity2.3 <span c
item	List of number theory topics	http://en.wikipedia.org/wiki/List_of_number_theory_topics	This is a list of number theory topics, by Wikipedia page. See alsolist of recreational number theory topics,list of cryptology topics.Contents1 Factors2 Fractions3 Modular arithmetic4 Arithmetic functions5 Analytic number theory: additive problems6 Algebraic number theory7 Quadratic forms8 L-functions9 Diophantine equations10 Diophantine approximation<li class="tocl
item	List of numbers	http://en.wikipedia.org/wiki/List_of_numbers	This is a list of articles about numbers (not about numerals).Contents1 Rational numbers1.1 Notable rational numbers1.1.1 Natural numbers1.1.2 Powers of ten1.2 Integers1.2.1 Notable integers1.2.2 Named integers1.3 Prime numbers1.4 Perfect numbers1.5 Cardinal numbers1.5.1 Small numbers1.5.2 English names for powers of 10</l
item	Table of bases	http://en.wikipedia.org/wiki/Table_of_bases	This article is about "bases" as that term is used in discussion of certain numeral systems.
item	List of numeral system topics	http://en.wikipedia.org/wiki/List_of_numeral_system_topics	This is a list of numeral system topics, by Wikipedia page. It does not systematically list computer formats for storing numbers (computer numbering formats). See also number names.[edit]
item	List of numerical analysis topics	http://en.wikipedia.org/wiki/List_of_numerical_analysis_topics	This is a list of numerical analysis topics, by Wikipedia page.Contents1 General2 Error3 Numerical linear algebra4 Interpolation5 Finding roots of nonlinear equations6 Optimization7 Numerical integration8 Numerical ordinary differential equations9 Numerical partial differential equations10 Monte Carlo method11 Applications12 Software
item	List of numerical analysis software	http://en.wikipedia.org/wiki/List_of_numerical_analysis_software	Listed here are a number of computer programs used for performing numerical calculations:Baudline is a time-frequency browser for numerical signals analysis and scientific visualization.DADiSP is a commercial program focused on DSP that combines the numerical capability of MATLAB with a spreadsheet like interface.Expensive Desk Calculator (historical), written for the TX-0 and PDP-1 in the late 1950s or early 1960s.GAUSSIDL programming language, a commercial interpreted language based on FORTRAN with some vectorization. Widely used in the solar physics and medical communities. A free alternative is available:GNU data language, a free compiler designed as a drop-in replacement for IDL.IGOR Pro, a software package with emphasis on time series and image analysis, and curve fitting. It comes with its own programming language but can also be used interactively.IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C# .NET, and Fortran.<a href="/wiki/IMTEK_Mathematica_Supplement" title="IMTEK Math
item	List of numerical computational geometry topics	http://en.wikipedia.org/wiki/List_of_numerical_computational_geometry_topics	List of numerical computational geometry topics enumerates the topics of computational geometry that deals with geometric objects as continuous entities and applies methods and algorithms of nature characteristic to numerical analysis. This area is also called "machine geometry", computer-aided geometric design, and geometric modelling.
item	List of order topics	http://en.wikipedia.org/wiki/List_of_order_topics	This is a list of order topics, by Wikipedia page.
item	List of partial differential equation topics	http://en.wikipedia.org/wiki/List_of_partial_differential_equation_topics	This is a list of partial differential equation topics, by Wikipedia page.Contents1 General topics2 Specific partial differential equations3 Numerical methods for PDEs4 Related areas of mathematics
item	List of partition topics	http://en.wikipedia.org/wiki/List_of_partition_topics	In mathematics, a partition may bea partition of a set or an ordered partition of a set, ora partition of an integer, ora partition of an interval, ora partition of unity, ora partition of a matrix; see block matrix, ora partition of the sum of squares in statistics problems, especially in the analysis of variance.[edit]
item	List of permutation topics	http://en.wikipedia.org/wiki/List_of_permutation_topics	This is a list of topics on mathematical permutations.Alternating groupAlternating permutationBijectionCircular shiftCombinationCycle indexCycle notationCyclic orderCyclic permutationDerangementEven and odd permutationsEwens' sampling formulaFactorialFalling factorialJosephus permutationLevi-Civita symbolOrder statisticPermutationPermutation (music)Permutation groupPermutation matrix<a href="/wiki/Generalized
item	List of topics related to %CF%80	http://en.wikipedia.org/wiki/List_of_topics_related_to_%CF%80	This is a list of topics related to π (pi), the fundamental mathematical constant.Arithmetic-geometric meanBailey-Borwein-Plouffe formulaBasel problemBorwein's algorithmBorwein's algorithm (others)Buffon's needleCadaeic CadenzaCircleEuler's identityFeynman pointGauss-Legendre algorithmGaussian functionHistory of πHistory of numerical approximations of πChronology of computation of πLindemann-Weierstrass theoremList of circle topics<a hre
item	List of planar symmetry groups	http://en.wikipedia.org/wiki/List_of_planar_symmetry_groups	This article summarizes the classes of planar symmetry groups:2 infinite set of point groups7 Frieze groups17 wallpaper groupsContents1 Point groups2 Frieze Groups3 Wallpaper groups4 See also5 External references
item	List of polygons%2C polyhedra and polytopes	http://en.wikipedia.org/wiki/List_of_polygons%2C_polyhedra_and_polytopes	This is a list of polygons, polyhedra and polytopes, by Wikipedia page. See also list of regular polytopes, list of geometry topics.10-sided dice24-cell600-cell120-cellAntiprismArchimedean solidBipyramidCatalan solidChiliagonConcave polygonCross-polytopeCubeCuboidCuboctahedronCupola (geometry)Cyclic polygonDecagonDeltahedronDeltoidal hexecontahedronDeltoidal icositetrahedronDiamond - see rhombus<a href="/wiki/Disdyakis_dodecahedron" title="Disdy
item	List of polynomial topics	http://en.wikipedia.org/wiki/List_of_polynomial_topics	This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.Contents1 Basics2 Theory of equations3 Calculus with polynomials4 Polynomial interpolation5 Weierstrass approximation theorem6 Linear algebra7 Named polynomials and polynomial sequences8 Knot polynomials
item	Table of prime factors	http://en.wikipedia.org/wiki/Table_of_prime_factors	This table contains the integer factorization for the numbers from 1 to 1002.
item	List of probabilists	http://en.wikipedia.org/wiki/List_of_probabilists	A probabilist is either a mathematician specializing in probability theory, or one who espouses probabilism in theology or philosophy.
item	List of probability topics	http://en.wikipedia.org/wiki/List_of_probability_topics	This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.Contents1 General aspects2 Foundations of probability theory3 Random variables4 Conditional probability5 Probability distributions6 Properties of probability distributions7 Applied probability8 Stochastic processes9 Geometric probability10 <span
item	List of mathematical proofs	http://en.wikipedia.org/wiki/List_of_mathematical_proofs	Wikipedia contains a number of articles with mathematical proofs:Contents1 Theorems of which articles are primarily devoted to proving them2 Articles devoted to theorems of which a (sketch of a) proof is given3 Articles devoted to algorithms in which their correctness is proven4 Articles where example statements are proven5 Other articles containing proofs6 Articles which mention dependencies of theorems7 Articles giving mathematical proofs within a physical model8 Other related articles
item	List of publications in mathematics	http://en.wikipedia.org/wiki/List_of_publications_in_mathematics	This is a list of important publications in mathematics, organized by field.
item	List of mathematical topics in quantum theory	http://en.wikipedia.org/wiki/List_of_mathematical_topics_in_quantum_theory	This is a list of mathematical topics in quantum theory, by Wikipedia page. See also list of functional analysis topics, list of Lie group topics.Contents1 Mathematical formulation of quantum mechanics2 Schrödinger equation3 Symmetry4 Quantum states5 Dirac equation6 Interpretations of quantum mechanics7 Quantum field theory8 Computation9 Supersymmetry10 Quantum gravity<a href=
item	List of real analysis topics	http://en.wikipedia.org/wiki/List_of_real_analysis_topics	This is a list of real analysis topics.
item	List of properties of sets of reals	http://en.wikipedia.org/wiki/List_of_properties_of_sets_of_reals	This page lists some properties of sets of real numbers. The general study of these concepts forms descriptive set theory, which has a rather different emphasis from general topology.[edit]
item	List of recreational number theory topics	http://en.wikipedia.org/wiki/List_of_recreational_number_theory_topics	This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins in challenging problems posed purely for their own sake.
item	List of mathematics reference tables	http://en.wikipedia.org/wiki/List_of_mathematics_reference_tables	See also: List of reference tables[edit]
item	List of regular polytopes	http://en.wikipedia.org/wiki/List_of_regular_polytopes	This page lists the regular polytopes in Euclidean, spherical and hyperbolic spaces.
item	List of mathematical topics in relativity	http://en.wikipedia.org/wiki/List_of_mathematical_topics_in_relativity	This is a list of mathematical topics in relativity, by Wikipedia page.[edit]
item	List of rotational symmetry polyhedral sets	http://en.wikipedia.org/wiki/List_of_rotational_symmetry_polyhedral_sets	There are an unlimited number of polyhedral sets which can be defined with rotational symmetry.
item	List of rules of inference	http://en.wikipedia.org/wiki/List_of_rules_of_inference	This is a list of rules of inference.Contents1 Introduction2 Rules for classical sentential calculus2.1 Rules for negations2.2 Rules for conditionals2.3 Rules for conjunctions2.4 Rules for disjunctions2.5 Rules for biconditionals3 Rules of classical predicate calculus
item	List of set theory topics	http://en.wikipedia.org/wiki/List_of_set_theory_topics	This page is a list of articles related to set theory.Contents1 Articles on individual set theory topics2 Lists related to set theory3 Set theorists4 Societies and organizations
item	List of mathematical shapes	http://en.wikipedia.org/wiki/List_of_mathematical_shapes	Following is a list of some mathematically well-defined shapes. See also list of polygons, polyhedra and polytopes and list of geometric shapes.Contents1 no D with no surface2 0D with no surface3 1D with 0D surface4 2D with 1D surface5 3D with 1D surface6 3D with 2D surface7 4D with 2D surface8 4D with 3D surface9 5D with 4D surfaces10 <sp
item	List of Slovenian mathematicians	http://en.wikipedia.org/wiki/List_of_Slovenian_mathematicians	This is a list of the most famous Slovenian mathematicians.
item	List of spherical symmetry groups	http://en.wikipedia.org/wiki/List_of_spherical_symmetry_groups	//[edit]List of symmetry groups on the sphereSpherical symmetry groups are also called point groups (in 3D).There are four fundamental symmetry classes: dihedral, tetrahedral, octahedral, icosahedral which have triangular fundamental domains. The dihedral symmetry groups are an infinite set.The final classes, under other have digonal or monogonal fundamental domains.[edit]DihedralThere are an infinite set of dihedral symmetries. n can be any positive integer 2 or greater.NameSchönfliescrystallographicnotationCoxeternotationConway'sorbifoldnotationOrderFundamentaldomainPolyditropicDn[2,n]+22n2n<
item	List of statistical packages	http://en.wikipedia.org/wiki/List_of_statistical_packages	This is an incomplete list of software that is designed for the explicit purpose of performing statistical analyses.Contents1 Commercial1.1 Add-ons2 Open source3 See also4 External links4.1 Collections of Free Statistical Software
item	List of basic statistical topics	http://en.wikipedia.org/wiki/List_of_basic_statistical_topics	Below is a list of basic topics in statistics -- topics which will help the beginner become familiar with the field of statistics. For a comprehensive list, see List of statistical topics.ANOVA --binomial distribution --census --chi-square distribution --combinatorics --data --degrees of freedom (statistics) --descriptive statistics --errors and residuals in statistics --experimental design --frequency table --histogram --inferential statistics --mean --median --mode --modeling --Monte Carlo method --<a href="/wiki/Normal_distri
item	List of statisticians	http://en.wikipedia.org/wiki/List_of_statisticians	Statisticians or people who made notable contributions to the theories of statistics, or related aspects of probability, or machine learning:
item	List of statistical topics	http://en.wikipedia.org/wiki/List_of_statistical_topics	Please add any Wikipedia articles related to statistics that are not already on this list.
item	List of publications in statistics	http://en.wikipedia.org/wiki/List_of_publications_in_statistics	This is a list of important publications in statistics, organized by field.
item	List of stochastic processes topics	http://en.wikipedia.org/wiki/List_of_stochastic_processes_topics	In the mathematics of probability, a stochastic process can be thought of as a random function. In practical applications, the domain over which the function is defined is a time interval (time series) or a region of space (random field).
item	List of string theory topics	http://en.wikipedia.org/wiki/List_of_string_theory_topics	This is a list of string theory topics, by Wikipedia page. See also: list of mathematical topics in quantum theory.Contents1 String theory1.1 String dualities1.2 Particles and fields1.3 Branes2 Supersymmetry3 Conformal field theory4 Geometry5 Holography6 Gauge theory7 People (partial listing)
item	List of surfaces	http://en.wikipedia.org/wiki/List_of_surfaces	//[edit]List of famous geometric surfaces[edit]Minimal surfacesCosta surfaceCatenoidRiemann's surfaceSaddle towerGyroidCatalan surfaceEnneper surface[edit]Non-orientable surfaces<a href="/wiki/Klein_bott
item	Table of mathematical symbols	http://en.wikipedia.org/wiki/Table_of_mathematical_symbols	The following table lists many specialized symbols commonly used in mathematics. For the HTML codes of mathematical symbols see mathematical HTML.Contents1 Basic mathematical symbols2 See also3 External links4 Special characters
item	Table of Newtonian series	http://en.wikipedia.org/wiki/Table_of_Newtonian_series	In mathematics, a Newtonian series is a sum over a sequence an written in the form
item	List of theorems	http://en.wikipedia.org/wiki/List_of_theorems	This is a list of theorems, by Wikipedia page. See alsolist of fundamental theoremslist of lemmaslist of conjectureslist of inequalitieslist of mathematical proofs
item	List of mathematical theories	http://en.wikipedia.org/wiki/List_of_mathematical_theories	This is a list of mathematical theories, by Wikipedia page.Algebraic K-theoryApproximation theoryAutomata theoryBraid theoryBrill-Noether theoryCatastrophe theoryCategory theoryCharacter theoryChoquet theoryClass field theoryCoding theoryCohomology theoryComputation theoryDeformation theoryDimension theoryDistribution theoryField theoryElimination theoryExtremal graph theoryGalois theoryGame theory<a href="/wiki/Graph_t
item	List of transforms	http://en.wikipedia.org/wiki/List_of_transforms	This is a list of transforms in mathematics, by Wikipedia page.Contents1 Integral transforms2 Discrete transforms3 Data-dependent transforms4 Other transforms5 General6 External links
item	List of trigonometry topics	http://en.wikipedia.org/wiki/List_of_trigonometry_topics	This is a list of trigonometry topics, by Wikipedia page.AngleAngle excessChebyshev polynomialsDe Moivre's formulaDirichlet kernelEuler's formulaExact trigonometric constantsExponential sumGenerating trigonometric tablesGrad (angle)Gudermannian functionHaversine formulaHyperbolic functionLaw of cosinesLaw of sinesLaw of tangentsLissajous curvePtolemaios' theoremRadianRational trigonometry<a href="/wiki/Spherical_trigonometry" title="Spherical 
item	List of trivia lists	http://en.wikipedia.org/wiki/List_of_trivia_lists	//[edit]Material[edit]General intellectual[edit]Mathematics[edit]Trivia for mathematiciansList of matricesList of groups[edit]Linguistic[<a href="/w/index.php?title=List_of_trivia_lists&amp;action=edit&amp;section=6" ti
item	List of Ukrainian mathematicians	http://en.wikipedia.org/wiki/List_of_Ukrainian_mathematicians	This a list of the most famous Ukrainian mathematicians. This list includes Polish, Russian and Soviet mathematicians that lived or worked in Ukraine.
item	Wikimedia Commons	http://en.wikipedia.org/wiki/Wikimedia_Commons	Wikimedia Commons logo by Reid BeelsThe Wikimedia Commons (English homepage; also called "Commons" or "Wikicommons") is a repository of free content images, sound and other multimedia files. It is another project of the Wikimedia Foundation like Wikipedia, but one that is a common resource repository to all the various Wikimedia sister projects regardless of language.Files uploaded to the Commons repository can be used like locally uploaded files on all other projects on the Wikimedia servers in all languages, including Wikipedia, Wikibooks, Wikisource and Wikinews, or indeed downloaded for offsite use, as all of the content is either in the public domain or released under fr
item	Wikibooks	http://en.wikipedia.org/wiki/Wikibooks	Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of books. It is a Wikimedia Foundation project.Contents1 History2 Content3 Criticisms4 Subprojects5 References6 Other languages7 See also8 External links
item	Algebra	http://en.wikipedia.org/wiki/Algebra	Algebra (from Arabic: الجبر, al-ğabr) is a branch of mathematics concerning the study of structure, relation and quantity. Elementary algebra is often taught in secondary education and gives an introduction to the basic ideas of algebra: studying what happens when numbers are added or multiplied, and how to make polynomials and find their roots.
item	Arabic language	http://en.wikipedia.org/wiki/Arabic_language	The Arabic language (Arabic: اللغة العربية‎ ​ transliterated: al-lughah al-‘Arabīyyah), or simply Arabic (Arabic: عربي‎ ​ transliterated: ‘Arabī), is the largest member of the Semitic branch of the Afro-Asiatic language family (classification: South Central Semitic) and is closely related to Hebrew and Aramaic. It is spoken throughout the Arab world and is widely studied and known throughout the Islamic world. Arabic has been a literary language since at least the 6th century and is the liturgical language of Islam. Because of its liturgical role, Arabic has lent many words to other Islamic languages, akin to the role Latin has in Western European languages. During the Middle Ages Arabic
item	Arithmetic	http://en.wikipedia.org/wiki/Arithmetic	Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numbers. Professional mathematicians sometimes use arithmetic as a synonym for number theory, but this should not be confused with elementary arithmetic. It is the oldest and simplest branch of mathematics, used widely by almost everyone from simple daily counting to more advanced science and business.Contents1 History2 Decimal Arithmetic3 Arithmetic operations3.1 Addition (+)3.2 Subtraction (−)3.3 Multiplication (× or *)<a href="#Division_.28.C3.B7_
item	Abel%E2%80%93Ruffini theorem	http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem	The Abel–Ruffini theorem states that there is no general solution in radicals to polynomial equations of degree five or higher.
item	Algebra homomorphism	http://en.wikipedia.org/wiki/Algebra_homomorphism	A homomorphism between two algebras over a field K, A and B, is a map  such that for all k in K and x,y in A,F(kx) = kF(x)F(x + y) = F(x) + F(y)F(xy) = F(x)F(y)
item	Algebraic element	http://en.wikipedia.org/wiki/Algebraic_element	In mathematics, the roots of polynomials are in abstract algebra called algebraic elements. They can be created in a larger structure ('adjoined'), not simply found to exist in a given one.
item	Algebraic extension	http://en.wikipedia.org/wiki/Algebraic_extension	In abstract algebra, a field extension L /K is called algebraic if every element of L is algebraic over K, i.e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions which are not algebraic, i.e. which contain transcendental elements, are called transcendental.
item	Algebraic function	http://en.wikipedia.org/wiki/Algebraic_function	In mathematics, an algebraic function of indeterminatesX1, X2, ..., Xn,
item	Algebraic number	http://en.wikipedia.org/wiki/Algebraic_number	In mathematics, an algebraic number is any number that is a root of an algebraic equation, a non-zero polynomial with integer (or equivalently, rational) coefficients. Without further qualification, it is assumed that an algebraic number is a complex number, but one can also consider algebraic numbers in other fields, such as fields of p-adic numbers. All these algebraic numbers belong to some algebraic number field.
item	Algebraic solution	http://en.wikipedia.org/wiki/Algebraic_solution	The solution of an algebraic equation, often one that seeks zeros of a polynomial, is sometimes said to admit an "algebraic solution" or a "solution in radicals" if function that expresses the solution in terms of the coefficients relies only on addition, subtraction, multiplication, division, and the extraction of roots. The most well-known example is the solution
item	Anyonic Lie algebra	http://en.wikipedia.org/wiki/Anyonic_Lie_algebra	In mathematics, an anyonic Lie algebra is a U(1) graded vector space L over C equipped with a bilinear operator [.,.] and linear maps ε:L-&gt;C and Δ:L -&gt; L⊗L satisfyingε([X,Y]) = ε(X)ε(Y)
item	Associative algebra	http://en.wikipedia.org/wiki/Associative_algebra	In mathematics, an associative algebra is a vector space (or more generally, a module) which also allows the multiplication of vectors in a distributive and associative manner. They are thus special algebras.Contents1 Definition2 Examples3 Algebra homomorphisms4 Index-free notation5 Generalizations6 Coalgebras7 Representations7.1 Motivation for a Hopf algebra7.2 Motivation for a Lie algebra<li class="toclevel
item	Automorphism	http://en.wikipedia.org/wiki/Automorphism	In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.Contents1 Definition2 Automorphism group3 Examples4 Inner and outer automorphisms5 See also6 Reference7 External links
item	Binary operation	http://en.wikipedia.org/wiki/Binary_operation	In mathematics, a binary operation is a calculation involving two input quantities, in other words, an operation whose arity is two. Binary operations can be accomplished using either a binary function or binary operator. Binary operations are sometimes called dyadic operations in order to avoid confusion with the binary numeral system. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division.
item	Binomial	http://en.wikipedia.org/wiki/Binomial	In elementary algebra, a binomial is a polynomial with two terms: the sum of two monomials. It is the simplest kind of polynomial.[edit]
item	Binomial theorem	http://en.wikipedia.org/wiki/Binomial_theorem	In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version reads
item	Brahmagupta-Fibonacci identity	http://en.wikipedia.org/wiki/Brahmagupta-Fibonacci_identity	In algebra, Brahmagupta's identity, also sometimes called Fibonacci's identity, says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares (and in two different ways). In other words, the set of all sums of two squares is closed under multiplication.
item	Buchberger%27s algorithm	http://en.wikipedia.org/wiki/Buchberger%27s_algorithm	In computational algebraic geometry and computational commutative algebra, Buchberger's algorithm is a method of transforming a given set of generators for a polynomial ideal into a Gröbner basis with respect to some monomial order. It was invented by Austrian mathematician Bruno Buchberger. One can view it as a generalization of the Euclidean algorithm for univariate GCD computation and of Gaussian elimination for linear systems.
item	Canonical form	http://en.wikipedia.org/wiki/Canonical_form	Generally, in mathematics, a canonical form is a function that is written in the most standard, conventional, and logical way. For example, polynomials are usually written with the terms in descending powers: it is more usual to write x2 + x + 30 than x + 30 + x2, although the two forms are essentially equivalent.
item	Closed-form expression	http://en.wikipedia.org/wiki/Closed-form_expression	In mathematics, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed analytically in terms of a bounded number of certain "well-known" functions . Typically, these well-known functions are defined to be elementary functions; infinite series, limits, and continued fractions are not permitted.
item	Coefficient	http://en.wikipedia.org/wiki/Coefficient	In mathematics, a coefficient is a constant multiplicative factor of a certain object. The object can be such things as a variable, a vector, a function, etc. For example, the coefficient of 9x2 is 9. In some cases, the objects and the coefficients are indexed in the same way, leading to expressions such as
item	Completing the square	http://en.wikipedia.org/wiki/Completing_the_square	Very simply, given a problem of the form:x2 + bx = cWe may transform the equation such that we no longer have both "x" and "x squared" with a method called "completing the square". To do this we take one half of the coefficient of "x", square it, and add it to both sides of the equation, like so:More specifically, Completing the square is a technique of elementary algebra wherein an expressionx2 + bxis replaced by one of the form(x + c)2 + dSpecifically, we have:<img class='tex' src="http://upload.wikimedia.org/math/8/e/7/8e7791ab6e7cc1c
item	Congruence relation	http://en.wikipedia.org/wiki/Congruence_relation	In mathematics and especially in abstract algebra, a congruence relation or simply congruence is an equivalence relation that is compatible with some algebraic operation(s).Contents1 Modular arithmetic2 Linear algebra3 Universal algebra4 Group theory5 Ring theory6 General case of kernels7 See also8 References
item	Cuntz algebra	http://en.wikipedia.org/wiki/Cuntz_algebra	A Cuntz algebra is a separable, simple infinite C*-algebra. In particular, take n ≥ 2, with n possibly infinite. Then the Cuntz algebra  is defined to be the C*-algebra generated by a set
item	Cycle %28mathematics%29	http://en.wikipedia.org/wiki/Cycle_%28mathematics%29	Let S be a set. A cycle is a permutation (bijective function of a set onto itself) such that there exist distinct elements  of S such that
item	Degree %28mathematics%29	http://en.wikipedia.org/wiki/Degree_%28mathematics%29	In mathematics, there are several meanings of degree depending on the subject.Contents1 Degree of a polynomial2 Degree of a field extension3 Degree of a vertex in a graph4 Degree of a continuous map4.1 From a circle to itself4.2 Between manifolds4.3 Properties5 Degree of freedom
item	Determinant	http://en.wikipedia.org/wiki/Determinant	In algebra, a determinant is a function depending on n that associates a scalar det(A) to every n×n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor for volume when A is regarded as a linear transformation. Determinants are important both in calculus, where they enter the substitution rule for several variables, and in multilinear algebra.
item	Digital root	http://en.wikipedia.org/wiki/Digital_root	The digital root (also Repeated digital sum) of a number is the number received by adding all the digits, then adding the digits of that number, and then continuing until a single-digit number is reached.
item	Dimension	http://en.wikipedia.org/wiki/Dimension	In common usage, a dimension (Latin, "measured out") is a parameter or measurement required to define the characteristics of an object—i.e. length, width, and height or size and shape. In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space —where the dimensions of a space are the total number of different parameters used for all possible objects considered in the model. Generalizations of the concept are possible and, different fields of study will define their spaces by their own relevant dimensions, and use these spaces as frameworks upon which all other study (in that area) is based. In specialized contexts, units of measurement may sometimes be "dimensions"—meters or feet in geographical space models, or cost and price in models of a local economy.
item	Distributive lattice	http://en.wikipedia.org/wiki/Distributive_lattice	In mathematics, distributive lattices are lattices for which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattices is – up to isomorphism – given as such a lattice of sets.Contents1 Formal definition2 Morphisms3 Examples4 Characteristic properties5 Representation theory6 Free distributive lattices7 Literature
item	Elementary divisor	http://en.wikipedia.org/wiki/Elementary_divisor	In Linear Algebra if we have a matrix M in smith normal form as seen below.The elements αi are unique, and are referred to as elementary divisors.
item	Expression %28mathematics%29	http://en.wikipedia.org/wiki/Expression_%28mathematics%29	An expression is a combination of numbers, operators, grouping symbols (such as brackets and parentheses) and/or free variables and bound variables arranged in a meaningful way which can be evaluated. Bound variables are assigned values within the expression (they are for internal use) while free variables can take on values from outside the expression.
item	Filtration %28abstract algebra%29	http://en.wikipedia.org/wiki/Filtration_%28abstract_algebra%29	In mathematics, a filtration is an indexed set Si of subobjects of a given algebraic structure S, with an index set I that is a totally ordered set, subject only to the condition that if i ≤ j in I then Si is contained in Sj.
item	Generalized arithmetic progression	http://en.wikipedia.org/wiki/Generalized_arithmetic_progression	In mathematics, a multiple arithmetic progression, generalized arithmetic progression, or k-dimensional arithmetic progression, is a set of integers constructed as an arithmetic progression is, but allowing several possible differences. So, for example, we start at 17 and may add a multiple of 3 or of 5, repeatedly. In algebraic terms we look at integersa + mb + nc + ...
item	Goursat%27s lemma	http://en.wikipedia.org/wiki/Goursat%27s_lemma	Goursat's lemma is an algebraic theorem.
item	Group action	http://en.wikipedia.org/wiki/Group_action	In mathematics, a symmetry group describes all symmetries of objects. This is formalized by the notion of a group action: every element of the group "acts" like a bijective map (or "symmetry") on some set. In this case, the group is also called a permutation group (especially if the set is finite or not a vector space) or transformation group (especially if the set is a vector space and the group acts like linear transformations of the set). A permutation representation of a group G is a representation of G as a group of permutations of the set (usually if the set is finite), and may be described as a group representation of G by permutation matrices, and is usually considered in the finite-dimensional case—it is the same as a group action of G on an ordered basis of a vector space.Contents1 Definition2 Examples<a href="#Types_of_actions
item	Identity element	http://en.wikipedia.org/wiki/Identity_element	In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them. This is used for groups and related concepts.
item	Indeterminate %28variable%29	http://en.wikipedia.org/wiki/Indeterminate_%28variable%29	In mathematics, more precisely in algebra, an indeterminate is a quantity that is not known, and cannot be solved for. An indeterminate is different from a variable, which is solvable, at least conditionally, from a given equation or set of equations. To make this distinction in an example, compare these two situations.
item	Intersection %28set theory%29	http://en.wikipedia.org/wiki/Intersection_%28set_theory%29	In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
item	Inverse element	http://en.wikipedia.org/wiki/Inverse_element	In mathematics, the idea of inverse element generalises the concepts of negation, in relation to addition, and reciprocal, in relation to multiplication. The intuition is of an element that can 'undo' the effect of combination with another given element.[edit]
item	Irreducible polynomial	http://en.wikipedia.org/wiki/Irreducible_polynomial	In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non-trivial factors in a given set. See also factorization.
item	Isomorphism	http://en.wikipedia.org/wiki/Isomorphism	In mathematics, an isomorphism (Greek:isos "equal", and morphe "shape") is a bijective map f such that both f and its inverse f&#160;−1 are homomorphisms, i.e. structure-preserving mappings.
item	Iterated binary operation	http://en.wikipedia.org/wiki/Iterated_binary_operation	In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation.
item	K-theory	http://en.wikipedia.org/wiki/K-theory	In mathematics, K-theory is, firstly, an extraordinary cohomology theory which consists of topological K-theory. It also includes algebraic K-theory. It spans the subjects of algebraic topology, abstract algebra and some areas of application like operator algebras and algebraic geometry. It leads to the construction of families of K-functors, which contain useful but often hard-to-compute information.
item	K-theory %28physics%29	http://en.wikipedia.org/wiki/K-theory_%28physics%29	In string theory, K-theory, which is a central object of study in abstract algebra and in algebraic topology, has been conjectured to classify the allowed Ramond-Ramond field strengths; and also the charges of stable D-branes.Contents1 The Literature1.1 History1.2 Applications1.3 Open Problems2 The K-Theory Classification of RR Fluxes3 The K-Theory Classification of D-Branes3.1 K-theory Charge vs BPS Charge3.2 K-Theory from Tachyon Condensation<a href="#Twisted_K-Theory_from_MMS_Inst
item	Kernel of a function	http://en.wikipedia.org/wiki/Kernel_of_a_function	In mathematics, the kernel of a function f may be taken to be eitherthe equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function f can tell", orthe corresponding partition of the domain.
item	Lattice %28order%29	http://en.wikipedia.org/wiki/Lattice_%28order%29	In mathematics, a lattice is a partially ordered set (or poset) whose nonempty finite subsets all have a supremum (called join) and an infimum (called meet). Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These "lattice-like" structures all admit order-theoretic as well as algebraic descriptions.Contents1 Lattices as posets2 Lattices as algebraic structures3 Connection between the two definitions4 Examples</li
item	Laws of Form	http://en.wikipedia.org/wiki/Laws_of_Form	The phrase Laws of Form refers to either of two things:The book, hereinafter abbreviated LoF by G. Spencer-Brown.The algebraic structure set out and interpreted in LoF, especially the "primary algebra" (hereinafter abbreviated pa and described in section 4 below), a provocative and economical notation for the two-element Boolean algebra (hereinafter abbreviated as 2), Boolean logic, and the sentential calculus.Contents1 The book2 The Form3 The primary arithmetic and its axioms3.1 The notion of 'canon'4 The primary algebra4.1 Axiomatics4.2 Proof theory<a href="#Applying_
item	Leibniz formula %28determinant%29	http://en.wikipedia.org/wiki/Leibniz_formula_%28determinant%29	In algebra, the Leibniz formula expresses the determinant of a square matrix in terms of permutations of the matrix' elements. Named in honor of Gottfried Leibniz, the formula is
item	Monomial	http://en.wikipedia.org/wiki/Monomial	In mathematics, a monomial is a particular kind of polynomial, having just one term. Given a natural number n and a variable x, the power function defined by the rule f(x)=xn is therefore a monomial. Given several unknown variables (say, x, y, z) and corresponding natural number exponents (say, a, b, c), the product of the resulting univariate monomials is also a monomial (e.g., the function determined by the rule f(x)=xaybzc).
item	Monomial basis	http://en.wikipedia.org/wiki/Monomial_basis	In mathematics a monomial basis is a way to uniquely describe a polynomial using a linear combination of monomials. This description, the monomial form of a polynomial, is often used because of the simple structure of the monomial basis.
item	Multinomial theorem	http://en.wikipedia.org/wiki/Multinomial_theorem	In mathematics, the multinomial formula is an expression of a power of a sum in terms of powers of the addends. For any positive integer m and any nonnegative integer n, the multinomial formula is
item	Multiplicative inverse	http://en.wikipedia.org/wiki/Multiplicative_inverse	In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. It is denoted 1/x or x-1.
item	Nested radicals	http://en.wikipedia.org/wiki/Nested_radicals	Nested radicals in algebra are radical expressions that have another radical expression nested inside a radical. Examples include
item	Operand	http://en.wikipedia.org/wiki/Operand	In mathematics, an operand is one of the inputs (arguments) of an operator. For instance, in3 + 6 = 9
item	Operator	http://en.wikipedia.org/wiki/Operator	In mathematics, an operator is a function, usually of a special kind depending on the topic. For instance, in linear algebra an "operator" is a linear operator. In analysis an "operator" may be a differential operator, generalizing the ordinary derivative, or an integral operator, generalizing ordinary integration. Often, an "operator" is a function that acts on functions to produce other functions; or it may be a generalization of such a function, as in linear algebra, where some of the terminology reflects the origin of the subject in operations on the functions that are solutions of differential equations. One often thinks of an operator as dynamic, changing something into something else, whence the name; but this is only a way of thinking and not a formal definition.
item	Order of operations	http://en.wikipedia.org/wiki/Order_of_operations	In arithmetic and algebra, certain rules are used for the order in which the operations in expressions are to be evaluated. These precedence rules (which are mere notational conventions, not mathematical facts) are also used in many programming languages and by most modern calculators. In computing, the standard algebraic notation is known as infix notation. This article assumes the reader is familiar with addition, subtraction, multiplication, division, exponents, and roots (such as square roots, cube roots, and so on).Contents1 The standard order of operations2 Mathematical precedence3 Examples<span class="tocnumber
item	Ordered field	http://en.wikipedia.org/wiki/Ordered_field	In mathematics, an ordered field is a field (F,+,*) together with a total order ≤ on F that is compatible with the algebraic operations in the following sense:if a ≤ b then a + c ≤ b + cif 0 ≤ a and 0 ≤ b then 0 ≤ a b
item	Pairing	http://en.wikipedia.org/wiki/Pairing	The concept of pairing treated here occurs in mathematics.[edit]
item	Partial fraction	http://en.wikipedia.org/wiki/Partial_fraction	In algebra, the partial fraction decomposition or (partial fraction expansion) is used to reduce the degree of either the numerator or the denominator of a rational function. The outcome of partial fraction expansion expresses that function as a sum of fractions, where:the denominator of each term is a power of an irreducible (not factorable) polynomial andthe numerator is a polynomial of smaller degree than the denominator.
item	Perfect square	http://en.wikipedia.org/wiki/Perfect_square	The term perfect square is used in mathematics in two meanings:an integer which is the square of some other integer, i.e. can be written in the form n2 for some integer n (and because of this a square is always nonnegative)Examples: 0, 1, 4, 9, 16, 25, 36, 49, ... See square number.an algebraic expression that can be factored as the square of some other expression, e.g. a2 ± 2ab + b2 = (a ± b)2. (see Square (algebra)).
item	Power set	http://en.wikipedia.org/wiki/Power_set	In mathematics, given a set S, the power set (or powerset) of S, written  or 2S, is the set of all subsets of S. In axiomatic set theory (as developed e.g. in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set.
item	Projection-valued measure	http://en.wikipedia.org/wiki/Projection-valued_measure	In mathematics, projection-valued measures are used to express results in spectral theory. A projection-valued measure on a measurable space (X, M) is a mapping π from M to the set of self-adjoint projections on a Hilbert space H such that
item	Ratio	http://en.wikipedia.org/wiki/Ratio	In number and more generally in algebra, a ratio is the linear relationship between two quantities. It is expressed as two numbers separated by a colon (pronounced "to"). The ratio of 2:3 means 2 parts of one to 3 parts of the other. This means 2 fifths of the mixture is of the one and 3 fifths is of the other since there are 5 parts in total. A rate is a special kind of ratio where the two quantities being compared are of a different unit.[edit]
item	Rational function	http://en.wikipedia.org/wiki/Rational_function	In mathematics, a rational function is any function whose output can be given by a formula that is the ratio of two polynomials. For a function of one variable, x, any rational function can be expressed asf(x) = P(x)/Q(x)
item	Rational root theorem	http://en.wikipedia.org/wiki/Rational_root_theorem	In algebra, the rational root theorem states a constraint on solutions (also called "roots") to the polynomial equationan xn + an-1 xn -1 + ... + a1 x + a0 = 0
item	Recurrence relation	http://en.wikipedia.org/wiki/Recurrence_relation	In mathematics, a recurrence relation, is an equation which defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. A difference equation is a specific type of recurrence relation.
item	Relation algebra	http://en.wikipedia.org/wiki/Relation_algebra	In mathematics, relation algebra (RA) is an algebraic structure, a proper extension of the two-element Boolean algebra 2 intended to capture the mathematical properties of binary relations. RA consists of two binary operations, juxtaposition and relative product, two unary operations, complementation and converse, and the constant 1. Given any set, RA stands to its Cartesian square as Boolean algebra stands to its power set.
item	Ring theory	http://en.wikipedia.org/wiki/Ring_theory	In mathematics, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers.
item	Slope-intercept form	http://en.wikipedia.org/wiki/Slope-intercept_form	There are several forms that the equation of a line can take. They may look different, but they all describe the same line; a line can be described by many equations. All linear equations describing a particular line, however, are equivalent.
item	Square %28algebra%29	http://en.wikipedia.org/wiki/Square_%28algebra%29	In algebra, the square of a number is that number multiplied by itself. Its notation is a superscripted "2"; a number x squared is written as x2. Thus:
item	Symbolic method	http://en.wikipedia.org/wiki/Symbolic_method	In mathematics, the symbolic method in invariant theory is a highly formal algorithm developed in the 19th century for computing form invariants — invariants of algebraic forms. It is based on repeated applications of the Omega process (which involves symbolic partial differentiation -- hence the name) to increase the number of variables of a homogeneous form while decreasing the degree. By clever mathematics, the invariant of the form is then reduced to a vector invariant of many dependent variables, most of which then cancel out.
item	Symmetric difference	http://en.wikipedia.org/wiki/Symmetric_difference	In mathematics, the symmetric difference of two sets is the set of elements which are in one of either set, but not in both. This operation is the set-theoretic equivalent of the exclusive disjunction (XOR operation) in Boolean logic. The symmetric difference of the sets A and B is commonly denoted byVenn diagram of A&#160;Δ&#160;B. The symmetric difference is in solid green.
item	System of linear equations	http://en.wikipedia.org/wiki/System_of_linear_equations	In mathematics and linear algebra, a system of linear equations is a set of linear equations such as3x1 + 2x2 − x3 = 12x1 − 2x2 + 4x3 = −2−x1 + ½x2 − x3 = 0.
item	Temperley-Lieb algebra	http://en.wikipedia.org/wiki/Temperley-Lieb_algebra	In statistical mechanics, the Temperley-Lieb algebra is an algebra generated by certain transfer matrices, invented by Temperley and Lieb in about 1971. It is also related to knot theory, the braid group, and subfactors of von Neumann algebras.[edit]
item	Theory of equations	http://en.wikipedia.org/wiki/Theory_of_equations	In mathematics, the theory of equations comprises a major part of traditional algebra. Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations.
item	Topological module	http://en.wikipedia.org/wiki/Topological_module	In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous.[edit]
item	Transforming polynomials	http://en.wikipedia.org/wiki/Transforming_polynomials	In mathematics, a polynomial is a function of the form . This article will discuss various polynomial transformations.Contents1 Reciprocals of the roots2 Constant multiples of the roots3 Roots that differ by a constant4 The pattern
item	Trinomial	http://en.wikipedia.org/wiki/Trinomial	In elementary algebra, a trinomial is a polynomial consisting of three terms; in other words, a trinomial is the sum of three monomials.
item	Union %28set theory%29	http://en.wikipedia.org/wiki/Union_%28set_theory%29	In set theory and other branches of mathematics, the union of a collection of sets is the set that contains everything that belongs to any of the sets, but nothing else.
item	Unital	http://en.wikipedia.org/wiki/Unital	In mathematics, an algebra is unital (some authors use unitary) if it contains a multiplicative identity element (or unit), i.e. an element 1 with the property 1x = x1 = x for all elements x of the algebra.
item	Variable	http://en.wikipedia.org/wiki/Variable	In computer science and mathematics, a variable (sometimes called a pronumeral) is a symbol denoting a quantity or symbolic representation. In mathematics, a variable often represents an unknown quantity that has the potential to change; in computer science, it represents a place where a quantity can be stored. Variables are often contrasted with constants, which are known and unchanging.
item	Heuristic	http://en.wikipedia.org/wiki/Heuristic	A heuristic is a particular technique of directing one's attention in learning, discovery, or problem-solving. It is originally derived from the Greek "heurisko" (ευρίσκω, the verb from which Archimedes's famous exclamation of "eureka" was derived), which roughly means "I found". The term was introduced in the 4th century AD by Pappus of Alexandria.
item	Iteration	http://en.wikipedia.org/wiki/Iteration	The word iteration is sometimes used in everyday English with a meaning virtually identical to repetition.[edit]
item	Boolean logic	http://en.wikipedia.org/wiki/Boolean_logic	Boolean logic is a complete system for logical operations. It was named after George Boole, an English mathematician at University College Cork who first defined an algebraic system of logic in the mid 19th century. Boolean logic has many applications in electronics, computer hardware and software. In 1938, Claude Shannon showed how electric circuits with relays were a model for Boolean logic. This fact soon proved enormously consequential with the emergence of the electronic computer.
item	Inequality	http://en.wikipedia.org/wiki/Inequality	In mathematics, an inequality is a statement about the relative size or order of two objects. (See also: equality)The notation  means that a is less than b andThe notation  means that a is greater than b.
item	Algorithm	http://en.wikipedia.org/wiki/Algorithm	In mathematics and computing, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. The computational complexity and efficient implementation of the algorithm are important in computing, and this depends on suitable data structures.
item	%28a%2Cb%29-tree	http://en.wikipedia.org/wiki/%28a%2Cb%29-tree	A search tree with the restrictions that all leaves are at the same depth and all internal nodes have between a and b children, where a and b are integers such that . The root may have as few as 2 children.[edit]
item	AC-3 algorithm	http://en.wikipedia.org/wiki/AC-3_algorithm	The AC-3 algorithm (short for Arc Consistency Algorithm #3) is one of a series of algorithms used for the solution of constraint satisfaction problems (or CSP's). It was developed by Alan Mackworth in 1977. The earlier AC algorithms are often considered too inefficent, and many of the later ones are difficult to implement, and so AC-3 is the one most often taught and used in very simple constraint solvers.[edit]
item	AKS primality test	http://en.wikipedia.org/wiki/AKS_primality_test	The AKS primality test (also known as Agrawal-Kayal-Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by three Indian scientists named Manindra Agrawal, Neeraj Kayal and Nitin Saxena on August 6, 2002 in a paper titled "PRIMES is in P".
item	Adam7 algorithm	http://en.wikipedia.org/wiki/Adam7_algorithm	Adam7 is the interlacing algorithm specified for use in PNG images. An interlaced PNG image is broken into seven subimages, which are defined by replicating the 8×8 pattern shown on the right across the full image. The subimages are stored in the PNG file in numerical order.Adam7 is a two-dimensional interlacing scheme, unlike the one-dimensional scheme used in an interlaced GIF. This means the perceived quality of the image and the readability of text in the image rises much faster in the early passes than with GIF interlacing.[edit]SummaryTwo-dimensional interlacing schemePNG first interlace pass displays 1/64th of the image dataThe GIF format on the other hand displays 1/8th of the image dataPNG will send 4 passes to GIF's 1st pass[edit]History1 4 2 45 5 5 53 4 3 45 5 5 5
item	Algorithm %28medical%29	http://en.wikipedia.org/wiki/Algorithm_%28medical%29	A medical algorithm is any algorithm, i.e. a way of doing a computation, formula, look-up table, nomogram, etc., which is useful in health care or medicine. Medical algorithms are part of a broader field which is usually fit under the aims of medical informatics and medical decision making. Medical decisions occur in several areas of medical activity such as medical test selection, diagnosis, therapy and prognosis, automatic control of medical equipments and so forth.Image:Unstable-chest-pain-algorithm.gifExample of medical decision flowchart for chest pain
item	Algorithm of Inventive Problems Solving	http://en.wikipedia.org/wiki/Algorithm_of_Inventive_Problems_Solving	ARIZ (russ. acronym of Алгоритм решения изобретательских задач) - Algorithm of Inventive Problems Solving is problem solving technique in form of list of (about 85) step-by-step procedures that incrementally evolves a complex problem to a point where it is simple to solve. See also Genrich Altshuller.
item	Algorithmic efficiency	http://en.wikipedia.org/wiki/Algorithmic_efficiency	In computer science, efficiency is used to describe several desirable properties of an algorithm or other construct, besides clean design, functionality, etc. Efficiency is generally contained in two properties: speed, (the time it takes for an operation to complete), and space, (the memory or non-volatile storage used up by the construct). Optimization is the process of making code as efficient as possible, sometimes focusing on space at the cost of speed, or vice versa.
item	Algorithms for Recovery and Isolation Exploiting Semantics	http://en.wikipedia.org/wiki/Algorithms_for_Recovery_and_Isolation_Exploiting_Semantics	In computer science, Algorithms for Recovery and Isolation Exploiting Semantics, or ARIES is a recovery algorithm designed to work with a no-force, steal database approach. ARIES is a popular algorithm used by IBM DB2, Microsoft SQL Server and many other database systems.
item	Alias method	http://en.wikipedia.org/wiki/Alias_method	The alias method is an efficient algorithm for creating random numbers with a non-uniform distribution.[edit]
item	Amortized analysis	http://en.wikipedia.org/wiki/Amortized_analysis	In analysis of algorithms, amortized analysis refers to finding the average running time per operation over a worst-case sequence of operations. Amortized analysis differs from average-case performance in that probability is not involved; amortized analysis guarantees the time per operation over worst-case performance.
item	Analysis of algorithms	http://en.wikipedia.org/wiki/Analysis_of_algorithms	To analyze an algorithm is to determine the amount of resources (such as time and storage) necessary to execute it. Most algorithms are designed to work with inputs of arbitrary length. Usually the efficiency or complexity of an algorithm is stated as a function relating the input length to the number of steps (time complexity) or storage locations (space or memory complexity) required to execute the algorithm.
item	Astronomical algorithm	http://en.wikipedia.org/wiki/Astronomical_algorithm	Astronomical algorithms are the algorithms used to calculate ephemerides, calendars, and positions (as in celestial navigation or satellite navigation). Examples of large and complex astronomical algorithms are those used to calculate the position of the Moon. A simple example is the calculation of the Julian day.
item	Asymptotically optimal	http://en.wikipedia.org/wiki/Asymptotically_optimal	In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor worse than the best possible algorithm. It is a term commonly encountered in computer science research as a result of widespread use of big-O notation.
item	Automatic distillation of structure	http://en.wikipedia.org/wiki/Automatic_distillation_of_structure	Automatic Distillation of Structure (ADIOS) is an algorithm that can analyse source material such as text and come up with meaningful information about the structures used in the source. One application of the algorithm is grammar: ADIOS can read a source text and teach itself grammatical rules based on structures and patterns found in the text. Using these, the system can then produce new, meaningful sentences.
item	Autonomy-oriented computation	http://en.wikipedia.org/wiki/Autonomy-oriented_computation	Autonomy-oriented computation is novel paradigm proposed by Liu (2001) which uses artificial systems imitating social animals' collective behaviours to solve hard computational problems. For example, ant colony optimization could be studied in this paradigm.[edit]
item	Bach%27s algorithm	http://en.wikipedia.org/wiki/Bach%27s_algorithm	Bach's algorithm is an efficient algorithm for generating random factored numbers. Bach's algorithm is named after its discoverer, Eric Bach. The algorithm is of interest because the straightforward method for generating a random factored number, namely generating a random number and then factoring it, is not known to be efficient, because no algorithm is known that efficiently factors numbers. Bach's algorithm is capable of generating random numbers along with their factorization efficiently.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wik
item	Backpropagation	http://en.wikipedia.org/wiki/Backpropagation	Backpropagation is a supervised learning technique used for training artificial neural networks. It was first described by Paul Werbos in 1974, and further developed by David E. Rumelhart, Geoffrey E. Hinton and Ronald J. Williams in 1986.
item	Baum-Welch algorithm	http://en.wikipedia.org/wiki/Baum-Welch_algorithm	In computer science and statistical computing, the Baum-Welch algorithm is used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm.[edit]
item	Best%2C worst and average case	http://en.wikipedia.org/wiki/Best%2C_worst_and_average_case	In computer science, best, worst and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. In almost all situations the resource being considered is running time, but it could also be memory, for instance. In real-time systems, the worst case execution time is often of particular concern since it important to know how much time might be needed in the worst case to guarantee the algorithm would always finish on time.
item	Branching factor	http://en.wikipedia.org/wiki/Branching_factor	In computing, tree data structures, and game theory, the branching factor is the number of children of each node. If this value is not uniform, an average branching factor can be calculated.
item	Brent-Salamin algorithm	http://en.wikipedia.org/wiki/Brent-Salamin_algorithm	The Brent-Salamin algorithm is an algorithm for computing π (pi). It was discovered independently by Richard Brent and Eugene Salamin about 1975, and is also known as the Gauss-Legendre algorithm since it depends on some results of Gauss and Legendre (but they did not invent the algorithm, probably because it is not much use for hand computation).[edit]
item	British Museum algorithm	http://en.wikipedia.org/wiki/British_Museum_algorithm	The British Museum algorithm is a general approach to find a solution by checking all possibilities one by one, beginning with the smallest. The term refers to a conceptual, not a practical, technique where the number of possibilities are enormous.
item	Bully algorithm	http://en.wikipedia.org/wiki/Bully_algorithm	The bully algorithm is a method in distributed computing for dynamically selecting a coordinator by process ID number.
item	C4.5 algorithm	http://en.wikipedia.org/wiki/C4.5_algorithm	c4.5 is a decision tree generating algorithm, based on the ID3 algorithm. It contains several improvements, especially needed for software implementation. Improvements contains:Choosing an appropriate attribute selection measure.Handling training data with missing attribute values.Handling attributes with differing costs.Handling continuous attributesContents1 Data Structures2 Tree building3 Pruning4 Iteration case5 Counting gain6 External links
item	Cache algorithms	http://en.wikipedia.org/wiki/Cache_algorithms	Cache algorithms are optimizing instructions&#160;– algorithms&#160;– that a computer program can follow to manage a cache of information stored on the computer. Cache size is usually limited, and if the cache is full, the computer (that is, the programmer) must decide which items to keep and which to discard to make room for new items.
item	Cascade correlation algorithm	http://en.wikipedia.org/wiki/Cascade_correlation_algorithm	Cascade-Correlation is an architecture and supervised learning algorithm for artificial neural networks developed by Scott Fahlman. Instead of just adjusting the weights in a network of fixed topology, Cascade-Correlation begins with a minimal network, then automatically trains and adds new hidden units one by one, creating a multi-layer structure. Once a new hidden unit has been added to the network, its input-side weights are frozen. This unit then becomes a permanent feature-detector in the network, available for producing outputs or for creating other, more complex feature detectors. The Cascade-Correlation architecture has several advantages over existing algorithms: it learns very quickly, the network determines its own size and topology, it retains the structures it has built even if the training set changes, and it requires no back-propagation of error signals through the connections of the network.[edit]
item	Chung Kwei %28algorithm%29	http://en.wikipedia.org/wiki/Chung_Kwei_%28algorithm%29	Chung Kwei is a SPAM filtering algorithm based on the Tiresias algorithm for finding coding genes within bulk DNA.[edit]
item	Circular reference	http://en.wikipedia.org/wiki/Circular_reference	A circular reference, or sometimes known as a run-around by some people, is a series of references where the last object references the first, thus causing the whole series of references to be unusable.Contents1 Circular references in business2 Circular references in computer programming3 Circular reference as an explanation4 See also
item	Circular shift	http://en.wikipedia.org/wiki/Circular_shift	In combinatorial mathematics, a circular shift is a permutation of the entries in a tuple where the last element becomes the first element and all the other elements are shifted, or where the first element becomes the last element and all the other are shifted. Equivalently, a circular shift is a permutation with only one cycle.
item	Color quantization	http://en.wikipedia.org/wiki/Color_quantization	In computer graphics, color quantization or color image quantization is a process that reduces the number of distinct colors used in an image, usually with the intention that the new image should be as visually similar as possible to the original image. Computer algorithms to perform color quantization on bitmaps have been studied since the 1970s. Color quantization is critical for displaying images with many colors on devices that can only display a limited number of colors, usually due to memory limitations, and enables efficient compression of certain types of images.The name "color quantization" is primarily used in computer graphics research literature; in applications, terms such as optimized palette generation, optimal palette generation, or decreasing color depth are used. Some of these are misleading, as the palettes generated by standard algorithms are not necessarily the best possible.Contents1 Algorithms2 History and applications2.1 Editor support3 See also4 References
item	Competitive analysis	http://en.wikipedia.org/wiki/Competitive_analysis	Competitive analysis shows how online algorithms perform and demonstrates the power of randomization in algorithms.
item	Control variate	http://en.wikipedia.org/wiki/Control_variate	In Monte Carlo methods, one or more control variates may be employed to achieve variance reduction by exploiting the correlation between statistics.[edit]
item	Course-of-value recursion	http://en.wikipedia.org/wiki/Course-of-value_recursion	Course-of-value recursion allows the use of any number of values for previous arguments, as opposed to the primitive recursion where only the value for the immediately preceding argument can be used. Although apparently more general, this notion actually turns out to be reducible to the usual primitive recursion as well.[1][edit]
item	Cuthill-McKee algorithm	http://en.wikipedia.org/wiki/Cuthill-McKee_algorithm	In the mathematical subfield of matrix theory the Cuthill-McKee algorithm is an algorithm to reduce the bandwidth of sparse symmetric matrices.[edit]
item	Dancing Links	http://en.wikipedia.org/wiki/Dancing_Links	In computer science, Dancing Links, commonly known as DLX, is the technique suggested by Donald Knuth to efficiently implement his Algorithm X. Algorithm X is a recursive, nondeterministic, depth-first, brute-force algorithm that finds all solutions to the exact cover problem. Some of the better known exact cover problems include tiling, N-queens and Sudoku.
item	De Boor algorithm	http://en.wikipedia.org/wiki/De_Boor_algorithm	In the mathematical subfield of numerical analysis the de Boor algorithm is a fast and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of De Casteljau's algorithm for Bézier curves.[edit]
item	Dekker%27s algorithm	http://en.wikipedia.org/wiki/Dekker%27s_algorithm	Dekker's algorithm is a concurrent programming algorithm for mutual exclusion due to the Dutch mathematician T. J. Dekker that allows two processes to share a single-use resource without conflict, using only shared memory for communication.
item	Dictionary of Algorithms and Data Structures	http://en.wikipedia.org/wiki/Dictionary_of_Algorithms_and_Data_Structures	The Dictionary of Algorithms and Data Structures is a dictionary style reference for many algorithms, "algorithmic techniques", "archetypal problems" and data structures found in the field of Computer Science [1]. The dictionary is maintained by Paul E. Black [1], and is hosted by the Software Quality Group of the Software Diagnostics and Conformance Testing Division, Information Technology Laboratory, a part of the National Institute of Standards and Technology[1].[edit]
item	Difference of Gaussians	http://en.wikipedia.org/wiki/Difference_of_Gaussians	Difference of Gaussian(s) is a wavelet function which approximates the Mexican Hat wavelet by subtracting a wide gaussian from a narrow gaussian, as defined by this formula:
item	Dijkstra-Scholten Algorithm	http://en.wikipedia.org/wiki/Dijkstra-Scholten_Algorithm	The Dijkstra-Scholten Algorithm is an algorithm for detecting termination in a distributed system. The algorithm was proposed by Dijkstra and Scholten in 1980.
item	Disjoint-set data structure	http://en.wikipedia.org/wiki/Disjoint-set_data_structure	Given a set of elements, it is often useful to break them up or partition them into a number of separate, nonoverlapping groups. A disjoint-set data structure is a data structure that keeps track of such a partitioning. A union-find algorithm is an algorithm that performs two useful operations on such a data structure:Find: Determine which group a particular element is in. Also useful for determining if two elements are in the same group.Union: Combine or merge two groups into a single group.
item	Divide and conquer algorithm	http://en.wikipedia.org/wiki/Divide_and_conquer_algorithm	In computer science, divide and conquer (D&amp;C) is an important algorithm design paradigm. It works by recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
item	Divide-and-conquer eigenvalue algorithm	http://en.wikipedia.org/wiki/Divide-and-conquer_eigenvalue_algorithm	Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) become competitive in terms of stability and efficiency with more traditional algorithms such as the QR algorithm. The basic concept behind these algorithms is of course the famous divide-and-conquer approach from computer science. An eigenvalue problem is divided into two problems of roughly half the size, each of these are solved recursively, and the eigenvalues of the original problem are computed from the results of these smaller problems.
item	Doomsday %28weekday%29	http://en.wikipedia.org/wiki/Doomsday_%28weekday%29	For any year, Doomsday is the day of the week on which the last day of February falls. It is also the day of the week of 4/4, 6/6, 8/8, 10/10 and 12/12, as well as 5/9, 9/5, 7/11, and 11/7.
item	%CE%95-net	http://en.wikipedia.org/wiki/%CE%95-net	Let P be a probability distribution over some set X. An ε-net for a class  of subsets of X is any subset  such that for any 
item	Elevator algorithm	http://en.wikipedia.org/wiki/Elevator_algorithm	The elevator algorithm (also SCAN) is a disk scheduling algorithm to determine the motion of the disk's arm and head in servicing read and write requests.[edit]
item	Exponential backoff	http://en.wikipedia.org/wiki/Exponential_backoff	Exponential backoff is an algorithm that uses feedback to multiplicatively decrease the rate of some process, in order to gradually find an acceptable rate. It is often used in network congestion avoidance to help determine the correct sending rate. For example, a sender might send a message, set a timer to wait 0.25 seconds for an acknowledgment, and if none arrives, retransmit the message and wait 0.5 seconds for an acknowledgment. It will continue to retry until it receives an acknowledgement and will wait, 1s, 2s, 4s, 8s, etc. each time before retrying.[edit]
item	FNN algorithm	http://en.wikipedia.org/wiki/FNN_algorithm	The false nearest neighbor (FNN) algorithm is an algorithm for estimating the embedding dimension.[edit]
item	Fast Folding Algorithm	http://en.wikipedia.org/wiki/Fast_Folding_Algorithm	The Fast Folding Algorithm (Staelin, 1969) in signal processing is an efficient algorithm for the detection of approximately-periodic events within time series data. It computes superpositions of the signal modulo various window sizes simultaneously.
item	FastICA	http://en.wikipedia.org/wiki/FastICA	FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology. The algorithm is based on a fixed-point iteration scheme maximizing non-gaussianity as a measure of statistical independence. It can be also derived as an approximative Newton iteration.Contents1 Algorithm1.1 FastICA for one unit2 See also3 External links
item	Featherstone%27s algorithm	http://en.wikipedia.org/wiki/Featherstone%27s_algorithm	Featherstone's algorithm is a technique used for computing the effects of forces applied to a structure of joints and links (an "open kinematic chain") such as a skeleton used in ragdoll physics.[edit]
item	Felicific calculus	http://en.wikipedia.org/wiki/Felicific_calculus	The felicific calculus was an algorithm formulated by Jeremy Bentham for calculating the degree or amount of happiness that a specific action is likely to cause, and hence its degree of moral rightness. It is also known as the "Utility calculus", the "Hedonistic calculus" and the "Hedonic calculus".
item	Fibonacci number program	http://en.wikipedia.org/wiki/Fibonacci_number_program	In many beginning computer science courses, an introduction to the concept of recursion often includes a program to calculate and print Fibonacci numbers (or computing the factorial of a number). The following list includes examples of code in various programming languages that will calculate the Fibonacci sequence.Contents1 Common Lisp2 Haskell3 Perl3.1 One example3.2 Binary recursion, snippet3.3 Binary recursion with special Perl "caching", snippet3.4 Iterative, snippet3.5 Command line iterative4 PostScript<a href="#
item	First fit algorithm	http://en.wikipedia.org/wiki/First_fit_algorithm	The first fit algorithm is an algorithm which provides a fast but often nonoptimal solution to the bin packing problem. It requires Θ(n&#160;log&#160;n) time.[edit]
item	Flood fill	http://en.wikipedia.org/wiki/Flood_fill	Flood fill, also called seed fill, is an algorithm that determines the area connected to a given node in a multi-dimensional array. It is used in the "bucket" fill tool of paint programs to determine which parts of a bitmap to fill with color, and in puzzle games such as Puyo Puyo, Lumines, Magical Drop, and some implementations of Tetris (but not Columns) for determining which pieces are cleared.
item	Flowchart	http://en.wikipedia.org/wiki/Flowchart	A flowchart (also spelled flow-chart and flow chart) is a schematic representation of a process. They are commonly used in business/economic presentations to help the audience visualize the content better, or to find flaws in the process.
item	Force-based algorithms	http://en.wikipedia.org/wiki/Force-based_algorithms	Force-directed algorithms are a class of algorithms for drawing graphs in an aesthetically pleasing way. Their purpose is to position the nodes of a graph in two dimensional or three dimensional space so that all the edges are of more or less equal length and there are as few crossing edges as possible.
item	Freivald%27s algorithm	http://en.wikipedia.org/wiki/Freivald%27s_algorithm	//[edit]IntroductionFreivald's algorithm is a randomized algorithm used to verify matrix multiplication. Given three n x n matrices A, B, and C, a general problem is to verify whether A x B = C. A naïve algorithm would compute the product A x B explicitly and compare term by term whether this product equals C. However, this approach takes O(n3) time. To resolve this, Freivald's algorithm utilizes randomization in order to reduce this time bound to O(n2).[edit]The Algorithm===Input=== Three n x n matrices A, B, C. ===Output=== Yes, if A x B = C; No, otherwise.<div class="editsection" style="float:right;margin-left:
item	Generic cell rate algorithm	http://en.wikipedia.org/wiki/Generic_cell_rate_algorithm	The generic cell rate algorithm (or GCRA) is an algorithm which measures cell rate at a specified timescale [1]. The GCRA is an implementation of the leaky bucket algorithm in ATM networks, and provides a traffic shaping function [2].Contents1 What is the GCRA used for?2 How does the algorithm work?3 Formal definition of the GCRA4 See also5 References
item	Genetic Fuzzy Systems	http://en.wikipedia.org/wiki/Genetic_Fuzzy_Systems	Genetic Fuzzy Systems are fuzzy systems using a genetic algorithm for determining the system parameters.Contents1 Fuzzy systems2 Genetic algorithms3 Genetic Fuzzy Systems4 Genetic Learning of Fuzzy Rule Base5 References6 External links
item	Gerchberg saxton algorithm	http://en.wikipedia.org/wiki/Gerchberg_saxton_algorithm	Gerchberg Saxton Algorithm
item	God%27s algorithm	http://en.wikipedia.org/wiki/God%27s_algorithm	God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It stands for any practical algorithm that produces a solution having the least possible number of moves, the idea being that an omniscient being would know an optimal step from any given configuration.[edit]
item	Graphplan	http://en.wikipedia.org/wiki/Graphplan	Graphplan is an algorithm for automated planning developed by Avrim Blum and Merrick Furst in 1995. Graphplan takes as input a planning problem expressed in STRIPS and produces, if any, a sequence of operations for reaching a goal state. The name graphplan is due its use of a planning graph as an intermediate structure to reduce the amount of search needed to find the solution.
item	Greedy algorithm	http://en.wikipedia.org/wiki/Greedy_algorithm	A Greedy Algorithm is an algorithm that follows the problem solving meta-heuristic of making the locally optimum choice at each stage with the hope of finding the global optimum. For instance, applying the greedy strategy to the traveling salesman problem yields the following algorithm: "At each stage visit the unvisited city nearest to the current city".
item	Guess value	http://en.wikipedia.org/wiki/Guess_value	A guess value is more commonly called a starting value or initial value. These are necessary for most nonlinear regression search algorithms, because those algorithms are mainly deterministic and iterative, and they need to start somewhere. The quality of the initial values can have a considerable impact on the success or lack of such of the search algorithm. This is because the fitness function (in this case the SSE) has a (conjectured) unique shape about the global minimum, similar to the shape that objective functions in Operations Research problems often have. To one "side" the SSE simply increases exponentially. To the other "side" the SSE increases parabolically and then asymptotes to the plateau of the sum of squares of the observations. Starting values that fall in the exponential region can lead to algorithm failure because of overflow. Starting values that fall in the asymptotic plateau region can lead to algorithm failure because of "dithering<
item	HITS algorithm	http://en.wikipedia.org/wiki/HITS_algorithm	The HITS ("hypertext induced topic selection") algorithm is an algorithm for rating,(J.Kleinberg) and therefore also ranking, Web pages. HITS uses two values for each page, the authority value and the hub value. Authority and hub values are defined in terms of one another in a mutual recursion. An authority value is computed as the sum of the scaled hub values that point to that page. A hub value is the sum of the scaled authority values of the pages it points to. Relevance of the linked pages is also considered in some implementations.
item	Hash join	http://en.wikipedia.org/wiki/Hash_join	The Hash Join is an example of a join algorithm and is used in the implementation of a relational database management system.
item	Heuristic %28computer science%29	http://en.wikipedia.org/wiki/Heuristic_%28computer_science%29	In computer science, besides the common use as "rule of thumb" (see heuristic), the term heuristic has two well-defined technical meanings.Contents1 Heuristic algorithms2 Heuristics in shortest-path problems2.1 Effect of heuristics on computational performance2.2 Finding heuristics3 See also
item	Hshieh-Hammond algorithm	http://en.wikipedia.org/wiki/Hshieh-Hammond_algorithm	The Hshieh-Hammond Dimensions algorithm is a mapping expansion to CYSTHS, a bone scan uptake quantification program. It is based on the CHASM algorithm, the Pixel Scan algorithm, and a generic rotation algorithm. Dimensions does not use the Java 3D API for compatibility issues. Dimensions was developed by Alan Hshieh and Lydia Hammond in 2005.
item	Huang%27s Algorithm	http://en.wikipedia.org/wiki/Huang%27s_Algorithm	Huang's Algorithm is an algorithm for detecting termination in a distributed system. The algorithm was proposed by Shing-Tsaan Huang in 1989 in the Journal of Computers.[edit]
item	Hungarian algorithm	http://en.wikipedia.org/wiki/Hungarian_algorithm	The Hungarian algorithm is a combinatorial optimization algorithm which solves assignment problems in polynomial time. The first version, known as the Hungarian method, was invented and published by Harold Kuhn in 1955. This was revised by James Munkres in 1957, and has been known since as the Hungarian algorithm, the Munkres assignment algorithm, or the Kuhn-Munkres algorithm.
item	Hyphenation algorithm	http://en.wikipedia.org/wiki/Hyphenation_algorithm	One of the reasons for the complexity of the rules of word-breaking, or hyphenation algorithm, is that different 'dialects' of English tend to differ on the rule: American English tends to work on sound, while British English tends to look to the origins of the word and then to sound. There are also a large number of exceptions which further complicates matters.
item	In-place algorithm	http://en.wikipedia.org/wiki/In-place_algorithm	In computer science, an in-place algorithm is an algorithm which transforms a data structure using a small, constant amount of extra storage space. The input is usually overwritten by the output as the algorithm executes. An algorithm which is not in-place is sometimes called not-in-place or out-of-place.
item	Intersection algorithm	http://en.wikipedia.org/wiki/Intersection_algorithm	The Intersection Algorithm is an agreement algorithm used to select sources for estimating accurate time from a number of noisy time sources, it forms part of the modern Network Time Protocol. It is a modified form of Marzullo's algorithm.
item	Iterative Closest Point	http://en.wikipedia.org/wiki/Iterative_Closest_Point	Iterative Closest Point (ICP) is an algorithm employed to match two clouds of points. This matching is used to reconstruct 3D surfaces from different scans, to localize robots, to match bone models with measures in real-time, etc.
item	Iterative reconstruction	http://en.wikipedia.org/wiki/Iterative_reconstruction	Iterative reconstruction is a method or group of algorithms used to reconstruct 2D and 3D images from the projections of an object. The technique differs greatly from the more ubiquitous filtered back projection (FBP) method.
item	Itoh-Tsujii inversion algorithm	http://en.wikipedia.org/wiki/Itoh-Tsujii_inversion_algorithm	The Itoh-Tsujii inversion algorithm is used to invert elements in a finite field. It was introduced in 1988 and first used over GF(2m) using the normal basis representation of elements, however the algorithm is generic and can be used for other bases, such as the polynomial basis. It can also be used in any finite field, GF(pm).
item	K-means algorithm	http://en.wikipedia.org/wiki/K-means_algorithm	The K-means algorithm is an algorithm to cluster objects based on attributes into k partitions. It is a variant of the expectation-maximization algorithm in which the goal is to determine the k means of data generated from gaussian distributions. It assumes that the object attributes form a vector space. The objective it tries to achieve is to minimize total intra-cluster variance, or, the function
item	Knuth%27s Algorithm X	http://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X	Donald Knuth's Algorithm X, first presented in November of 2000, is a recursive, nondeterministic, depth-first, brute-force algorithm that finds all solutions to the exact cover problem.
item	Knuth-Bendix completion algorithm	http://en.wikipedia.org/wiki/Knuth-Bendix_completion_algorithm	The Knuth-Bendix completion algorithm is an algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it has effectively solved the word problem for the specified algebra. Hence, it can also be used to solve the coset enumeration problem. The word problem is, in general, undecidable, hence the algorithm cannot always terminate successfully. If it does not succeed, it will either run forever, or fail when it encounters an unorientable equation (i.e. an equation that it cannot turn into a rewrite rule). The enhanced completion without failure will not fail on unorientable equations and provides a semi-decision procedure for the word problem.
item	Kuwaiti algorithm	http://en.wikipedia.org/wiki/Kuwaiti_algorithm	Microsoft uses the Kuwaiti algorithm to convert between dates in the Western standard Gregorian calendar and dates in the Hijri or Islamic calendar. There is no fixed correspondence defined in advance between the Gregorian solar calendar and the Islamic lunar calendar, since the latter is defined by the visibility of the new moon by religious authorities and can therefore vary by a day or two, depending on the particular Islamic authority, weather conditions, and other variables. As an attempt to make conversions between the calendars somewhat predictable, Microsoft claims to have created this algorithm based on statistical analysis of historical data from Kuwait. However, its results are identical to a variation of the tabular Islamic calendar, which was introduced by Islamic astronomers around the eighth century.
item	Lamport%27s bakery algorithm	http://en.wikipedia.org/wiki/Lamport%27s_bakery_algorithm	Lamport's bakery algorithm is a computer algorithm devised by computer scientist Dr Leslie Lamport, which is intended to improve the robustness of multiple thread-handling processes by means of mutual exclusion.Contents1 Nature of the problem2 Algorithm2.1 Analogy2.2 Critical section2.3 Non-critical section3 Implementation of the algorithm3.1 Pseudocode3.2 Discussion4 See also5 References</ta
item	Lanczos algorithm	http://en.wikipedia.org/wiki/Lanczos_algorithm	The Lanczos algorithm is a popular method to find a zero vector in the process of the quadratic sieve. It is supposed to be one of the most efficient ways of finding a zero vector, which is a crucial part of the Quadratic Sieve and Continued Fraction factoring algorithms.
item	Las Vegas algorithm	http://en.wikipedia.org/wiki/Las_Vegas_algorithm	In computing, a Las Vegas algorithm is a randomized algorithm that is correct; that is, it always produces the correct result. In other words, a Las Vegas algorithm does not gamble with the verity of the result --- it only gambles with the resources used for the computation. A simple example is randomized quicksort, where the pivot is chosen randomly, but the result is always sorted. The usual definition of a Las Vegas algorithm includes the restriction that the expected run time always be finite, when the expectation is carried out over the space of random information, or entropy, used in the algorithm.
item	Leaky bucket	http://en.wikipedia.org/wiki/Leaky_bucket	Although the leaky bucket algorithm has several uses, it is best understood in the context of network traffic shaping or rate limiting. Typically, the algorithm is used to control the rate at which data is injected into a network, smoothing out "burstiness" in the data rate.Contents1 Traffic shaping algorithms2 What is the Leaky-Bucket algorithm used for?3 Automobile traffic analogy4 The Leaky-bucket algorithm5 Inefficiency of the Leaky-bucket implementation6 See also7 References8 External links
item	Lenstra-Lenstra-Lov%C3%A1sz lattice basis reduction algorithm	http://en.wikipedia.org/wiki/Lenstra-Lenstra-Lov%C3%A1sz_lattice_basis_reduction_algorithm	The Lenstra-Lenstra-Lovász lattice basis reduction (LLL) is a polynomial time algorithm which, given a lattice basis as input, outputs a basis with short, nearly orthogonal vectors. More precisely, given as input d lattice basis vectors with n-dimensional integer coordinates and a norm lesser than B, the LLL algorithm outputs an LLL-reduced lattice basis in time O(d5nlog3B).
item	Linear search	http://en.wikipedia.org/wiki/Linear_search	In computer science, linear search is a search algorithm, also known as sequential search, that is suitable for searching a set of data for a particular value.
item	Lloyd%27s algorithm	http://en.wikipedia.org/wiki/Lloyd%27s_algorithm	In computer graphics and electrical engineering, Lloyd's algorithm, also known as Voronoi iteration or relaxation, a method for evenly distributing samples or objects, usually points.
item	Lock-free and wait-free algorithms	http://en.wikipedia.org/wiki/Lock-free_and_wait-free_algorithms	In contrast to algorithms that protect access to shared data with locks, lock-free and wait-free algorithms are specially designed to allow multiple threads to read and write shared data concurrently without corrupting it. "Lock-free" refers to the fact that a thread cannot lock up: every step it takes brings progress to the system. This means that no synchronization primitives such as mutexes or semaphores can be involved, as a lock-holding thread can prevent global progress if it is switched out. "Wait-free" refers to the fact that a thread can complete any operation in a finite number of steps, regardless of the actions of other threads. It is possible for an algorithm to be lock-free but not wait-free.It has been suggested that this article or section be merged into Non-blocking synchronization. (Discuss)Contents1 Motivation2 The lock-free approach<span cla
item	MISER algorithm	http://en.wikipedia.org/wiki/MISER_algorithm	The MISER algorithm is a method for reducing error in the Monte Carlo simulation by focusing the search in areas of the function with higher variance using recursive stratified sampling.[edit]
item	MaMF	http://en.wikipedia.org/wiki/MaMF	MaMF, or Mammalian Motif Finder, is an algorithm for identifying motifs to which transcription factors bind.
item	Maekawa%27s algorithm	http://en.wikipedia.org/wiki/Maekawa%27s_algorithm	Maekawa's Algorithm is an algorithm for mutual exclusion on a distributed system. The basis of this algorithm is a quorum like approach where any one site needs only to seek permissions from a subset of other sites.Contents1 Algorithm1.1 Terminology1.2 Algorithm1.3 Performance2 See also
item	Marzullo%27s algorithm	http://en.wikipedia.org/wiki/Marzullo%27s_algorithm	Marzullo's algorithm, invented by Keith Marzullo for his Ph.D. dissertation, is an agreement algorithm used to select sources for estimating accurate time from a number of noisy time sources. A refined version of it, renamed the "Intersection algorithm", forms part of the modern Network Time Protocol.Contents1 Purpose2 Method3 Efficiency4 References5 External links
item	Maze generation algorithm	http://en.wikipedia.org/wiki/Maze_generation_algorithm	There are a number of different maze generation algorithms, that is, automated methods for the creation of mazes.
item	Medical algorithm	http://en.wikipedia.org/wiki/Medical_algorithm	A medical algorithm is any computation, formula, statistical survey, or look-up table, useful in healthcare. Medical algorithms include decision tree approaches to healthcare treatment (i.e., if symptoms A, B, and C are evident, then use treatment X) and also less clear-cut tools aimed at reducing or defining uncertainty. An example would be an algorithm used to determine what next investigation or management to apply to a possible deep vein thrombosis.
item	Memory bound function	http://en.wikipedia.org/wiki/Memory_bound_function	Memory bound refers to a situation in which the time to complete a given computational problem is decided primarily by the amount of available memory to hold data. In other words, the limiting factor of solving a given problem is the memory access speed. The application of memory bound functions could prove to be valuable in preventing spam, which has become a problem of epidemic proportions on the Internet.Contents1 Memory bound functions and memory functions2 Using memory bound functions to prevent spam3 See also4 References5 External links
item	Mental poker	http://en.wikipedia.org/wiki/Mental_poker	Mental poker is the common name for a set of cryptographic problems that concerns playing a fair game over distance without the need for a trusted third party. The term is also applied to the theories surrounding these problems and their possible solutions. The name stems from the card game poker which is one of the games to which this kind of problems apply. A similar problem is flipping a coin over a distance.
item	Merge algorithm	http://en.wikipedia.org/wiki/Merge_algorithm	Merge algorithms are a family of algorithms that run sequentially over multiple sorted lists, typically producing more sorted lists as output. This is well-suited for machines with tape drives. Use has declined due to large random access memories, and many applications of merge algorithms have faster alternatives when you have a random-access memory that holds all your data.
item	Meta-algorithm	http://en.wikipedia.org/wiki/Meta-algorithm	A meta-algorithm is an algorithm that can be usefully considered to have other significant algorithms, not just elementary operations and simple control structures, as its constituents; also an algorithm that has subordinate algorithms as variable and replaceable parameters. Thus a meta-algorithm defines a class of concrete algorithms.
item	Microsoft Point-to-Point Compression	http://en.wikipedia.org/wiki/Microsoft_Point-to-Point_Compression	Microsoft Point-to-Point Compression, or MPPC, is an algorithm for compressing data between point-to-point links. The algorithm is patented in the United States by Hifn Inc..
item	Minimum degree algorithm	http://en.wikipedia.org/wiki/Minimum_degree_algorithm	In numerical analysis the minimum degree algorithm is an algorithm used to permute the rows and columns of a symmetric sparse matrix before applying the Cholesky decomposition, to reduce the number of non-zeros in the Cholesky factor. This results in reduced storage requirements and means that the Cholesky factor, or sometimes an incomplete Cholesky factor used as a preconditioner (for example in the preconditioned conjugate gradient algorithm) can be applied with fewer arithmetic operations.
item	Monte Carlo method	http://en.wikipedia.org/wiki/Monte_Carlo_method	Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms. Because of the repetition of algorithms and the large number of calculations involved, Monte Carlo is a method suited to calculation using a computer, utilizing many techniques of computer simulation.
item	Multivariate division algorithm	http://en.wikipedia.org/wiki/Multivariate_division_algorithm	In mathematics, polynomials in more than one variable do not form a Euclidean domain, so it is not possible to construct a true division algorithm; but an approximate multivariate division algorithm can be constructed.
item	Nagle%27s algorithm	http://en.wikipedia.org/wiki/Nagle%27s_algorithm	Nagle's algorithm is a means of improving the efficiency of TCP/IP networks by reducing the number of packets that need to be sent over the network. It is named after John Nagle, then at Ford Aerospace and lately at Animats.
item	Negascout	http://en.wikipedia.org/wiki/Negascout	NegaScout or Principal Variation Search is a minimax algorithm that can be faster than alpha-beta pruning. Like alpha-beta pruning, NegaScout is a directional search algorithm for computing the minimax value of a node in a tree. It dominates alpha beta pruning in the sense that it will never examine a node that can be pruned by alpha beta; however it relies on accurate move ordering to capitalize on this advantage.
item	Non-blocking algorithm	http://en.wikipedia.org/wiki/Non-blocking_algorithm	In concurrent programming, non-blocking algorithms are those algorithms designed to avoid requiring a critical section. Often, these algorithms allow multiple processes to make progress on a problem without ever blocking each other.
item	Non-blocking synchronization	http://en.wikipedia.org/wiki/Non-blocking_synchronization	In computer science, non-blocking synchronization ensures that threads competing for a shared resource do not have their execution indefinitely postponed by mutual exclusion. Literature up to the turn of the century used "non-blocking" synonymously with lock-free: an algorithm with guaranteed system-wide progress. However, since 2003 [1], the term has been weakened to only prevent progress-blocking interactions with a preemptive scheduler.
item	Nonlinear dimensionality reduction	http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction	High-dimensional data can be difficult to interpret. One approach is to assume that the data lies on an embedded non-linear manifold. If that manifold is of low enough dimension then the data can be visualised in the low-dimensional space.
item	Null-move heuristic	http://en.wikipedia.org/wiki/Null-move_heuristic	In computer chess programs, the null-move heuristic is a heuristic technique used to enhance the speed of the alpha-beta pruning algorithm.Contents1 Rationale2 Implementation3 Problems with the null-move heuristic4 Verified null-move pruning5 See also
item	Particle-in-cell	http://en.wikipedia.org/wiki/Particle-in-cell	Particle-In-Cell (PIC) is an algorithm to compute (for example) the trajectories of charged particles in an electromagnetic field. The field is computed in a grid of cells, and the force on the particles is interpolated from the fields on the grid. The action of the moving charged particles is taken into account by integrating the convection current caused by the moving charges.
item	Peterson%27s algorithm	http://en.wikipedia.org/wiki/Peterson%27s_algorithm	Peterson's algorithm is a concurrent programming algorithm for mutual exclusion that allows just two processes to share a single-use resource without conflict, using only shared memory for communication. [Note: Peterson's Algorithm can be generalised for more than two processes, as discussed in "Operating Systems Review, January 1990 ('Proof of a Mutual Exclusion Algorithm', M Hofri)".]
item	Pohlig-Hellman algorithm	http://en.wikipedia.org/wiki/Pohlig-Hellman_algorithm	In mathematics, the Pohlig-Hellman algorithm is an algorithm for the computation of discrete logarithms in a multiplicative group whose order is a smooth integer. The algorithm is based on the Chinese remainder theorem and runs in polynomial time.
item	Polynomial long division	http://en.wikipedia.org/wiki/Polynomial_long_division	In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
item	Priority fill	http://en.wikipedia.org/wiki/Priority_fill	In the context of computer graphics, priority fill is a Hidden Line/Removal Surface algorithm which establishes a priority list based upon the depth of parts of an object, so that the parts farthest from the viewer are rendered first.
item	Proportionally Fair	http://en.wikipedia.org/wiki/Proportionally_Fair	The Proportionally Fair algorithm is an algorithm that schedules the channel for the station that has the maximum of the priority function, where T denotes the data rate potentially achievable for the station at the present moment (in the present time slot), R is the average data rate of this station. The time and station indexes are omitted for convenience. Parameters α and β tune the fairness of the scheduler, that is, is it fair to all stations giving them equal bandwidth or is the scheduler maximizing the throughput of the channel.This article related to telecommunications is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Proportionally_Fair"			<a
item	Prosthaphaeresis	http://en.wikipedia.org/wiki/Prosthaphaeresis	Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximating products using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally-applicable way of approximating products quickly. Its name comes from the Greek prosthesis and aphaeresis, meaning addition and subtraction, two steps in the process.Contents1 History and motivation2 The identities3 The algorithm4 Decreasing the error5 Reverse identities6 Sources
item	Pseudo-LRU	http://en.wikipedia.org/wiki/Pseudo-LRU	Pseudo-LRU (also known as Tree-LRU) is an efficient algorithm to find an item that most likely has not been accessed very recently, given a set of items and a sequence of access events to the items. This technique is used in the cache of the Intel 486 and in the L1 cache of the Apple G4.
item	RANSAC	http://en.wikipedia.org/wiki/RANSAC	RANSAC is an abbreviation for "RANdom SAmple Consensus". It is an algorithm to estimate parameters of a mathematical model from a set of observed data which contains outliers. A basic assumption is that the data consists of "inliers", i. e., data points which can be explained by some set of model parameters, and "outliers" which are data points that do not fit the model. In addition to this, the data points can be subject to noise. The outliers can come, e. g., from extreme values of the noise or from erroneous measurements or incorrect hypotheses about the interpretation of data. RANSAC also assumes that, given a (usually small) set of inliers, there exists a procedure which can estimate the parameters of a model that optimally explains or fits this data. The algorithm was first published by Fischler and Bolles in 1981.
item	ROAM	http://en.wikipedia.org/wiki/ROAM	ROAM, or Real Time Optimally Adapting Mesh, is a continuous level of detail algorithm that optimizes terrain meshes. On modern computers, sometimes it is more effective to send a small amount of unneeded polygons to the GPU, rather than burden the CPU with LOD calculations -- making algorithms like geo mip mapping more effective than ROAM.[edit]
item	Rainflow-counting algorithm	http://en.wikipedia.org/wiki/Rainflow-counting_algorithm	The rainflow-counting algorithm (also known as the "rain-flow counting method") is used in the analysis of fatigue data in order to reduce a spectrum of varying stress into a set of simple stress reversals. Its importance is that it allows the application of Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The algorithm was developed by Tatsuo Endo and M. Matsuiski in 19681. Though there are a number of cycle-counting algorithms for such applications, the rainflow method is, as of 2004, the most popular.
item	Randomized algorithm	http://en.wikipedia.org/wiki/Randomized_algorithm	A randomized algorithm or probabilistic algorithm is an algorithm which employs a degree of randomness as part of its logic. In common practice, this means that the machine implementing the algorithm has access to a pseudo-random number generator. The algorithm typically uses the random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case". Formally, the algorithm's performance will be a random variable determined by the random bits, with (hopefully) good expected value; this expected value is called the expected runtime. The "worst case" is typically so unlikely to occur that it can be ignored.Contents1 Motivation2 Complexity3 Applications4 Derandomization5 Randomized Algorithms for Robustness6 References
item	Reconstruction algorithm	http://en.wikipedia.org/wiki/Reconstruction_algorithm	In tomography, a variety of practical reconstruction algorithms have been developed to implement the process of reconstruction of a 3-dimensional object from its projections. These algorithms are designed largely based on the mathematics of the radon transform, statistical knowledge of the data acquisition process and geometry of the data imaging system. In medical tomography, the filtered back projection algorithm and its variants are the most efficient algorithms currently in use.
item	Recursion	http://en.wikipedia.org/wiki/Recursion	In mathematics and computer science, recursion specifies (or constructs) a class of objects or methods (or an object from a certain class) by defining a few very simple base cases or methods (often just one), and then defining rules to break down complex cases into simpler cases.
item	Rete algorithm	http://en.wikipedia.org/wiki/Rete_algorithm	The Rete algorithm is an efficient pattern matching algorithm for implementing rule-based ("expert") systems. The Rete algorithm was designed by Dr. Charles L. Forgy of Carnegie Mellon University in 1979. Rete has become the basis for many popular expert systems, including JRules, OPS5, CLIPS, JESS, Drools, and LISA.
item	Ricart-Agrawala algorithm	http://en.wikipedia.org/wiki/Ricart-Agrawala_algorithm	The Ricart-Agrawala Algorithm is an algorithm for mutual exclusion on a distributed system. This algorithm is an extension and optimization of Lamport's Distributed Mutual Exclusion Algorithm, by removing the need for release messages.Contents1 Algorithm1.1 Terminology1.2 Algorithm1.3 Performance1.4 Common Optimizations2 See also
item	Richardson-Lucy deconvolution	http://en.wikipedia.org/wiki/Richardson-Lucy_deconvolution	The Richardson-Lucy algorithm, also known as Richardson-Lucy deconvolution, is an iterative procedure for recovering a latent image that has been blurred by a known point spread function.
item	Risch algorithm	http://en.wikipedia.org/wiki/Risch_algorithm	The Risch algorithm is an algorithm for the calculus operation of indefinite integration (i.e. finding antiderivatives). The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. Robert Risch, who developed the algorithm in 1968, called it a decision procedure, because it is a method for deciding if a function has a simple-looking function as an indefinite integral; and also, if it does, determining it. The Risch-Norman algorithm, a faster but less powerful technique, was developed in 1976.
item	Robinson-Schensted algorithm	http://en.wikipedia.org/wiki/Robinson-Schensted_algorithm	In mathematics, the Robinson–Schensted algorithm is a combinatorial algorithm, first discovered by Robinson in 1938, which establishes a bijective correspondence between elements of the symmetric group Sn and pairs of standard Young tableaux of the same shape. It can be viewed as a simple, constructive proof of the combinatorial identity:
item	Rsync	http://en.wikipedia.org/wiki/Rsync	The correct title of this article is rsync. The initial letter is capitalized due to technical restrictions.rsync is a computer program for Unix systems which synchronizes files and directories from one location to another while minimizing data transfer using delta encoding when appropriate. An important feature of rsync not found in most similar programs/protocols is that the mirroring takes place with only one transmission in each direction.rsync can copy or display directory contents and copy files, optionally using compression and recursion.rsync has the default TCP port of 873.Contents1 Algorithm2 Variations2.1 
item	Run-time algorithm specialisation	http://en.wikipedia.org/wiki/Run-time_algorithm_specialisation	In computer science, Run-time algorithm specialisation is a methodology for creating efficient algorithms for costly computation tasks of certain kinds. The methodology originates in the field of automated theorem proving and, more specifically, in the Vampire theorem prover project.
item	Scale-invariant feature transform	http://en.wikipedia.org/wiki/Scale-invariant_feature_transform	Scale-invariant feature transform (or SIFT) is a computer vision algorithm for extracting distinctive features from images, to be used in algorithms for tasks like matching different views of an object or scene (e.g. for stereo vision) and Object recognition. The features are invariant to image scale, rotation, and partially invariant (i.e. robust) to changing viewpoints, and change in illumination. The name Scale-invariant feature transform was chosen, as the algorithm transforms image data into scale-invariant coordinates relative to local features. However, there also exist other scale invariant image descriptors in the computer vision literature.
item	Schreier vector	http://en.wikipedia.org/wiki/Schreier_vector	In computational group theory, a Schreier vector is a tool for reducing the time and space complexity required to calculate transversal elements.[edit]
item	Schreier-Sims algorithm	http://en.wikipedia.org/wiki/Schreier-Sims_algorithm	The Schreier-Sims algorithm is an efficient method of computing a base and strong generating set (BSGS) of a permutation group. In particular, an SGS determines the order of a group and makes it easy to test membership in the group. Since the SGS is critical for many algorithms in computational group theory, computer algebra systems typically rely on the Schreier-Sims algorithm for efficient calculations in groups.
item	Schwartz-Zippel lemma and testing polynomial identities	http://en.wikipedia.org/wiki/Schwartz-Zippel_lemma_and_testing_polynomial_identities	Polynomial identity testing is the problem of determining whether a given multivariate polynomial is the 0-polynomial or identically equal to 0. The input to the problem is an n-variable polynomial over a field F. It can occur in the following forms:Algebraic form&#160;e.g. Is . To solve this, we can multiply it out and check that all the co-efficients are 0. However, this takes exponential time.Determinant of a matrix polynomial&#160;Let  be the determinant of the polynomial matrix.Read-once branching program&#160;also called binary decision diagrams.
item	Scoreboarding	http://en.wikipedia.org/wiki/Scoreboarding	Scoreboarding is a centralized method of dynamically scheduling a pipeline so that instructions can execute out of order when there are no conflicts and the hardware is available. In a scoreboard, the data dependencies of every instruction are logged. Instructions are released only when the scoreboard determines that there are no conflicts with previously issued and incomplete instructions. If an instruction is stalled because it is unsafe to continue, the scoreboard monitors the flow of executing instructions until all dependencies have been resolved before the stalled instruction is issued.
item	Selection algorithm	http://en.wikipedia.org/wiki/Selection_algorithm	In computer science, a selection algorithm is an algorithm for finding the kth smallest (or kth largest) number in a list. This includes the simple common cases of finding the minimum, maximum, and median elements. These are also called order statistics. Relatively simple algorithms for finding the minimum, maximum, and kth smallest element in average linear time exist. It is also possible to find the kth smallest element in worst-case linear time or multiple order statistics at once. Selection is a subproblem of many more complex problems like the nearest neighbor problem and shortest path problems.Contents1 Selection with sorting algorithm2 Linear minimum/maximum algorithms3 Nonlinear general selection algorithm4 Partition based general selection algorithm5 Linear general selection algorithm - "Median of Medians algorithm"<a href=
item	Semidefinite embedding	http://en.wikipedia.org/wiki/Semidefinite_embedding	Similar to locally linear embedding and Isomap, Semidefinite embedding (SDE) is an algorithm to perform non-linear dimensionality reduction.
item	Snapshot algorithm	http://en.wikipedia.org/wiki/Snapshot_algorithm	The snapshot algorithm is an algorithm used in distributed systems for recording a consistent global state of an asynchronous system. It is also known as "Chandy-Lamport Algorithm for the determination of consistent global states."Contents1 History2 Definition3 Working4 References
item	Soft output Viterbi algorithm	http://en.wikipedia.org/wiki/Soft_output_Viterbi_algorithm	The soft output Viterbi algorithm (SOVA) is a variant of the classical Viterbi algorithm.
item	Sort-merge join	http://en.wikipedia.org/wiki/Sort-merge_join	The Sort-Merge Join is an example of a join algorithm and is used in the implementation of a relational database management system.
item	Spigot algorithm	http://en.wikipedia.org/wiki/Spigot_algorithm	A spigot algorithm is an algorithm used to compute the value of a mathematical constant such as π or e. Unlike recursive algorithms, a spigot algorithm yields digits incrementally without using previously computed digits. The number of digits to be computed is specified in advance, and the algorithm may yield incorrect values for the last few digits.[edit]
item	Stable algorithm	http://en.wikipedia.org/wiki/Stable_algorithm	In computer science, a stable sorting algorithm is a sorting algorithm that preserves the order of records with equal keys.In numerical analysis, a numerically stable algorithm is an algorithm that is numerically stable.This is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Stable_algorithm"			Categories: Algorithms | Disambiguation																Views						 Article				 <a href="/w/in
item	Strassen algorithm	http://en.wikipedia.org/wiki/Strassen_algorithm	In the mathematical discipline of linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm used for matrix multiplication. It is asymptotically faster than the standard matrix multiplication algorithm, but slower than the fastest known algorithm.Contents1 History2 Algorithm3 Numerical analysis4 External links5 References
item	Subquadratic time	http://en.wikipedia.org/wiki/Subquadratic_time	An algorithm is said to run in subquadratic time if its running time f(n) is o(n2)
item	Swap by addition and subtraction	http://en.wikipedia.org/wiki/Swap_by_addition_and_subtraction	Standard swapping algorithms require the use of a temporary storage area - standard intuitive algorithms to swap x and y involve:copying&#160;&#160;y aside to a temporary storage areasetting&#160;&#160;y to be xcopying the temporary storage value back to x.
item	Synchronizer %28algorithm%29	http://en.wikipedia.org/wiki/Synchronizer_%28algorithm%29	In computer science, a synchronizer is an algorithm that can be used to run a synchronous algorithm on top of an asynchronous processor network, so enabling the asynchronous system to run as a synchronous network.
item	Temporally-ordered routing algorithm	http://en.wikipedia.org/wiki/Temporally-ordered_routing_algorithm	The Temporally-Ordered Routing Algorithm (TORA) is an algorithm for routing data across Wireless Mesh Networks or Mobile ad-hoc networks.
item	Timeline of algorithms	http://en.wikipedia.org/wiki/Timeline_of_algorithms	The following timeline outlines the development of algorithms since their inception.Contents1 Before 19402 1940s3 1950s4 1960s5 1970s6 1980s7 1990s8 2000s
item	Todd-Coxeter algorithm	http://en.wikipedia.org/wiki/Todd-Coxeter_algorithm	The Todd-Coxeter algorithm, discovered by Todd and Coxeter in 1936, is a procedure that can solve the coset enumeration problem. Given a group presentation , where X is a set of generators and R is a set of relations, and a subgroup , we wish to compute the action of H on G. The Todd-Coxeter algorithm is guaranteed to succeed in a finite number of steps provided | G:H | is finite, although the running time is unpredictable. Specifically, no recursive function of | G:H | and the input can bound the running time.
item	Token bucket	http://en.wikipedia.org/wiki/Token_bucket	Although the token bucket algorithm has several uses, it is best understood in the context of network traffic shaping or rate limiting. Typically, the algorithm is used to control the amount of data that is injected into a network, allowing for "bursts" of data to be sent.
item	Tomasulo algorithm	http://en.wikipedia.org/wiki/Tomasulo_algorithm	The Tomasulo algorithm is an algorithm developed by Robert Tomasulo from IBM to execute instructions out of order. This algorithm differs from scoreboarding because scoreboarding does not have register renaming. Instead, scoreboarding resolves Write-after-Write (WAW) and Write-after-Read (WAR) hazards by stalling, whereas the Tomasulo algorithm can still issue instructions. Also, the Tomasulo algorithm uses a common data bus on which computed values are broadcast to all reservation stations that may need it. This allows for improved parallel execution of instructions, that may have been stalled in scoreboarding.
item	Trabb Pardo-Knuth algorithm	http://en.wikipedia.org/wiki/Trabb_Pardo-Knuth_algorithm	The Trabb Pardo-Knuth algorithm is a program introduced by Donald Knuth and Luis Trabb Pardo to illustrate the evolution of computer programming languages.
item	Trim %28programming%29	http://en.wikipedia.org/wiki/Trim_%28programming%29	In programming, trim or strip is a string manipulation function or algorithm which removes leading and trailing whitespace from a string.
item	Truncated binary exponential backoff	http://en.wikipedia.org/wiki/Truncated_binary_exponential_backoff	In a variety of computer networks, binary exponential backoff or truncated binary exponential backoff refers to an algorithm used to space out repeated retransmissions of the same block of data.
item	Ukkonen%27s algorithm	http://en.wikipedia.org/wiki/Ukkonen%27s_algorithm	In 1995, Esko Ukkonen proposed a linear-time, online algorithm for constructing suffix trees that has come to be known as Ukkonen's algorithm.
item	VEGAS algorithm	http://en.wikipedia.org/wiki/VEGAS_algorithm	The VEGAS algorithm, due to G. P. Lepage, is a method for reducing error in the Monte Carlo simulation by using a known or approximate probability distribution function to concentrate the search in those areas of the graph that make the greatest contribution to the final integral.
item	Vector clocks	http://en.wikipedia.org/wiki/Vector_clocks	Vector Clocks is an algorithm for generating a total ordering of events in a distributed system. Just as in Lamport timestamps, interprocess messages contain the state of the sending processes logical clock. Vector clock of a system of N processes is an array of N logical clocks, one per process, a local copy of which is kept in each process with the following rules for clock updates:Example of a system of vector clocksinitially all clocks are zeroeach time a process experiences an internal event, it increments its own logical clock in the vector by oneeach time a process prepares to send a message, it increments its own logical clock in the vector by one and then sends its entire vector along with the message being senteach time a process receives a message, it increments its own logical clock in the vector by one and updates each element in i
item	Viterbi algorithm	http://en.wikipedia.org/wiki/Viterbi_algorithm	The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states – called the Viterbi path – that result in a sequence of observed events, especially in the context of hidden Markov models. The forward algorithm is a closely related algorithm for computing the probability of a sequence of observed events. These algorithms form a subset of information theory.
item	XOR swap algorithm	http://en.wikipedia.org/wiki/XOR_swap_algorithm	In computer programming, the XOR swap is an algorithm which uses the exclusive disjunction (XOR) operation to swap distinct values of variables having the same data type without using a temporary variable. This algorithm works using the symmetric difference property of XOR: (A XOR B) XOR B = A, for every pair (A, B). The XOR swap has few advantages on modern computers—in fact, it may even be slower than performing the swap using a temporary variable.Contents1 The algorithm2 Explanation3 Code examples3.1 Pascal3.2 C4 Reasons for use in practice5 Reasons for avoidance in practice6 <span class=
item	Yao%27s Principle	http://en.wikipedia.org/wiki/Yao%27s_Principle	Andrew Yao proposed that to establish a lower bound on the expected worst-case cost of a randomized algorithm, evaluate the minimum cost of a deterministic algorithm on a probability distribution over the problem instances.&#160;This computer science-related article is a stub. You can help Wikipedia by expanding it.[edit]
item	Zeller%27s congruence	http://en.wikipedia.org/wiki/Zeller%27s_congruence	Zeller's congruence is an algorithm devised by Julius Christian Johannes Zeller to calculate the day of the week for any calendar date.Contents1 Formula2 Analysis3 Algorithm4 See also5 External links6 References
item	Real number	http://en.wikipedia.org/wiki/Real_number	In mathematics, the real numbers may be described informally in several different ways. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of 2; a real number can be given by an infinite decimal representation, such as 2.4871773339...., where the digits continue in some way; the real numbers may be thought of as points on an infinitely long number line.
item	Complex number	http://en.wikipedia.org/wiki/Complex_number	In mathematics, a complex number is a number of the form
item	Function %28mathematics%29	http://en.wikipedia.org/wiki/Function_%28mathematics%29	In mathematics, a function relates each of its inputs to exactly one output. A standard notation for the output of the function f with the input x is f(x). The set of all inputs which a function accepts is called the domain of the function. The set of all outputs is called the range.
item	Continuous function	http://en.wikipedia.org/wiki/Continuous_function	In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be discontinuous.
item	Integration	http://en.wikipedia.org/wiki/Integration	Integration is a process of combining or accumulating.
item	Derivative	http://en.wikipedia.org/wiki/Derivative	In mathematics, the derivative is defined as the instantaneous rate of change of a function. The derivative is one of the two central concepts of calculus. (The other is the integral; the two are related via the fundamental theorem of calculus.)The simplest type of derivative is the derivative of a real-valued function of a single real variable. It has several interpretations:The derivative gives the slope of the tangent to the graph of the function at a point. In this way, derivatives can be used to determine many geometrical properties of the graph, such as concavity or convexity.The derivative provides a mathematical formulation of rate of change; it measures the rate at which the function's value changes as the function's argument changes.This derivative is the kind usually encountered in a first course on calculus, and historically was the first to be discovered. However, there are also many generalizations of the derivative.The remainder of this article discusses only the simplest case (real-valued functions of real numbers).
item	Mathematical analysis	http://en.wikipedia.org/wiki/Mathematical_analysis	Analysis is a branch of mathematics that depends upon the concepts of limits and convergence. It studies closely related topics such as continuity, integration, differentiability and transcendental functions. These topics are often studied in the context of real numbers, complex numbers, and their functions. However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or more specifically "distance" (a metric space). Mathematical analysis has its beginnings in the rigorous formulation of calculus.[edit]
item	3-sphere	http://en.wikipedia.org/wiki/3-sphere	In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. An ordinary sphere, or 2-sphere, consists of all points equidistant from a single point in ordinary 3-dimensional Euclidean space, R3. A 3-sphere consists of all points equidistant from a single point in R4. Whereas a 2-sphere is a smooth 2-dimensional surface, a 3-sphere is an object with three dimensions, also known as 3-manifold.
item	Abel%27s theorem	http://en.wikipedia.org/wiki/Abel%27s_theorem	In real analysis, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel.
item	Abelian and tauberian theorems	http://en.wikipedia.org/wiki/Abelian_and_tauberian_theorems	In mathematics, a large number of methods have been proposed for the summation of divergent series. These generally take the form of some linear functional L with domain contained in some space S of numerical sequences. That is, firstly, a useful method for attributing a sum to a series that doesn't converge should at least be linear. Secondly, the sequence of partial sums of the series is considered, which is an equivalent way of presenting it.
item	Absolute convergence	http://en.wikipedia.org/wiki/Absolute_convergence	In mathematics, a series (or integral) is said to converge absolutely if the sum or integral of the absolute value of the summand or integrand is finite. The property of absolute convergence is important because it is generally required in order for rearrangements and products of sums to work in an intuitive fashion.
item	Advection equation	http://en.wikipedia.org/wiki/Advection_equation	The advection equation is the partial differential equation that governs the motion of a conserved scalar as it is advected by a known velocity field. It is derived using the scalar's conservation law, together with Gauss's theorem, and taking the infinitesimal limit.
item	Almost convergent sequence	http://en.wikipedia.org/wiki/Almost_convergent_sequence	A bounded real sequence (xn) is said to be almost convergent to L if each Banach limit assigns the same value L to the sequence (xn).
item	Almost periodic function	http://en.wikipedia.org/wiki/Almost_periodic_function	In mathematics, almost periodicity is a property of dynamical systems that appear to retrace their paths through phase space, but not exactly. An example would be a planetary system, with planets in orbits moving with periods that are not commensurable (i.e., with a period vector that is not proportional to a vector of integers). A theorem of Kronecker from diophantine approximation can be used to show that any particular configuration that occurs once, will recur to within any specified accuracy: if we wait long enough we can observe the planets all return to within a second of arc to the positions they once were in.Contents1 Definition and properties2 Quasiperiodic signals in audio and music synthesis3 See also4 External links5 Reference
item	Analytic function	http://en.wikipedia.org/wiki/Analytic_function	In mathematics, an analytic function is a function that is locally given by a convergent power series. Analytic functions can be thought of as a bridge between polynomials and general functions. There exist real analytic functions and complex analytic functions, which have similarities as well as differences.Contents1 Definitions2 Examples3 Properties of analytic functions4 Analyticity and differentiability5 Real versus complex analytic functions6 Analytic functions of several variables
item	Asymptote	http://en.wikipedia.org/wiki/Asymptote	An asymptote is a straight or curved line which a curve approaches as one moves along the curve. As one moves along the curve, the space between the curve and the asymptote tends to become smaller and smaller, and can be made as small as one could wish by going far enough along the curve.
item	Asymptotic distribution	http://en.wikipedia.org/wiki/Asymptotic_distribution	In mathematics and statistics, an asymptotic distribution is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. A distribution is an ordered set of random variablesZi
item	Asymptotic expansion	http://en.wikipedia.org/wiki/Asymptotic_expansion	In mathematics an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point.
item	Baire function	http://en.wikipedia.org/wiki/Baire_function	Baire functions refer to certain sets of functions which are studied in real analysis.
item	Banach fixed point theorem	http://en.wikipedia.org/wiki/Banach_fixed_point_theorem	The Banach fixed point theorem is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps of metric spaces, and provides a constructive method to find those fixed points. The theorem is named after Stefan Banach (1892-1945), and was first stated by Banach in 1922.Contents1 The theorem2 Proof3 Applications4 Converses5 Generalizations6 References
item	Big O notation	http://en.wikipedia.org/wiki/Big_O_notation	Big O notation is a mathematical notation used to describe the asymptotic behavior of functions. Its purpose is to characterize a function's behavior for large inputs in a simple but rigorous way that enables comparison to other functions. More precisely, it is used to describe an asymptotic upper bound for the magnitude of a function in terms of another, usually simpler, function. It has two main areas of application: in mathematics, it is usually used to characterize the residual term of a truncated infinite series, especially an asymptotic series, and in computer science, it is useful in the analysis of the complexity of algorithms.
item	Borel summation	http://en.wikipedia.org/wiki/Borel_summation	In mathematics, a Borel summation is a generalisation of the usual notion of summation of a series. In particular it gives a definition of a quantity that in many ways behaves formally like the sum, even if the series is in fact divergent.[edit]
item	Bounded function	http://en.wikipedia.org/wiki/Bounded_function	In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded. In other words, there exists a number M&gt;0 such that
item	Bounded mean oscillation	http://en.wikipedia.org/wiki/Bounded_mean_oscillation	The space of functions of Bounded Mean Oscillation (BMO) plays an important role in Harmonic analysis.
item	Bounded set	http://en.wikipedia.org/wiki/Bounded_set	In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely a set which is not bounded is called unbounded.Contents1 Definition2 Metric space3 Boundedness in topological vector spaces4 Boundedness in order theory5 See also
item	Bounded variation	http://en.wikipedia.org/wiki/Bounded_variation	In mathematics, given f, a real-valued function on the interval [a, b] on the real line, the total variation of f on that interval is
item	Calculus of variations	http://en.wikipedia.org/wiki/Calculus_of_variations	Calculus of variations is a field of mathematics that deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions: those making the functional attain a maximum or minimum value. Perhaps the simplest example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is obviously a straight line, but if the curve is constrained to lie on a surface in space, then it is less obvious. The solutions of the latter problem are called geodesics. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, where the optical length depends upon the material of the medium. A corresponding idea in mechanics is the principle of stationary action. The theory of optimal control concerns a specific kind of problem in the calculus of variations.
item	Cauchy index	http://en.wikipedia.org/wiki/Cauchy_index	In mathematical analysis, the Cauchy index is an integer associated to a real rational function over an interval. By the Routh-Hurwitz theorem, we have the following interpretation: the Cauchy index ofr(x)=p(x)/q(x)
item	Cauchy principal value	http://en.wikipedia.org/wiki/Cauchy_principal_value	In mathematics, the Cauchy principal value of certain improper integrals is defined as eitherthe finite numberwhere b is a point at which the behavior of the function f is such thatfor any a &lt; b andfor any c &gt; b (one sign is "+" and the other is "−").
item	Cauchy sequence	http://en.wikipedia.org/wiki/Cauchy_sequence	In mathematics, a Cauchy sequence, named after Augustin Cauchy, is a sequence whose elements become close as the sequence progresses. To be more precise, by dropping a finite number of elements from the start of the sequence we can make the maximum distance between two remaining elements arbitrarily small.
item	Ces%C3%A0ro summation	http://en.wikipedia.org/wiki/Ces%C3%A0ro_summation	In mathematical analysis, Cesàro summation is an alternative means of assigning a sum to an infinite series. If the series converges in the usual sense to a sum α, then the series is also Cesàro summable and has Cesàro sum α. The significance of Cesàro summation is that a series which diverges may still have a well-defined Cesàro sum.
item	Characterizations of the exponential function	http://en.wikipedia.org/wiki/Characterizations_of_the_exponential_function	In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other. As a special case of these considerations, we will see that the three most common definitions given for the mathematical constant e are also equivalent to each other.Contents1 Characterizations2 Why each characterization makes sense2.1 Characterization 12.2 Characterization 22.3 Characterization 33 Equivalence of the characterizations3.1 Equivalence of characterizations 1 and 2
item	Chisini mean	http://en.wikipedia.org/wiki/Chisini_mean	In mathematics, a function f of n variablesx1, ..., xn
item	Classification of discontinuities	http://en.wikipedia.org/wiki/Classification_of_discontinuities	Continuous functions are of utmost importance in mathematics and applications. However, not all functions are continuous, or a function might not be continuous everywhere. If a function is not continuous at a point, one says that it has a discontinuity there. This article describes the classification of discontinuities in the simplest case of a function of a single real variable.
item	Coincidence point	http://en.wikipedia.org/wiki/Coincidence_point	In mathematics, a coincidence point (or simply coincidence) of two mappings is a point in their domain having the same image point under both mappings.
item	Complex analysis	http://en.wikipedia.org/wiki/Complex_analysis	Complex analysis is the branch of mathematics investigating functions of complex numbers, and is of enormous practical use in many branches of mathematics, including applied mathematics.
item	Concave function	http://en.wikipedia.org/wiki/Concave_function	In calculus, a differentiable function f is convex on an interval if its derivative function f ′ is increasing on that interval: a convex function has an increasing slope. Similarly, a differentiable function f is concave on an interval if its derivative function f ′ is decreasing on that interval: a concave function has a decreasing slope.
item	Constructivist analysis	http://en.wikipedia.org/wiki/Constructivist_analysis	In mathematics, constructive analysis is mathematical analysis done according to the principles of constructivist mathematics. This contrasts with classical analysis, which (in this context) simply means analysis done according to the (ordinary) principles of classical mathematics.
item	Continued fraction	http://en.wikipedia.org/wiki/Continued_fraction	In mathematics, a continued fraction is an expression such as
item	Convex analysis	http://en.wikipedia.org/wiki/Convex_analysis	Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex optimization, a subdomain of optimization theory.[edit]
item	Convex combination	http://en.wikipedia.org/wiki/Convex_combination	A convex combination is a linear combination of data points (which can be vectors or scalars) where all coefficients are non-negative and sum up to 1. It is called "convex combination", since all possible convex combinations (given the base vectors) will be within the convex hull of the given datapoints. In fact, the set of all convex combinations constitutes the convex hull.
item	Convex function	http://en.wikipedia.org/wiki/Convex_function	In mathematics, convex function is a real-valued function f defined on an interval (or on any convex subset C of some vector space), if for any two points x and y in its domain C and any t in [0,1], we haveConvex function on an interval.
item	Convex set	http://en.wikipedia.org/wiki/Convex_set	In Euclidean space, an object is convex if for any pair of points within the object, any point on the straight line segment that joins them is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it is not convex.Contents1 Convex sets1.1 Properties of convex sets2 Star-convex sets3 Non-Euclidean geometry4 Generalized convexity4.1 Orthogonal convexity5 Abstract (axiomatic) convexity6 See also7 References
item	Credence %28probability theory%29	http://en.wikipedia.org/wiki/Credence_%28probability_theory%29	In probability theory, credence is a subjectively assessed probability.[edit]
item	Darboux function	http://en.wikipedia.org/wiki/Darboux_function	In mathematics, a Darboux function, named for Gaston Darboux (1842-1917), is a real-valued function f which has the "intermediate value property": on the interval between a and b, f assumes every real value between f(a) and f(b). Formally, for all real numbers a and b, and for every z such that f(a) &lt; z &lt; f(b), there exists some x with a &lt; x &lt; b such that f(x) = z.
item	Difference operator	http://en.wikipedia.org/wiki/Difference_operator	In mathematics, a difference operator maps a function, f(x), to another function, f(x + a) − f(x + b).
item	Differentiability class	http://en.wikipedia.org/wiki/Differentiability_class	A differentiability class in mathematics is a class of functions which share differentiability features. The class C0 comprises of all continuous functions. Furthermore the class Ck comprises all functions whose derivative belongs to Ck − 1. The class C∞ includes those functions which have derivatives of all orders (the smooth functions), while Cω contains those functions which have convergent Taylor series (the analytic functions).
item	Dini test	http://en.wikipedia.org/wiki/Dini_test	In mathematics, the Dini and Dini-Lipschitz tests are highly precise tests that can be used to prove that the Fourier series of a function converges at a given point. These tests are named after Ulisse Dini and Rudolf Lipschitz.Contents1 Definition2 Precision3 See also4 References
item	Dirac delta function	http://en.wikipedia.org/wiki/Dirac_delta_function	The Dirac delta function, often referred to as the unit impulse function and introduced by the British theoretical physicist Paul Dirac, can usually be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere. The integral from minus infinity to plus infinity is 1. The discrete analog of the delta "function" is the degenerate distribution which is sometimes known as a delta function. Note that the Dirac delta is not a function, but a distribution that is also a measure.Contents1 Overview2 Definitions2.1 The delta function as a measure2.2 The delta function as a probability density function<a href="#Delta_function_of_more_compli
item	Dirichlet kernel	http://en.wikipedia.org/wiki/Dirichlet_kernel	In mathematical analysis, the Dirichlet kernel is the collection of functions
item	Dirichlet principle	http://en.wikipedia.org/wiki/Dirichlet_principle	In mathematics, Dirichlet's principle in potential theory states that the harmonic function u on a domain Ω with boundary conditionu = g on 
item	Divergent series	http://en.wikipedia.org/wiki/Divergent_series	In mathematics, a divergent series is an infinite series that does not converge. That is, divergent series and convergent series are antonyms.
item	Engel expansion	http://en.wikipedia.org/wiki/Engel_expansion	//[edit]DefinitionThe Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers {a1,a2,a3,...} such that:Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion.[edit]Algorithm for computing Engel expansionsTo find the Engel expansion of x, letu1 = x,, anduk + 1 = ukak − 1
item	Equicontinuity	http://en.wikipedia.org/wiki/Equicontinuity	In mathematical analysis, a sequence of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood (a precise definition appears below).
item	Exhaustion by compact sets	http://en.wikipedia.org/wiki/Exhaustion_by_compact_sets	In mathematics, especially analysis, exhaustion by compact sets of an open set E in the Euclidean space Rn (or a manifold with countable base) is an increasing sequence of compact sets Kj, where by increasing we mean Kj is a subset of Kj + 1, with the limit (union) of the sequence being E.
item	Extended real number line	http://en.wikipedia.org/wiki/Extended_real_number_line	In mathematics, the extended real number line is obtained from the real number line R by adding two elements: +∞ and −∞. These new elements are not real numbers (note that this is not a judgment about their "reality" or lack of it; rather, "real number" has a technical meaning that ∞ and −∞ do not satisfy). It is useful in describing various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The extended real number line is denoted R or [−∞, +∞].
item	Finite difference	http://en.wikipedia.org/wiki/Finite_difference	In mathematics, a finite difference is like a differential quotient, except that it uses finite quantities instead of infinitesimal ones.
item	Fractional calculus	http://en.wikipedia.org/wiki/Fractional_calculus	In mathematics, fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers of the differential operator
item	Fr%C3%B6licher space	http://en.wikipedia.org/wiki/Fr%C3%B6licher_space	In mathematics, Frölicher spaces extend the notions of calculus and smooth manifolds. They were introduced in 1982 by the mathematician Alfred Frölicher.[edit]
item	Function of a real variable	http://en.wikipedia.org/wiki/Function_of_a_real_variable	In mathematics, a function of a real variable is a mathematical function whose domain is the real line. More loosely, a function of a real variable is sometimes taken to mean any function whose domain is a subset of the real line.
item	Functional equation	http://en.wikipedia.org/wiki/Functional_equation	In mathematics or its applications, a functional equation is an equation expressed in terms of both independent variables and unknown functions, which are to be solved for. Properties of functions can for instance be determined by considering the types of functional equations they satisfy. The term functional equation is usually reserved for equations that are not in a simple sense reducible to algebraic equations, often because two or more known functions are substituted as arguments into an unknown function, which is to be solved for.Contents1 Examples2 Solving functional equations3 See also4 External links
item	Fundamental lemma of calculus of variations	http://en.wikipedia.org/wiki/Fundamental_lemma_of_calculus_of_variations	The fundamental lemma of the calculus of variations states that if f is a smooth function over the interval [a,b], and
item	Generalized function	http://en.wikipedia.org/wiki/Generalized_function	In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognised theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going to extremes) describing physical phenomena such as point charges. They are applied extensively, especially in physics and engineering.
item	Geometric continuity	http://en.wikipedia.org/wiki/Geometric_continuity	Geometrical or geometric continuity, was a concept of geometry primarily applied to the conic sections and related shapes by mathematicians such as Leibnitz, Kepler, and Poncelet. The concept was an early attempt at describing, through geometry rather than algebra, the concept of continuity as expressed through a parametric function.
item	Geometric function theory	http://en.wikipedia.org/wiki/Geometric_function_theory	Geometric function theory is the study of geometric properties of analytic functions.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Geometric_function_theory"			Categories: Mathematics stubs | Mathematical analysis | Complex analysis</a
item	Gradient conjecture	http://en.wikipedia.org/wiki/Gradient_conjecture	In mathematics, the gradient conjecture, due to René Thom, was proved in 2000 by K. Kurdyka, T. Mostowski and A. Parusinski. It states that given an analytic function f in Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, there exists a limit (in the projective space PRn) for the secants of x(t) near x0.[edit]
item	Grunwald-Letnikov differintegral	http://en.wikipedia.org/wiki/Grunwald-Letnikov_differintegral	In mathematics, the combined differentiation/integration operator used in fractional calculus is called the differintegral. It takes a few different forms, depending on context. The Grunwald-Letnikov differintegral has one of the simplest definitions, and is a commonly used form of the differintegral. It was introduced by Anton Karl Grünwald (1838-1920) from Prague, in 1867, and by Aleksey Vasilievich Letnikov (1837-1888) in Moscow in 1868.
item	Haar measure	http://en.wikipedia.org/wiki/Haar_measure	In mathematical analysis, the Haar measure is a way to assign an "invariant volume" to subsets of locally compact topological groups and subsequently define an integral for functions on those groups.
item	Half iterate	http://en.wikipedia.org/wiki/Half_iterate	The half iterate of a function f (denoted by f1/2) is any function which satisfies the following:f1/2(f1/2(x)) = f(x)
item	Harmonic analysis	http://en.wikipedia.org/wiki/Harmonic_analysis	Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms. The basic waves are called "harmonics", hence the name "harmonic analysis." In the past two centuries, it has become a vast subject with applications in areas as diverse as signal processing, quantum mechanics, and neuroscience.
item	Hemicontinuity	http://en.wikipedia.org/wiki/Hemicontinuity	In mathematics, the concept of continuity as it is defined for single-valued functions is not immediately extendible to multi-valued mappings or correspondences. In order to derive a more generalized definition, the dual concepts of upper hemicontinuity and lower hemicontinuity are introduced.Contents1 Upper hemicontinuity2 Lower hemicontinuity3 Implications for continuity4 See also
item	Hyperbolic growth	http://en.wikipedia.org/wiki/Hyperbolic_growth	When a quantity grows towards a singularity under a finite variation it is said to undergo hyperbolic growth. Hyperbolic growth is highly nonlinear and it is a stronger form of growth than exponential growth.
item	Hyperfunction	http://en.wikipedia.org/wiki/Hyperfunction	In mathematics, hyperfunctions are sums of boundary values of holomorphic functions, and can be thought of informally as distributions of infinite order.Contents1 Motivation2 Formal definition3 Examples4 Further reading
item	Improper integral	http://en.wikipedia.org/wiki/Improper_integral	It is recommended that the reader be familiar with antiderivatives, integrals, and limits.In calculus, an improper integral is the limit of a definite integral, as an endpoint of the interval of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits.If the function f being integrated from a to c has a discontinuity at c, especially in the form of a vertical asymptote, or if c&#160;=&#160;∞, then there may be no more convenient way to compute the integralthan by finding the limitIn some cases, the integral from a to c is not even defined, because the integrals of the positive and negative parts of f(x)&#160;dx from a to c are both infinite, but nonetheless the limit may exist. Such cases are "properly improper" integrals, i.e. their values cannot be defined except as such limits.The integralcan be interp
item	Indeterminate form	http://en.wikipedia.org/wiki/Indeterminate_form	In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression whose limit cannot be evaluated by substituting the limits of the subexpressions.Contents1 Discussion2 Some examples and nonexamples3 Evaluating indeterminate forms4 List of indeterminate forms
item	Infinite product	http://en.wikipedia.org/wiki/Infinite_product	In mathematics, for a sequence of numbers a1, a2, a3, ... the infinite product
item	Integral transform	http://en.wikipedia.org/wiki/Integral_transform	In mathematics, an integral transform is any transform T of the following form:
item	Isoperimetric dimension	http://en.wikipedia.org/wiki/Isoperimetric_dimension	In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large scale behavior of the manifold resembles that of a Euclidean space (unlike the topological dimension or the Hausdorff dimension which compare different local behaviors against those of the Euclidean space).
item	Jensen%27s inequality	http://en.wikipedia.org/wiki/Jensen%27s_inequality	In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.Contents1 Finite form2 General statement2.1 In general measure-theoretic notation2.2 In probability-theory notation3 Proof4 Applications and special cases4.1 Form involving a probability density function4.2 Alternative finite form4.3 Statistical physics<span class="to
item	Kantorovich inequality	http://en.wikipedia.org/wiki/Kantorovich_inequality	In mathematics, the Kantorovich inequality is a particular case of the Cauchy-Schwarz inequality, which is itself a generalization of the triangle inequality.
item	Kontorovich-Lebedev transform	http://en.wikipedia.org/wiki/Kontorovich-Lebedev_transform	In mathematics, the Kontorovich-Lebedev transform is an integral transform which uses a Macdonald function (modified Bessel function of the second kind) with imaginary index as its kernel. Unlike other Bessel function transforms, such as the Hankel transform, this transform involves integrating over the index of the function rather than its argument.
item	Lebesgue point	http://en.wikipedia.org/wiki/Lebesgue_point	In mathematics, given a Lebesgue integrable function f, a point x in the domain of f is a Lebesgue point if
item	Limit of a sequence	http://en.wikipedia.org/wiki/Limit_of_a_sequence	The limit of a sequence is one of the oldest concepts in mathematical analysis. It provides a rigorous definition of the idea of a sequence converging towards a point called the limit.
item	Limit superior and limit inferior	http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior	In mathematics, the limit inferior and limit superior (also called infimum limit and supremum limit, or liminf and limsup) of a sequence can be thought of as limiting bounds on the sequence. (See limit of a function.)
item	Lipschitz continuity	http://en.wikipedia.org/wiki/Lipschitz_continuity	In mathematics, a functionf&#160;: D → R
item	Local boundedness	http://en.wikipedia.org/wiki/Local_boundedness	In mathematics, a function is locally bounded, if it is bounded around every point. A family of functions is locally bounded, if for any point in their domain all the functions are bounded around that point and by the same number.Contents1 Locally bounded function2 Examples3 Locally bounded family4 Examples5 Topological vector spaces5.1 Locally bounded topological vector spaces5.2 Locally bounded functions6 External links
item	Logarithmic integral	http://en.wikipedia.org/wiki/Logarithmic_integral	In mathematics, the logarithmic integral can refer toThe logarithmic integral function, defined asThe offset logarithmic integral, defined asThe logarithmic integral defined as
item	Mathematical singularity	http://en.wikipedia.org/wiki/Mathematical_singularity	In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. See singularity theory for general discussion of the geometric theory, which only covers some aspects.
item	Maxima and minima	http://en.wikipedia.org/wiki/Maxima_and_minima	In mathematics, maxima and minima, also known as extrema, are points in the domain of a function at which the function takes the largest (maximum), or smallest (minimum) value either within a given neighbourhood (local extrema), or on the function domain in its entirety (global extrema).Contents1 Definitions2 Finding maxima and minima3 Examples4 Functions of more variables5 See also
item	Mercator series	http://en.wikipedia.org/wiki/Mercator_series	In mathematics, the Mercator series or Newton-Mercator series is the Taylor series for the natural logarithm. It is given by
item	Mimetic	http://en.wikipedia.org/wiki/Mimetic	The goal of numerical analysis is to approximate the continuum, so instead of solving a partial differential equation one aims in solve a discrete version of the continuum problem. A numerical method is called mimetic when it mimics (or imitates) some properties of the continuum vector calculus.
item	Modulus of continuity	http://en.wikipedia.org/wiki/Modulus_of_continuity	In mathematics, the modulus of continuity is a precise way to measure the smoothness of a function. It is used as a delicate tool in mathematical analysis, to discuss highly non-smooth functions, which nonetheless enjoy some (very generalized) kind of smoothness. Similar but less refined notions such as Lipschitz continuity and Hölder class are subsumed by the explicit use of the modulus of continuity.
item	Moment %28mathematics%29	http://en.wikipedia.org/wiki/Moment_%28mathematics%29	The concept of moment in mathematics evolved from the concept of moment in physics. The nth moment of a real-valued function f(x) of a real variable about a value c is
item	Moment problem	http://en.wikipedia.org/wiki/Moment_problem	In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequences of moments
item	Monodromy	http://en.wikipedia.org/wiki/Monodromy	In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology and differential geometry behave as they 'run round' a singularity. As the name implies, monodromy's fundamental meaning comes from 'running round singly'. It is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions we may wish to define fail to be single-valued as we 'run round' a path encircling a singularity. The failure of monodromy is best measured by defining a monodromy group: a group of transformations acting on the data that codes what does happen as we 'run round'.Contents1 Definition2 Example3 Differential equations in the complex domain4 Topological and geometric aspects</a
item	Mountain pass theorem	http://en.wikipedia.org/wiki/Mountain_pass_theorem	The mountain pass theorem is an existence theorem from the calculus of variations.
item	Multiplicity	http://en.wikipedia.org/wiki/Multiplicity	In mathematics, the multiplicity of a member of a multiset is how many memberships in the multiset it has. For example, the term is used to refer to the value of the totient valence function, or the number of times a given polynomial equation has a root at a given point.
item	Negligible set	http://en.wikipedia.org/wiki/Negligible_set	In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose. As common examples, finite sets can be ignored when studying the limit of a sequence, and null sets can be ignored when studying the integral of a measurable function.
item	Neighbourhood %28mathematics%29	http://en.wikipedia.org/wiki/Neighbourhood_%28mathematics%29	In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containing the point where you can "wiggle" or "move" the point a bit without leaving the set.
item	Non-analytic smooth function	http://en.wikipedia.org/wiki/Non-analytic_smooth_function	In mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument is smooth. The converse is not true, with this article constructing a counterexample.Contents1 The function2 How it is ill-behaved2.1 f is smooth on R2.2 f is not analytic3 How this is a good thing...3.1 ...in negative terms3.2 ...in positive terms4 Exter
item	Non-classical analysis	http://en.wikipedia.org/wiki/Non-classical_analysis	In mathematics, non-classical analysis is any system of analysis, other than classical real analysis, and complex, vector, tensor, etc., analysis based upon it.
item	Normed vector space	http://en.wikipedia.org/wiki/Normed_vector_space	In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space Rn. It turns out that the following properties of "vector length" are the crucial ones.The zero vector, 0, has zero length; every other vector has a positive length.Multiplying a vector by a positive number has the same effect on the length.The triangle inequality holds. That is, taking norms as distances, the distance from A through B to C is never shorter than going directly from A to C, or the shortest distance between any two points is a straight line.
item	P-adic analysis	http://en.wikipedia.org/wiki/P-adic_analysis	In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.
item	Paley%E2%80%93Wiener theorem	http://en.wikipedia.org/wiki/Paley%E2%80%93Wiener_theorem	In mathematics the Paley–Wiener theorem relates growth properties of entire functions on Cn and Fourier transformation of Schwartz distributions of compact support.
item	Pappus%27s centroid theorem	http://en.wikipedia.org/wiki/Pappus%27s_centroid_theorem	Pappus's centroid theorem (also known as the Guldinus theorem, Pappus-Guldinus theorem or Pappu's theorem) is the name of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.
item	Paraconsistent analysis	http://en.wikipedia.org/wiki/Paraconsistent_analysis	Paraconsistent analysis is a branch of paraconsistent mathematics, that attempts to rework mathematical analysis on a paraconsistent framework.
item	Partition of an interval	http://en.wikipedia.org/wiki/Partition_of_an_interval	In mathematics, a partition of an interval [a, b] on the real line is a finite sequence of the forma = x0 &lt; x1 &lt; x2 &lt; ... &lt; xn = b.
item	Picard%E2%80%93Lindel%C3%B6f theorem	http://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem	In mathematics, the Picard–Lindelöf theorem or Picard's existence theorem on existence and uniqueness of solutions of differential equations (Picard 1890, Lindelöf 1894) states that an initial value problem
item	Poincar%C3%A9 inequality	http://en.wikipedia.org/wiki/Poincar%C3%A9_inequality	Assume that , Ω is precompact open subset of Rn, such that closure of Ω is a manifold with C1 boundary. Then one statement of the Poincaré inequality is that there exists C = C(Ω,p,n) such that for all ,
item	Polylogarithmic	http://en.wikipedia.org/wiki/Polylogarithmic	A polylogarithmic function in n is a polynomial in the logarithm of n,
item	Power series	http://en.wikipedia.org/wiki/Power_series	In mathematics, a power series (in one variable) is an infinite series of the form
item	Probability theory	http://en.wikipedia.org/wiki/Probability_theory	Probability theory is the mathematical study of probability.
item	Proof techniques	http://en.wikipedia.org/wiki/Proof_techniques	In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true.
item	Quantum calculus	http://en.wikipedia.org/wiki/Quantum_calculus	Quantum calculus is equivalent to traditional infinitesimal calculus without the notion of limits. It defines "q-calculus" and "h-calculus". h stands for Planck's constant while q stands for quantum. The two parameters are related by the formulaq = exp(ih)
item	Ramp function	http://en.wikipedia.org/wiki/Ramp_function	The ramp function is an elementary unary real function, easily computable as the mean of its independent variable and its absolute value.
item	Rate of convergence	http://en.wikipedia.org/wiki/Rate_of_convergence	In numerical analysis (a branch of mathematics), the speed at which a convergent sequence approaches its limit is called the rate of convergence. Although strictly speaking, a limit does not give information about any finite first part of the sequence, this concept is of practical importance if we deal with a sequence of successive approximations for an iterative method, as then typically fewer iterations are needed to yield a useful approximation if the rate of convergence is higher. This may even make the difference between needing ten or a million iterations.Contents1 The definition of rate of convergence2 The extended definition of rate of convergence3 Examples4 References
item	Regularization %28mathematics%29	http://en.wikipedia.org/wiki/Regularization_%28mathematics%29	In mathematics, inverse problems are often ill-posed. To solve these problems numerically one must introduce some additional information about the solution, such as an assumption on the smoothness or a bound on the norm. The same idea arose in many fields of science. A simple form of regularization applied to integral equations, generally termed Tikhonov regularization after Andrey Nikolayevich Tychonoff, is essentially a trade-off between fitting the data and reducing a norm of the solution. More recently, non-linear regularization methods, including total variation regularization have become popular.
item	Riemann-Liouville differintegral	http://en.wikipedia.org/wiki/Riemann-Liouville_differintegral	In mathematics, the combined differentiation/integration operator used in fractional calculus is called the differintegral, and it has a few different forms which are all equivalent, provided that they are initialized (used) properly.
item	Sard%27s lemma	http://en.wikipedia.org/wiki/Sard%27s_lemma	Sard's lemma, also known as Sard's theorem or the Morse-Sard theorem, is a result of mathematical analysis characterising the image of the critical points of a smooth function F from one Euclidean space to another as having Lebesgue measure 0 (and so small, in a definite sense). More precisely, ifF: Rn → Rm
item	Semi-continuity	http://en.wikipedia.org/wiki/Semi-continuity	In mathematical analysis, semi-continuity (or semicontinuity) is a property of real-valued functions that is weaker than continuity. A real-valued function f is upper semi-continuous at a point x0 if, roughly speaking, the function values for arguments near x0 are either close to f(x0) or less than f(x0). If "less than" is replaced by "greater than", the function is called lower semi-continuous at x0.[edit]
item	Semi-differentiability	http://en.wikipedia.org/wiki/Semi-differentiability	In mathematics, a real-valued function f of a real variable is called semi-differentiable at a point x0 if the one-sided limits
item	Silverman%E2%80%93Toeplitz theorem	http://en.wikipedia.org/wiki/Silverman%E2%80%93Toeplitz_theorem	In mathematics the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods which are regular. A regular matrix summability method is a matrix transformation of a convergent sequence which preserves the limit.[edit]
item	Smooth function	http://en.wikipedia.org/wiki/Smooth_function	In mathematics, a smooth function is one that is infinitely (indefinitely) differentiable, i.e., has derivatives of all finite orders:A function is called C, or more commonly C0, if it is a continuous function. A function is C1 if it has a derivative that is continuous; such functions are also called continuously differentiable. A function is called Cn for n ≥ 1 if it can be differentiated n times, leaving a continuous n-th derivative.The smooth functions are those that lie in the class Cn for all n; they are often referred to as C∞ functions.
item	Smooth infinitesimal analysis	http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis	Smooth infinitesimal analysis is a mathematically rigorous reformulation of the calculus in terms of infinitesimals. These nilsquare or nilpotent infinitesimals are numbers x wherex ² = 0 is true,
item	Squeeze theorem	http://en.wikipedia.org/wiki/Squeeze_theorem	In calculus, the squeeze theorem (also known as the pinching theorem or the sandwich theorem) is a theorem regarding the limit of a function. The theorem asserts that if two functions approach the same limit at a point, and if a third function is "squeezed" ("pinched", "sandwiched") between those functions, then the third function also approaches that limit at that point.
item	Stationary phase approximation	http://en.wikipedia.org/wiki/Stationary_phase_approximation	In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to oscillatory integrals
item	Stieltjes moment problem	http://en.wikipedia.org/wiki/Stieltjes_moment_problem	In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions that a sequence {&#160;μn,&#160;:&#160;n&#160;=&#160;0,&#160;1,&#160;2,&#160;...&#160;} be of the form
item	Stone-Weierstrass theorem	http://en.wikipedia.org/wiki/Stone-Weierstrass_theorem	In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on an interval [a,b] can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are the simplest functions, and computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation. The original version of this result has been established by Karl Weierstraß in 1885.
item	Subadditive function	http://en.wikipedia.org/wiki/Subadditive_function	In mathematics, a subadditive function is a function f&#160;: A → B, having a domain A and a codomain B that are both closed under addition, with the following property:
item	Sublinear	http://en.wikipedia.org/wiki/Sublinear	In mathematics, sublinear or sub-linear means "less than linear", in particular in the following contexts:In subjects related to big O notation, it means a growth of o(n) (or sometimes O(n) but not Ω(n)).In analysis, sublinear functions, in particular seminorms, satisfy subadditivity and convexity.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Sublinear"			<a href="/w/i
item	Subsequential limit	http://en.wikipedia.org/wiki/Subsequential_limit	(UTC)In mathematics, a subsequential limit is the limit of some subsequence.
item	Summa	http://en.wikipedia.org/wiki/Summa	The term summa is the Latin word for sum. It is also used as the name for the elongated 's' symbol used to represent the integral in calculus. It was first used to represent the limiting sum (Riemann sum) that inspired the integral by Leibniz on October 29, 1675.[edit]
item	Superadditive	http://en.wikipedia.org/wiki/Superadditive	A sequence { an }, n ≥ 1, is called superadditive if it satisfies the inequality
item	Symmetry of second derivatives	http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives	In mathematics, the symmetry of second derivatives refers to the possibility of interchanging the order of taking partial derivatives of a functionf(x1, x2, ..., xn)
item	Taylor series	http://en.wikipedia.org/wiki/Taylor_series	In mathematics, the Taylor series of an infinitely differentiable real (or complex) function f defined on an open interval (a − r, a + r) is the power series. The series is named in honor of English mathematician Brook Taylor.
item	Total variation	http://en.wikipedia.org/wiki/Total_variation	In mathematics, the total variation of a real-valued function f on the bounded interval [a, b] is
item	Unconditional convergence	http://en.wikipedia.org/wiki/Unconditional_convergence	In mathematical analysis, a series  in a Banach space X is unconditionally convergent if for every permutation  the series  converges.
item	Uniform boundedness	http://en.wikipedia.org/wiki/Uniform_boundedness	In mathematics, bounded functions are functions for which there exists a lower bound and an upper bound, in other words, a constant which is larger than the absolute value of any value of this function. If we consider a family of bounded functions, this constant can vary between functions. If it is possible to find one constant which bounds all functions, this family of functions is uniformly bounded.
item	Uniform continuity	http://en.wikipedia.org/wiki/Uniform_continuity	In mathematical analysis, a function f(x) is called uniformly continuous if, roughly speaking, small changes in the input x affect small changes in the output f(x) ("continuity"), and furthermore the size of the changes in f(x) depends only on the size of the changes in x but not on x itself ("uniformity"). In other words, the function never has an infinite slope.
item	Vertical tangent	http://en.wikipedia.org/wiki/Vertical_tangent	In mathematics, a vertical tangent is intuitively a tangent line with infinite slope, thus being vertical. Generally speaking, vertical tangents occur at vertical asymptotes, but this is not always the case.[edit]
item	Volterra integral equation	http://en.wikipedia.org/wiki/Volterra_integral_equation	In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind.
item	Wave front set	http://en.wikipedia.org/wiki/Wave_front_set	In mathematical analysis, more precisely in microlocal analysis, the wave front (set) WF(f) characterizes the singularities of a generalized function f, not only in space, but more precisely also with respect to its Fourier transform at each point.Contents1 Introduction2 Definition2.1 Example2.2 Applications3 See also4 References
item	Weight function	http://en.wikipedia.org/wiki/Weight_function	A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more of a "weight" than others. They occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be constructed in both discrete and continuous settings.[edit]
item	Weighted geometric mean	http://en.wikipedia.org/wiki/Weighted_geometric_mean	In statistics, given a set of data,X = { x1, x2, ..., xn}
item	Weighted harmonic mean	http://en.wikipedia.org/wiki/Weighted_harmonic_mean	In statistics, given a set of data,X = { x1, x2, ..., xn}
item	Weighted mean	http://en.wikipedia.org/wiki/Weighted_mean	In statistics, given a set of data,X = { x1, x2, ..., xn}
item	Whitney extension theorem	http://en.wikipedia.org/wiki/Whitney_extension_theorem	In mathematics, in particular in mathematical analysis, Whitney's extension theorem is a partial converse to Taylor's theorem. Roughly speaking, the theorem asserts that if A is a closed subset of a Euclidean space, then it is possible to extend a given function off A in such a way as to have prescribed derivatives at the points of A. It is a result of Hassler Whitney.
item	Zeta function regularization	http://en.wikipedia.org/wiki/Zeta_function_regularization	In mathematics and theoretical physics, zeta-function regularization is a type of regularization or summability method that assigns finite values to superficially divergent sums. The technique is now commonly applied to problems in physics, but has its origins in attempts to give precise meanings to ill-conditioned sums appearing in number theory.Contents1 Definition2 Relation to other regularizations3 History4 See also5 References
item	Numerical analysis	http://en.wikipedia.org/wiki/Numerical_analysis	Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). Some of the problems it deals with arise directly from the study of calculus; other areas of interest are real variable or complex variable questions, numerical linear algebra over the real or complex fields, the solution of differential equations, and other related problems arising in the physical sciences and engineering.Contents1 General introduction1.1 Direct and iterative methods1.2 Discretization1.3 The generation and propagation of errors1.4 Applications<a href="#Areas_
item	Linear programming	http://en.wikipedia.org/wiki/Linear_programming	In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear.
item	Optimization	http://en.wikipedia.org/wiki/Optimization	In mathematics, optimization is the discipline which is concerned with finding the maxima and minima of functions, possibly subject to constraints. An example of an optimization problem is the following: maximize the profit of a manufacturing operation while ensuring that none of the resources exceed certain limits and also satisfying as much of the demand faced as possible. Optimization has many practical applications in logistics and design problems.
item	Operations research	http://en.wikipedia.org/wiki/Operations_research	Operations research, operational research, or simply OR is an interdisciplinary science which deploys scientific methods like mathematical modeling, statistics, and algorithms to decision making in complex real world problems which are concerned with coordination and execution of the operations within an organization. The nature of organization is essentially immaterial. The eventual intention behind using this science is to elicit a best possible solution to a problem scientifically, which improve or optimize the performance of the organization.Contents1 Operations research in context2 Areas of application3 Professional societies4 Origins and the name5 Examples6 Operational Research journals7 Textbooks8 See also
item	Continuous modelling	http://en.wikipedia.org/wiki/Continuous_modelling	Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equations and are converse to discrete modelling.
item	Mathematical biology	http://en.wikipedia.org/wiki/Mathematical_biology	Mathematical biology or biomathematics is an interdisciplinary field of academic study which aims at modeling natural, biological processes using mathematical techniques and tools. It has both practical and theoretical applications in biological research.Contents1 Importance2 Research2.1 Population dynamics2.2 Modelling cell and molecular biology2.3 Mathematical methods2.4 Modelling physiological systems2.5 Spatial modelling3 Bibliographical references4 External references5 <span class="tocte
item	Bioinformatics	http://en.wikipedia.org/wiki/Bioinformatics	Bioinformatics and computational biology involve the use of techniques from applied mathematics, informatics, statistics, and computer science to solve biological problems. Research in computational biology often overlaps with systems biology. Major research efforts in the field include sequence alignment, gene finding, genome assembly, protein structure alignment, protein structure prediction, prediction of gene expression and protein-protein interactions, and the modeling of evolution.
item	Information theory	http://en.wikipedia.org/wiki/Information_theory	Information theory is a discipline in applied mathematics involving the quantification of data with the goal of enabling as much data as possible to be reliably stored on a medium and/or communicated over a channel. The measure of data, known as information entropy, is usually expressed by the average number of bits needed for storage or communication. For example, if a daily weather description has 3 bits of entropy, then, over enough days, we can describe daily weather with an average of approximately 3 bits per day (each bit being a 0 or a 1). Applications of fundamental topics of information theory include ZIP files (lossless data compression), MP3s (lossy data compression), and DSL (channel coding). The field is at the crossroads of mathematics, statistics, computer science, physics and electrical engineering, and its impact has been crucial to success of the Voyager missions to deep space, the invention of the CD, the feasibility of <a href="/wiki/Mobile_phone" title="Mobile 
item	Game theory	http://en.wikipedia.org/wiki/Game_theory	Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. First developed as a tool for understanding economic behavior and then by the RAND Corporation to define nuclear strategies, game theory is now used in many diverse academic fields, ranging from biology and psychology to sociology and philosophy. Beginning in the 1970s, game theory has been applied to animal behavior, including species' development by natural selection. Because of interesting games like the prisoner's dilemma, in which rational self-interest hurts everyone, game theory has been used in political science, ethics and philosophy. Finally, game theory has recently drawn attention from computer scientists because of its use in artificial intelligence and cybernetics.
item	Probability	http://en.wikipedia.org/wiki/Probability	This article is about probability. For the South Park episode, see ProbablyThe word probability derives from the Latin probare (to prove, or to test). Informally, probable is one of several words applied to uncertain events or knowledge, being closely related in meaning to likely, risky, hazardous, and doubtful. Chance, odds, and bet are other words expressing similar notions. Just as the theory of mechanics assigns precise definitions to such everyday terms as work and force, the theory of probability attempts to quantify the notion of probable.Contents1 Historical remarks2 Formalization of probability2.1 Representation and interpretation of probability values2.2 Distributions3 Probability in mathematics3.1 <span class="toctex
item	Statistics	http://en.wikipedia.org/wiki/Statistics	Statistics is a mathematical science pertaining to collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines from the physical and social sciences to the humanities, as well as to business, government, medicine and industry.
item	Financial mathematics	http://en.wikipedia.org/wiki/Financial_mathematics	Mathematical finance is the branch of applied mathematics concerned with the financial markets. It overlaps heavily with the fields of financial engineering and computational finance. Arguably, all three terms are synonymous.The subject naturally has a close relationship with the discipline of financial economics, but mathematical finance is narrower in scope and more abstract. A central difference is that while a financial economist might study the structural reasons why a company may have a certain share price, a mathematician or financial engineer may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock.Contents1 Mathematical finance articles1.1 Mathematical tools1.2 Derivatives pricing2 See also3 External links
item	Actuarial science	http://en.wikipedia.org/wiki/Actuarial_science	Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. Actuaries are professionals who are qualified in this field through highly competitive examinations and experience.
item	Cryptography	http://en.wikipedia.org/wiki/Cryptography	Cryptography (or cryptology) is a discipline of mathematics and, in modern times, of computer science concerned with information security and related issues, particularly encryption and authentication and other applications such as access control.
item	Combinatorics	http://en.wikipedia.org/wiki/Combinatorics	Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. In particular, it is concerned with "counting" the objects in those collections (enumerative combinatorics), with deciding when the criteria can be met, with constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), with finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and with finding algebraic structures these objects may have (algebraic combinatorics).
item	Finite geometry	http://en.wikipedia.org/wiki/Finite_geometry	A finite geometry is any geometric system that has only a finite number of points. Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points, in fact precisely the same number of points as there are real numbers. A finite geometry can have any (finite) number of dimensions.[edit]
item	Graph theory	http://en.wikipedia.org/wiki/Graph_theory	In mathematics and computer science, graph theory has for its subject matter the properties of graphs. Informally speaking, a graph is a set of objects called points or vertices connected by links called lines or edges. In a graph proper, which is by default undirected, a line from point A to point B is considered to be the same thing as a line from point B to point A. In a digraph, short for directed graph, the two directions are counted as being distinct arcs or directed edges.
item	Network analysis	http://en.wikipedia.org/wiki/Network_analysis	Network analysis is the analysis of networks through network theory (or more generally graph theory).
item	Computer science	http://en.wikipedia.org/wiki/Computer_science	Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems.[1][2][3] Computer science has many sub-fields; some emphasize the computation of specific results (such as computer graphics), while others (such as computational complexity theory) relate to properties of computational problems. Still others focus on the challenges in implementing computations. For example, programming language theory studies approaches to describing computations, while computer programming applies specific programming languages to solve specific computational problems.Contents1 History2 Major achievements<a href="#Rel
item	Applied mathematics	http://en.wikipedia.org/wiki/Applied_mathematics	Applied Mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.Contents1 Divisions of Applied Mathematics2 Segregation within Universities3 See also4 External links
item	Actuarial notation	http://en.wikipedia.org/wiki/Actuarial_notation	Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables.
item	Actuarial present value	http://en.wikipedia.org/wiki/Actuarial_present_value	In actuarial science, an actuarial present value can be defined as the present value of a contingent event. In the field of life insurance, one can think of this as the market value of an insurance policy given some interest rate. The calculation of an actuarial present value draws from the theories of expected values, present values and interest theory, one must have a stong understanding of all concepts in order to calculate an actuarial present value. Implicit in all these factors is the evaluation of risk.Contents1 Life insurance2 Life annuities3 See also4 References
item	Annuity function	http://en.wikipedia.org/wiki/Annuity_function	Annuity Functions are mathematical functions frequently used by Actuarial science students in their introduction to the mathematics of finance and more specifically in their introduction to annuities.[edit]
item	Applied probability	http://en.wikipedia.org/wiki/Applied_probability	Much research involving probability is done under the auspices of applied probability, the application of probability theory to other scientific and engineering domains. However, while such research is motivated (to some degree) by applied problems, it is usually the mathematical aspects of the problems that are of most interest to researchers (as is typical of applied mathematics in general).
item	Differential equations from outside physics	http://en.wikipedia.org/wiki/Differential_equations_from_outside_physics	Most applications of differential equations occur in mathematical models in the physical sciences. However, some occur in biology, economics and other disciplines.[edit]
item	Discrete modelling	http://en.wikipedia.org/wiki/Discrete_modelling	Discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, discrete formulae are fit to data. A common method in this form of modelling is to use recurrence relations.This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Discrete_modelling"			Categories: Applied mathematics stubs | Applied mathematics																Views						 Article				 <li id
item	Inverse problem	http://en.wikipedia.org/wiki/Inverse_problem	The inverse problem is the task that often occurs in many branches of science and mathematics where the values of some model parameter(s) must be obtained via manipulation of observed data.
item	Inverse distance weighting	http://en.wikipedia.org/wiki/Inverse_distance_weighting	Inverse distance weighting (IDW) is a simple method for curve fitting, a process of assigning values to unknown points by using values from known points. A simple IDW weighting factor is,
item	Mathematical economics	http://en.wikipedia.org/wiki/Mathematical_economics	Mathematical economics is the sub-field of economics that explores the mathematical aspects of economic systems.
item	Mathematical finance	http://en.wikipedia.org/wiki/Mathematical_finance	Mathematical finance is the branch of applied mathematics concerned with the financial markets. It overlaps heavily with the fields of financial engineering and computational finance. Arguably, all three terms are synonymous.The subject naturally has a close relationship with the discipline of financial economics, but mathematical finance is narrower in scope and more abstract. A central difference is that while a financial economist might study the structural reasons why a company may have a certain share price, a mathematician or financial engineer may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock.Contents1 Mathematical finance articles1.1 Mathematical tools1.2 Derivatives pricing2 See also3 External links
item	Mathematical methods in electronics	http://en.wikipedia.org/wiki/Mathematical_methods_in_electronics	Mathematical methods are integral to the study of electronics. To become proficient in electronics it is also necessary to become proficient in mathematics.Contents1 Mathematics in Electronic Engineering careers2 Basic applications3 Components4 Complex numbers5 Signal analysis
item	Mathematical model	http://en.wikipedia.org/wiki/Mathematical_model	A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.Contents1 Examples of mathematical models2 Background3 Building blocks4 <span clas
item	Mohr-Coulomb theory	http://en.wikipedia.org/wiki/Mohr-Coulomb_theory	Mohr-Coulomb Theory is a mathematical model describing the response of a material such as rubble piles or concrete to shear stress as well as normal stress. Most of the classical engineering materials somehow follow this rule in at least a portion of their shear failure envelope.
item	Network theory	http://en.wikipedia.org/wiki/Network_theory	Network theory or diktyology is a branch of applied mathematics and physics, with the same general subject matter as graph theory. Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more generally, of asymmetric relations between discrete objects. Typically, the graphs of concern in network theory are complex networks, examples of which include the World Wide Web, the Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc. See list of network theory topics for the scope of the area.&#160;This mathematics-related article is a stub. You can <a href="/wiki/Wikipedia:Find_or_fix
item	Point process	http://en.wikipedia.org/wiki/Point_process	A point process is a type of stochastic process that is widely used in many fields of applied mathematics, such as queueing theory and computational neuroscience.[edit]
item	Postage stamp problem	http://en.wikipedia.org/wiki/Postage_stamp_problem	The postage stamp problem is the following:
item	Self-consistent mean field %28biology%29	http://en.wikipedia.org/wiki/Self-consistent_mean_field_%28biology%29	The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino acid side chain packing given a fixed protein backbone[1]. It is faster but less accurate than dead-end elimination and is generally used in situations where the protein of interest is too large for the problem to be tractable by DEE[2].Contents1 General principles2 Mean-field energies3 Energy of the system<span class="to
item	Superposition principle	http://en.wikipedia.org/wiki/Superposition_principle	In linear algebra, the principle of superposition states that, for a linear system, a linear combination of solutions to the system is also a solution to the same linear system. The superposition principle applies to linear systems of algebraic equations, linear differential equations, or systems of linear differential equations.
item	Theoretical biology	http://en.wikipedia.org/wiki/Theoretical_biology	Theoretical biology is a field of academic study and research that involves the use of quantitative tools in biology.
item	Timoshenko Medal	http://en.wikipedia.org/wiki/Timoshenko_Medal	The Timoshenko Medal is an award given annually by the American Society of Mechanical Engineers (ASME) to an individual "in recognition of distinguished contributions to the field of applied mechanics."
item	VisSim	http://en.wikipedia.org/wiki/VisSim	VisSim is a visual block diagram language for modeling, simulating and analyzing dynamic systems. It is developed by Visual Solutions.
item	Ackermann function	http://en.wikipedia.org/wiki/Ackermann_function	In the theory of computation, the Ackermann function or Ackermann-Péter function is a simple example of a recursive function that is not primitively recursive. It takes two natural numbers as arguments and yields another natural number. Its value grows extremely quickly; even for small inputs, for example (4,3), the values of the Ackermann function become so large that they cannot be feasibly computed, and in fact their decimal expansions require more digits than there are particles in the entire visible universe.Contents1 History2 Definition and properties3 Table of values4 Explanation5 Inverse6 Use as benchmark7 Ackermann numbers</sp
item	Addition	http://en.wikipedia.org/wiki/Addition	Addition is the mathematical operation of increasing one amount by another. The result of adding two quantities a and b is their sum, a + b; it is a more than b, and b more than a. For example, 3 + 2 = 5, since 5 is 2 more than 3. Addition also models many related processes, including joining two collections of objects, repeated incrementation, moving a point across the number line, and representing two successive translations as one.
item	Additive inverse	http://en.wikipedia.org/wiki/Additive_inverse	The additive inverse, or opposite, of a number n is the number which, when added to n, yields zero. The additive inverse of n is denoted −n.
item	Casting out nines	http://en.wikipedia.org/wiki/Casting_out_nines	Casting out nines is a sanity check to ensure that hand computations of sums, differences, products and quotients of integers are correct. By looking at the digital roots of the inputs and outputs, a user will catch the majority of errors. Its ease-of-use makes it amenable to schoolchildren, and they do not need to know the mathematical bases behind it.Contents1 Explanation2 Examples2.1 Addition2.2 Multiplication2.3 Division3 How it works4 History5 References
item	Division %28mathematics%29	http://en.wikipedia.org/wiki/Division_%28mathematics%29	In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.
item	Division algorithm	http://en.wikipedia.org/wiki/Division_algorithm	The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers. The name is something of a misnomer, as it is a theorem, not an algorithm, i.e. a well-defined procedure for achieving a specific task — although the division algorithm can be used to find the greatest common divisor of two integers.Contents1 Statement of theorem2 Examples3 Proof3.1 Existence3.2 Uniqueness4 Generalisations5 External links
item	Elementary arithmetic	http://en.wikipedia.org/wiki/Elementary_arithmetic	Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. Most people learn elementary arithmetic in elementary school.
item	Empty product	http://en.wikipedia.org/wiki/Empty_product	In mathematics, an empty product, or nullary product, is the result of multiplying no numbers. Its numerical value is 1, the multiplicative identity, just as the empty sum — the sum of no numbers — is zero, or the additive identity. The empty product is used in discrete mathematics, algebra, the study of power series, and computer programs.
item	Empty sum	http://en.wikipedia.org/wiki/Empty_sum	In mathematics, the empty sum, or nullary sum, is the result of adding no numbers. Its numerical value is zero.
item	Galley division	http://en.wikipedia.org/wiki/Galley_division	The galley method, also known as the batello or the scratch method, was the most widely used method of division in use prior to 1600. The names galea and batello refer to a boat which the outline of the work was thought to resemble.
item	Hyper operator	http://en.wikipedia.org/wiki/Hyper_operator	The hyper operators forming the hypern family are as follows:hypern (a, b) = 
item	Lecnac	http://en.wikipedia.org/wiki/Lecnac	In mathematics, the verb "to lecnac" (reverse spelling of "cancel") is used in a number of British schools to refer to the inverse operation of cancellation (or reduction) of a vulgar fraction.A fraction (3/4) lecnaced by 3:
item	Location arithmetic	http://en.wikipedia.org/wiki/Location_arithmetic	In his treatise Rabdology, John Napier described a technique to do binary arithmetic using a chessboard-like grid. He termed his technique Location arithmetic (Latin arithmeticæ localis) from the way that positions of counters on the board represented numbers.Using simple moves of counters on the board, Napier showed ways to multiply, divide and even find the square roots of binary numbers. He was so pleased by his discovery that he said in his preface... it might be well described as more of a lark than a labor, for it carries out addition, subtraction, multiplication, division and the extraction of square roots purely by moving counters from place to place. [1]Contents1 Location numerals2 The grid2.1 Addition2.2 Subtraction2.3 Some properties of the grid<a href="#Multiplica
item	Multiplication	http://en.wikipedia.org/wiki/Multiplication	In mathematics, multiplication is an elementary arithmetic operation. When one of the numbers is a whole number, multiplication is the repeated sum of the other number.
item	Precision %28arithmetic%29	http://en.wikipedia.org/wiki/Precision_%28arithmetic%29	The precision of a value describes the number of digits that are used to express that value. In a scientific setting this would be the total number of digits (sometimes called the significant digits) or, less commonly, the number of fractional digits or places (the number of digits following the point). This second definition is useful in financial and engineering applications where the number of digits in the fractional part has particular importance.
item	Promptuary	http://en.wikipedia.org/wiki/Promptuary	In mathematics, the promptuary is a more complex version of Napier's bones which makes it easier to perform multidigit multiplication.
item	Rabdology	http://en.wikipedia.org/wiki/Rabdology	Cover page of RabdologiæIn 1617 a treatise in Latin entitled Rabdologiæ and written by John Napier was published in Edinburgh. Printed three years after his treatise on the discovery of logarithms and in the same year as his death, it describes three devices to aid arithmetic calculations.The devices themselves don't use logarithms, rather they are tools to reduce multiplication and division of natural numbers to simple addition and subtraction operations.The first device, which by then was already popularly used and known as Napier's bones, was a set of rods inscribed with the multiplication table. Napier coined the word rabdology (from Greek ραβδoς [rabdos], rod and λoγoς [logos] calculation or reckoning) to describe this technique. The rods were used to multiply, divide and even find the square roots and cube roots of numbers.The second device was a promptuary (Latin promptuarium meaning storehouse) and consisted of a large set of strips that could multiply multidigit numbers more easily than the bones. In combination with a table of reciprocals, it could also divide numbers.The thir
item	Rounding	http://en.wikipedia.org/wiki/Rounding	Rounding is the process of reducing the number of significant digits in a number. The result of rounding is a "shorter" number having fewer non-zero digits yet similar in magnitude. The result is less precise but easier to use. There are several slightly different rules for rounding.
item	Saturation arithmetic	http://en.wikipedia.org/wiki/Saturation_arithmetic	Saturation arithmetic is a version of arithmetic in which all operations such as addition and multiplication are limited to a fixed range between a minimum and maximum value. If the result of an operation is above the maximum it is set to the maximum, while if it is below the minimum it is set to the minimum. The name comes from how the value becomes "saturated" once it reaches the maximum value; further additions will not increase it.
item	Shabakh	http://en.wikipedia.org/wiki/Shabakh	Shabakh is a method of multiplication that uses a lattice, developed in India from the twelfth century onwards and seen in Hindu works. It can be used to multiply any two numbers.[edit]
item	Subtraction	http://en.wikipedia.org/wiki/Subtraction	Subtraction is one of the four basic arithmetic operations; it is essentially the opposite of addition. Subtraction is denoted by an minus sign in infix notation.
item	Subtraction without borrowing	http://en.wikipedia.org/wiki/Subtraction_without_borrowing	//[edit]BackgroundA common subtraction method is known as dynamic subtraction¹. To perform a - b, using this method, the subtrahend b is written below the minuend a such that the digits of the two numbers are aligned in columns. When a digit of the minuend is smaller than the corresponding digit of the subtrahend below it, the procedure calls for borrowing one power of ten² from the digit of the minuend that is immediately to the left of the current digit.³ Then the value of the “lending” digit is reduced by 1. Anyone who performs subtraction with borrowing must do so from right to left, starting at the lowest-value digits and proceed toward the highest-value digits. It is also necessary to remember to reduce the value of each “lending” digit by 1 when subtracting the corresponding digit of the subtrahend from it. Because of these requirements, learning subtraction with borrowing is difficult for some students.[1]An alternative to <a href="/w/index.php?title=Dynamic_subtraction&amp;action=edit" class="new" title="Dynamic subtraction"
item	Sudan function	http://en.wikipedia.org/wiki/Sudan_function	In the theory of computation, the Sudan function is an example of a function that is recursive, but not primitive recursive. This is also true about the better known Ackermann function. The Sudan function was the first function having this property to be published.
item	Summation	http://en.wikipedia.org/wiki/Summation	Summation is the addition of a set of numbers; the result is their sum. For evaluation of sums in closed form see evaluating sums. The "numbers" to be summed may be natural numbers, complex numbers, matrices, or still more complicated objects. An infinite sum is a subtle procedure known as a series.Contents1 Notation1.1 Computerized notation1.2 Special cases2 Approximation by definite integrals3 Identities4 Growth rates5 See also6 External links<
item	Tetration	http://en.wikipedia.org/wiki/Tetration	Tetration (also exponential map, hyperpower, power tower, super-exponentiation, and hyper4) is iterated exponentiation, the first hyper operator after exponentiation. The portmanteau word tetration was coined by Reuben Louis Goodstein from tetra- (four) and iteration. Tetration is used for the notation of very large numbers. Tetration follows exponentiation in the sequence:additionmultiplicationexponentiationtetration
item	Two plus two make five	http://en.wikipedia.org/wiki/Two_plus_two_make_five	The phrase "two plus two make five" (or "2 + 2 = 5") is sometimes used as a succinct and vivid representation of an illogical statement, especially one made and maintained to suit an ideological agenda.
item	ACS Statistician of the Year	http://en.wikipedia.org/wiki/ACS_Statistician_of_the_Year	The Statistician of the Year was instituted in the year 1987 by the Association of Cricket Statisticians and Historians and is sponsored by Hamlyn.
item	Adams Prize	http://en.wikipedia.org/wiki/Adams_Prize	See also the Herbert Baxter Adams Prize of the American Historical Society
item	B%C3%B4cher Memorial Prize	http://en.wikipedia.org/wiki/B%C3%B4cher_Memorial_Prize	The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every five years for a notable research memoir in analysis that has appeared during the past six years in a recognized North American journal or was authored by a member of the Society. This provision, introduced in 1971 and modified in 1993, is a liberalization of the terms of the award. The current award is $5,000.[edit]
item	Cantor medal	http://en.wikipedia.org/wiki/Cantor_medal	The Cantor medal of the Deutsche Mathematiker-Vereinigung is named in honor of Georg Cantor. It is awarded at most every second year during the yearly meetings of the society. The prize winners are mathematicians who are associated with the German language.[edit]
item	Carl Friedrich Gauss Prize	http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss_Prize	The Carl Friedrich Gauss Prize for Applications of Mathematics is a Mathematics Award, awarded jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found significant applications outside of mathematics". It is to be awarded for the first time in 2006, and then every four years, at the International Congress of Mathematicians. It is named after the German mathematician Carl Friedrich Gauss.
item	Chauvenet Prize	http://en.wikipedia.org/wiki/Chauvenet_Prize	The Chauvenet Prize, consisting of a prize of $1,000 and a certificate, is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. The author(s) must be members of the organization in order to be eligible for the prize. It is named in honor of William Chauvenet and was established through a gift from J.L. Coolidge in 1925.
item	Clay Research Award	http://en.wikipedia.org/wiki/Clay_Research_Award	The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award:Manjul Bhargava (2005)Nils Denker (2005)Ben Green (2004)Gérard Laumon (2004)Bao-Châu Ngô (2004)Richard Hamilton (2003)Terence Tao (2003)Oded Schramm (2002)Manindra Agrawal (2002)Edward Witten (2001)Stanislav Smirnov (2001)Alain Connes (2000)Laurent Lafforgue (2000)Andrew Wiles (1999)[<a href="/w/index.php?title=Clay_Research_Award&amp;action=edit&am
item	Cole Prize	http://en.wikipedia.org/wiki/Cole_Prize	The Cole Prize is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who served the Society for 25 years.
item	Dannie Heineman Prize for Mathematical Physics	http://en.wikipedia.org/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics	Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman. As of 2006, the prize consists of 7500 American dollars.[edit]
item	De Morgan Medal	http://en.wikipedia.org/wiki/De_Morgan_Medal	The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society (LMS). The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the LMS.
item	Euler Medal	http://en.wikipedia.org/wiki/Euler_Medal	The Euler Medal, named after the 18th-century mathematician Leonhard Euler (pronounced "oiler"), is an honor awarded annually by the Institute of Combinatorics and its Applications to mathematicians with a distinguished lifetime contribution to combinatorial research who are still active in research.[edit]
item	Fields Medal	http://en.wikipedia.org/wiki/Fields_Medal	The Fields Medal is a prize awarded to up to four mathematicians not over forty years of age at each International Congress of the International Mathematical Union, which meets once every four years. Founded at the behest of Canadian mathematician John Charles Fields, the medal was first awarded in 1936 and has been regularly awarded since 1950. Its purpose is to give recognition and support to young mathematical researchers who have made important contributions.
item	Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student	http://en.wikipedia.org/wiki/Frank_and_Brennie_Morgan_Prize_for_Outstanding_Research_in_Mathematics_by_an_Undergraduate_Student	The Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student is an annual award given to an undergraduate student in the US, Canada, or Mexico who demonstrates superior mathematics research. The $1,000 award, endowed by Mrs. Frank Morgan of Allentown, Pennsylvania, was founded in 1995. The award is made jointly by the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics.[edit]
item	Fr%C3%B6hlich Prize	http://en.wikipedia.org/wiki/Fr%C3%B6hlich_Prize	The Fröhlich Prize of the London Mathematical Society is awarded in even numbered years in memory of Albrecht Fröhlich. The Prize is awarded for original and extremely innovative work in any branch of mathematics, and is awarded to mathematicians under 40 years of age normally resident in the United Kingdom.[edit]
item	Fulkerson Prize	http://en.wikipedia.org/wiki/Fulkerson_Prize	The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Programming Society (MPS) and the American Mathematical Society (AMS). Up to three awards of $1500 each are presented at each (triennial) International Symposium of the MPS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.[edit]
item	Keith Medal	http://en.wikipedia.org/wiki/Keith_Medal	The Keith Medal is a prize awarded by the Royal Society of Edinburgh, Scotland's national academy, for a scientific paper published in the society's scientific journals, preference being given to a paper containing a discovery, either in mathematics or earth sciences.
item	Leroy P. Steele Prizes	http://en.wikipedia.org/wiki/Leroy_P._Steele_Prizes	The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993 there has been a formal division into three categories.
item	Nemmers Prize in Mathematics	http://en.wikipedia.org/wiki/Nemmers_Prize_in_Mathematics	The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, by a $14 million donation from the Nemmers brothers. They envisioned creating an award that would be as prestigious as the Nobel prize. To this end, the majority of the income earned from the endowment is returned to the principal in order to increase the size of the award. Even so, it is still "believed to be the largest monetary awards in the United States designated specifically for academic excellence in mathematics."[1] Based on the impressive list of past recipients it seems likely that the award will indeed rival the Nobel Prize.
item	Nevanlinna Prize	http://en.wikipedia.org/wiki/Nevanlinna_Prize	The Nevanlinna Prize is a prize for major contributions to mathematical aspects of computer science. The prize was established in 1981 by the Executive Committee of the International Mathematical Union IMU and named to honour the Finnish mathematician Rolf Nevanlinna who had died a year earlier. The prize consists of a gold medal and cash prize.[edit]
item	Norbert Wiener Prize in Applied Mathematics	http://en.wikipedia.org/wiki/Norbert_Wiener_Prize_in_Applied_Mathematics	The Norbert Wiener Prize in Applied Mathematics is a $5000 prize awarded every three years to for an outstanding contribution to "applied mathematics in the highest and broadest sense." It was endowed in 1967 in honor of Norbert Wiener by MIT's mathematics department and is provided jointly by the American Mathematical Society and Society for Industrial and Applied Mathematics.[edit]
item	P%C3%B3lya Prize	http://en.wikipedia.org/wiki/P%C3%B3lya_Prize	The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – ie those in which the De Morgan Medal is not awarded. First given in 1987, the prize is named after Hungarian mathematician George Pólya who was a member of the society for over 60 years.
item	Salem Prize	http://en.wikipedia.org/wiki/Salem_Prize	The Salem Prize, founded by the widow of Raphael Salem, is awarded every year to a young mathematician judged to have done outstanding work in Salem's field of interest, primarily the theory of Fourier series.[edit]
item	Schock prize	http://en.wikipedia.org/wiki/Schock_prize	The Schock Prizes were instituted by the will of philosopher and artist Rolf Schock (1933-1986). The Prizes were first awarded in Stockholm, Sweden, 1993 and have been awarded every two years since. Each recipient currently receives 400,000 Swedish kronor, which is a little over $50,000 USD.
item	Smith%27s Prize	http://en.wikipedia.org/wiki/Smith%27s_Prize	The Smith's Prize is a prize awarded to research students in theoretical Physics, mathematics and applied mathematics at the University of Cambridge, Cambridge, England.
item	Sylvester Medal	http://en.wikipedia.org/wiki/Sylvester_Medal	The Sylvester Medal is a bronze medal awarded every three years by the Royal Society for the encouragement of mathematical research. Instituted in 1901, it will next be awarded in 2006. The medal is named after James Joseph Sylvester, Savilian professor of geometry, Oxford, in the 1880s.[edit]
item	William Lowell Putnam Mathematical Competition	http://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition	The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools. The competition was funded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam (Harvard 1882), who while alive was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.Contents1 The competition today2 Winners2.1 Top-scoring teams2.2 Teams ranked by historical performance2.3 
item	Wolf Prize in Mathematics	http://en.wikipedia.org/wiki/Wolf_Prize_in_Mathematics	Past winners of the Wolf Prize in Mathematics:1978 Israel Gelfand, Carl L. Siegel1979 Jean Leray, André Weil1980 Henri Cartan, Andrei Kolmogorov1981 Lars Ahlfors, Oscar Zariski1982 Hassler Whitney, Mark Grigoryevich Krein1983/4 Shiing-Shen Chern, Paul Erdős1984/5 Kunihiko Kodaira, Hans Lewy1986 Samuel Eilenberg, Atle Selberg1987 Kiyoshi Itō, Peter Lax1988 Friedrich Hirzebruch, Lars Hörmander1989 Alberto Calderón, John Milnor1990 <a href="/wiki/Ennio_de_Gi
item	Axiom	http://en.wikipedia.org/wiki/Axiom	An axiom is a sentence or proposition that is taken for granted as true, and serves as a starting point for deducing other truths. In many usages axiom and postulate are used as synonyms.
item	Axiomatization	http://en.wikipedia.org/wiki/Axiomatization	In mathematics, axiomatization is the process of defining the basic axiomatic systems from which mathematical theories can be derived.
item	Axiomatic system	http://en.wikipedia.org/wiki/Axiomatic_system	In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system; usually though the effort towards complete formalisation brings diminishing returns in certainty, and a lack of readability for humans. Therefore discussion of axiomatic systems is normally only semi-formal. A formal theory typically means an axiomatic system, for example formulated within model theory. A formal proof is a complete rendition of a mathematical proof within a formal system.Contents1 Properties2 Models3 Axiomatic method4 See also
item	Axiom schema	http://en.wikipedia.org/wiki/Axiom_schema	In symbolic logic, it is sometimes inconvenient or impossible to express an axiomatic system in a finite number of axioms. For this reason, an axiom schema is used. Formally, an axiom schema is a set (usually infinite) of well formed formulae, each of which is taken to be an axiom. Often, this set is constructed recursively. A well known axiom schema is the axiom schema of replacement.
item	Armstrong%27s axioms	http://en.wikipedia.org/wiki/Armstrong%27s_axioms	Armstrong's axioms are a set of axioms used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong on his paper Dependency Structures of Data Base Relationships published in 1974. The axioms are sound in that they generate only functional dependencies in the closure of a set of functional dependencies (denoted as F+) when applied to that set (denoted as F). They are also complete in that repeated application of these rules will generate all functional dependencies in the closure F+.Contents1 Axioms1.1 Axiom of reflexivity1.2 Axiom of augmentation1.3 Axiom of transitivity<span class="tocnumber"
item	Axiom S5	http://en.wikipedia.org/wiki/Axiom_S5	Axiom S5 is the distinctive axiom of the S5 system of modal logic and says that if possibly necessarily p, then necessarily p. (Or, equivalently: if possibly p then necessarily possibly p.) If the modality here is what Alvin Plantinga calls "broadly logical" necessity and possibility, then an argument for the axiom can be given as follows. If possibly necessarily p, then there is a possible world w at which p necessarily holds. Then, it is true at w that p is a broadly logically necessary truth, something whose negation would in a broadly logical sense be self-contradictory. But if something is self-contradictory at some possible world, then it is self-contradictory at all worlds, and Plantinga holds that this is true even in the case of broadly logical self-contradictions as well.
item	Axiom of Archimedes	http://en.wikipedia.org/wiki/Axiom_of_Archimedes	The Axiom of Archimedes can be stated in modern notation as follows:
item	Axiom of countability	http://en.wikipedia.org/wiki/Axiom_of_countability	In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that requires the existence of a countable set with certain properties, while without it such sets might not exist.
item	Blum axioms	http://en.wikipedia.org/wiki/Blum_axioms	In computational complexity theory the Blum axioms or Blum complexity axioms are axioms which specify desirable properties of complexity measures on the set of computable functions. The axioms were first defined by Manuel Blum in 1967.
item	Cantor-Dedekind axiom	http://en.wikipedia.org/wiki/Cantor-Dedekind_axiom	The phrase Cantor-Dedekind axiom has been used to describe the thesis that the real numbers are order-isomorphic to the linear continuum of geometry. It is not an axiom in the ordinary mathematical sense.[edit]
item	Eilenberg-Steenrod axioms	http://en.wikipedia.org/wiki/Eilenberg-Steenrod_axioms	In mathematics, specifically in algebraic topology, the Eilenberg-Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular homology.
item	Fundamental axiom of analysis	http://en.wikipedia.org/wiki/Fundamental_axiom_of_analysis	In mathematics, the fundamental axiom of analysis (or simply the fundamental axiom) states:Every non-decreasing sequence of real numbers which is bounded above tends to a limit.
item	Gluing axiom	http://en.wikipedia.org/wiki/Gluing_axiom	In mathematics, the gluing axiom is introduced to define what a sheaf F on a topological space X must satisfy, given that it is a presheaf, which is by definition a contravariant functorF: O(X) → C
item	Huzita-Hatori axioms	http://en.wikipedia.org/wiki/Huzita-Hatori_axioms	The Huzita-Hatori axioms are a set of rules related to the mathematical principles of paper folding. The axioms 1 to 6 were formulated by Italian-Japanese mathematician Humiaki Huzita in 1992, and describe the operations that can be made using origami. The axioms assume that the operations are completed on a plane (i.e. a perfect peice of paper).Contents1 The Seven Axioms2 Details2.1 Axiom 12.2 Axiom 22.3 Axiom 32.4 Axiom 42.5 Axiom 52.6 Axiom 62.7 Axiom 7</l
item	Kuratowski closure axioms	http://en.wikipedia.org/wiki/Kuratowski_closure_axioms	In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms which can be used to define a topological structure on a set. They are equivalent to the more commonly used open set definition. They were first introduced by Kazimierz Kuratowski, in a slightly different form that applied only to Hausdorff spaces.
item	Least upper bound axiom	http://en.wikipedia.org/wiki/Least_upper_bound_axiom	The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis. It is an axiom in the sense that it cannot be proven within the system of real analysis. However, like other axioms of classical fields of mathematics, it can be proven from Zermelo-Fraenkel set theory, an external system. The axiom says that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound. This axiom is very useful since it is essential to the proof that the real number line is a complete metric space. The rational number line does not satisfy the LUB axiom and hence is not complete. A perfect example is . 2 is certainly an upper bound for the set. However, this set has no least upper bound — for any , we can find a  with y &gt; x.[<a href="/w/index.php?title=Least_upper_bound_axiom&amp;action=edit&amp;section=1" title="Edit section:
item	Peano axioms	http://en.wikipedia.org/wiki/Peano_axioms	In mathematics, the Peano axioms (or Peano postulates) are a set of second-order axioms proposed by Giuseppe Peano which determine the theory of arithmetic. The axioms are usually encountered in a first-order form, where the crucial second-order induction axiom is replaced by an infinite first-order induction schema, and Peano Arithmetic (PA) is by convention the name of the widely used system of first-order arithmetic given using this first-order form. However, Peano arithmetic is essentially weaker than the second-order axiom system, since there are nonstandard models of Peano arithmetic, and the only model for the Peano axioms (considered as second-order statements) is the usual system of natural numbers (up to isomorphism).
item	Probability axioms	http://en.wikipedia.org/wiki/Probability_axioms	The probability P of some event E, denoted P(E), is defined with respect to a "universe", or sample space Ω, of all possible elementary events in such a way that P must satisfy the Kolmogorov axioms.
item	Tarski%27s axiomatization of the reals	http://en.wikipedia.org/wiki/Tarski%27s_axiomatization_of_the_reals	In 1936, Alfred Tarski axiomatized the real numbers and their arithmetic using only the 8 axioms shown below. Moreover, those axioms invoked a mere four primitive notions: the set of reals denoted R, a binary relation ordering R, denoted by infix &lt;, a binary operation of addition over R, denoted by infix ‘+’, and the constant 1.
item	Nicolas Bourbaki	http://en.wikipedia.org/wiki/Nicolas_Bourbaki	Nicolas Bourbaki is the collective allonym under which a group of mainly French 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for utmost rigour and generality, creating some new terminology and concepts along the way.
item	Armand Borel	http://en.wikipedia.org/wiki/Armand_Borel	Armand Borel (21 May 1923 - 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. He died in Princeton. (He used to answer the question of whether he was related to Émile Borel alternately by saying he was a nephew, and no relation.)
item	Henri Cartan	http://en.wikipedia.org/wiki/Henri_Cartan	Henri Cartan (born July 8, 1904) is a son of Élie Cartan, and is, as his father was, a distinguished and influential French mathematician.
item	Charles Ehresmann	http://en.wikipedia.org/wiki/Charles_Ehresmann	Charles Ehresmann (1905-1979) was a French mathematician who worked on differential topology and category theory. He is known for work on the topology of Lie groups, the jet concept (see jet bundle), and his seminar on category theory. He attended the École Normale Supérieure in Paris before performing a years military service.
item	Alexander Grothendieck	http://en.wikipedia.org/wiki/Alexander_Grothendieck	Alexander Grothendieck (born March 28, 1928 in Berlin) is one of the most important mathematicians of the 20th century. He is also one of its more eccentric scientific personalities, with achievements over a short span of years that are still astounding in their broad scope and sheer bulk, and a lifestyle later in his career that alienated even close followers. He made major contributions to algebraic geometry, homological algebra, and functional analysis. He was awarded the Fields Medal in 1966, and co-awarded the Crafoord Prize with Pierre Deligne in 1988. He declined the latter prize, on ethical grounds.
item	Jean Delsarte	http://en.wikipedia.org/wiki/Jean_Delsarte	Jean Frédéric Auguste Delsarte (October 19, 1903 - November 28, 1968) was a French mathematician.
item	Jean Dieudonn%C3%A9	http://en.wikipedia.org/wiki/Jean_Dieudonn%C3%A9	Jean-Alexandre-Eugène Dieudonné (July 1, 1906 - November 29, 1992) was a French mathematician, known for research in abstract algebra and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups (the book La Géométrie des groupes classiques was published in 1955), and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields.
item	Szolem Mandelbrojt	http://en.wikipedia.org/wiki/Szolem_Mandelbrojt	Szolem Mandelbrojt (1899 – 1983) was a French mathematician. He worked mainly in classical analysis; he was a student of Jacques Hadamard, and became Hadamard's successor as Professor at the Collège de France.
item	Ren%C3%A9 de Possel	http://en.wikipedia.org/wiki/Ren%C3%A9_de_Possel	Lucien Alexandre Charles René Possel (1905 - 1974) was a French mathematician, one of the founders of the Bourbaki group, and later a pioneer computer scientist, working in particular on optical character recognition.
item	Laurent Schwartz	http://en.wikipedia.org/wiki/Laurent_Schwartz	Laurent-Moïse Schwartz (5 March 1915 – 4 July 2002 in Paris) was a French mathematician.
item	Jean-Pierre Serre	http://en.wikipedia.org/wiki/Jean-Pierre_Serre	Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. With the Fields Medal in 1954 and the Abel Prize in 2003, he has received two of the highest honors in mathematics.Contents1 Life and career2 Early work3 Foundational work in algebraic geometry and the Weil conjectures4 Other work5 Awards6 See also7 Works8 External link</li
item	S%C3%A9minaire Nicolas Bourbaki	http://en.wikipedia.org/wiki/S%C3%A9minaire_Nicolas_Bourbaki	The Séminaire Nicolas Bourbaki (Bourbaki Seminar) is a series of seminars (in fact public lectures with printed notes distributed) that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of mathematical achievement, fashion, and reputation. It is named after the fictitious Nicolas Bourbaki, in fact a group of French and other mathematicians of variable membership.[edit]
item	S%C3%A9minaire Nicolas Bourbaki %281950-1959%29	http://en.wikipedia.org/wiki/S%C3%A9minaire_Nicolas_Bourbaki_%281950-1959%29	Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s.Contents1 1950/51 series2 1951/523 1952/534 1953/545 1954/556 1955/567 1956/578 1957/589 1958/5910 1959/6011 External link
item	S%C3%A9minaire Nicolas Bourbaki %281960-1969%29	http://en.wikipedia.org/wiki/S%C3%A9minaire_Nicolas_Bourbaki_%281960-1969%29	Continuation of the Séminaire Nicolas Bourbaki programme, for the 1960s.Contents1 1960/61 series2 1961/623 1962-634 External link
item	Andr%C3%A9 Weil	http://en.wikipedia.org/wiki/Andr%C3%A9_Weil	André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century, whether measured by his research work, its influence on future work, exposition or breadth. He is known for his foundational work in number theory and algebraic geometry. He was a founding member, and de facto the early leader, of the influential Bourbaki group. The philosopher Simone Weil was his sister.Contents1 Life2 Work3 Books4 See also5 External links6 Bibliography
item	Geometry	http://en.wikipedia.org/wiki/Geometry	Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See areas of mathematics and algebraic geometry.)Contents1 Early geometry2 Ancient Indian geometry (c. 3000 - 500 BC)2.1 Harappan geometry2.2 Vedic geometry3 Classical Greek geometry (c. 600 – 300 BC)3.1 Thales and Pythagoras3.2 <span c
item	Change	http://en.wikipedia.org/wiki/Change	Change is the word used to describe the transition that occurs from same to different.
item	Acceleration	http://en.wikipedia.org/wiki/Acceleration	In physics or physical science, acceleration (symbol: a) is defined as the rate of change (or derivative with respect to time) of velocity. It is thus a vector quantity with dimension length/time². In SI units, acceleration is measured in meters/second²
item	Curve	http://en.wikipedia.org/wiki/Curve	In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. Simple examples are the circle or the straight line. A large number of other curves have been studied in geometry.
item	Slope	http://en.wikipedia.org/wiki/Slope	The slope or the gradient is commonly used to describe the measurement of the steepness, incline or grade of a straight line. A higher slope value indicates a steeper incline. In normal UK usage, the gradient of a slope is defined as the ratio of the "rise" divided by the "run" between two points on a line. The term Grade is also used for this definition, which can be mathematically stated as the tangent of the angle of inclination – the ratio of the altitude change to the horizontal distance between any two points on the grade
item	Archimedes	http://en.wikipedia.org/wiki/Archimedes	Archimedes (Greek: Αρχιμήδης ) (c. 287 BC – 212 BC) was an ancient Greek mathematician, physicist, engineer, astronomer, and philosopher born in the seaport colony of Syracuse, Sicily. He is considered by some historians of mathematics to be one of the greatest mathematicians in antiquity; Carl Friedrich Gauss considered him one of the two greatest ever (the other being Isaac Newton).Contents1 Discoveries and inventions2 Writings by Archimedes3 Quotes about Archimedes4 See also5 Notes</s
item	Gottfried Leibniz	http://en.wikipedia.org/wiki/Gottfried_Leibniz	Gottfried Wilhelm Leibniz (also Leibnitz or von Leibniz)[1] (July 1 (June 21 Old Style) 1646 – November 14, 1716) was a German polymath.Educated in law and philosophy, and serving as factotum to two major German noble houses (one becoming the British royal family while he served it), Leibniz played a major role in the European politics and diplomacy of his day. He occupies an equally large place in both the history of philosophy and the history of mathematics. He invented calculus independently of Newton, and his notation is the one in general use since. In philosophy, he is most remembered for optimism, i.e., his conclusion that our universe is, in a restricted sense, the best possible one God could have made. He was, along with René Descartes and Baruch Spinoza, one of the three great 17th century rationalists, but his philosophy also both loo
item	Isaac Newton	http://en.wikipedia.org/wiki/Isaac_Newton	Sir Isaac Newton, President of the Royal Society, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English mathematician, physicist, astronomer, alchemist, chemist, inventor, and natural philosopher who is generally regarded as one of the greatest scientists and mathematicians in history. Newton wrote the Philosophiae Naturalis Principia Mathematica in which he described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics. By deriving <a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of pl
item	Isaac Barrow	http://en.wikipedia.org/wiki/Isaac_Barrow	Isaac Barrow (1630 - May 4, 1677) was an English divine, scholar and mathematician who is generally given minor credit for his role in the development of modern calculus; in particular, for his work regarding the tangent; for example, Barrow is given credit for being the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's. Lunar crater Barrow is named after him.
item	Ren%C3%A9 Descartes	http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes	For other things named Descartes, see Descartes (disambiguation).René Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, was a noted French philosopher, mathematician, and scientist. Dubbed the "Founder of Modern Philosophy" and the "Father of Modern Mathematics," he ranks as one of the most important and influential thinkers of modern times. For good or bad, much of subsequent western philosophy is a reaction to his writings, which have been closely studied from his time down to the present day. Descartes was one of the key thinkers of the Scientific Revolution in the Western World. He is also honoured by having the Cartesian coordinate system used in plane geometry and algebra named after him.Descartes frequently contrasted his views with those of his predecessors. In the opening section of the Passions of the Soul, he goes so far as to assert that he will write on his topic "as if no one had written on these matters before". Nevertheless many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like <a h
item	Pierre de Fermat	http://en.wikipedia.org/wiki/Pierre_de_Fermat	Pierre de Fermat (pronounced Fair-mah's) (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southwestern France, and a mathematician who is given credit for his contribution towards the development of modern calculus. With his insightful theorems Fermat created the modern theory of numbers. The depth of his work can be gauged by the fact that many of his results were not proved for over a century after his death, and one of them, the Last Theorem, took more than three centuries to prove.
item	Christian Huygens	http://en.wikipedia.org/wiki/Christian_Huygens	Christiaan Huygens (pronounced in English (IPA): [ˈhaɪg ənz]; in Dutch: [ˈhœy γəns]) (April 14, 1629–July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. He studied law at the University of Leiden and the College of Orange in Breda before turning to science. Historians commonly associate Huygens with the scientific revolution.
item	John Wallis	http://en.wikipedia.org/wiki/John_Wallis	John Wallis (November 23, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is also credited with introducing the symbol ∞ for infinity.Contents1 Life2 Mathematics3 See also4 References
item	Integral	http://en.wikipedia.org/wiki/Integral	In calculus, the integral of a function is a generalization of the concept of a sum, typically with direct physical interpretation pertaining to area, mass, or volume. The process of finding integrals is integration, in its mathematical meaning. Unlike the closely-related process of differentiation, there are several possible definitions of integration, with different technical underpinnings. They are, however, compatible; any two different ways of integrating a function will give the same result when they are both defined.The word "integral" may also refer to antiderivatives in a mild abuse of language. (The antiderivative of a function is that function whose derivative is equal to the first function.) Though they are closely related through the fundamental theorem of calculus, the two notions are conceptually distinct. When one wants to clarify this distinction, an antiderivative integral is referred to as an indefinite integral (a function), while the integrals discussed in this article are termed definite integrals.Intuitively, the integral of a continuous, positive real-valued function f of one real variable x between a left endpoint a and a right endpoint b re
item	Limit %28mathematics%29	http://en.wikipedia.org/wiki/Limit_%28mathematics%29	In mathematics, the concept of a "limit" is used to describe the behavior of a function as its argument either gets "close" to some point, or as it becomes larger and larger; or the behavior of a sequence's elements, as their index becomes larger and larger. Limits are used in calculus and other branches of mathematical analysis to define derivatives and continuity.
item	Alternating series	http://en.wikipedia.org/wiki/Alternating_series	In mathematics, an alternating series is an infinite series of the form
item	Archimedes%27 use of infinitesimals	http://en.wikipedia.org/wiki/Archimedes%27_use_of_infinitesimals	The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. His work with infinitesimals is found in the celebrated Archimedes Palimpsest. The palimpsest embodies Archimedes' account of his "mechanical method", so called because it relies on the concepts of torque exerted on a lever and of center of gravity. Both of those concepts were first introduced by Archimedes.
item	Binary logarithm	http://en.wikipedia.org/wiki/Binary_logarithm	In mathematics, the binary logarithm (log2 n) is the logarithm for base 2. It is the inverse function of 2n.
item	Binomial series	http://en.wikipedia.org/wiki/Binomial_series	In mathematics, the binomial series generalizes the purely algebraic binomial theorem. It is a special case of a Newton series. The binomial series is the series
item	Bohr%E2%80%93Mollerup theorem	http://en.wikipedia.org/wiki/Bohr%E2%80%93Mollerup_theorem	In mathematical analysis, the Bohr–Mollerup theorem is named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it. The theorem characterizes the gamma function, defined for x &gt; 0 by
item	Calculus on Manifolds	http://en.wikipedia.org/wiki/Calculus_on_Manifolds	Michael Spivak's Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) is a text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. Notable features include a long problem entitled "A First Course in Complex Analysis" and the book's cover, a reproduction of Lord Kelvin's letter to Stokes in which Stokes's theorem is first stated.Retrieved from "http://en.wikipedia.org/wiki/Calculus_on_Manifolds"			Categories: 1965 books | Calculus | Mathematics books																Views						 Article				 Discussion				 Edit this page				 History						<h
item	Calculus with polynomials	http://en.wikipedia.org/wiki/Calculus_with_polynomials	In mathematics, polynomials are perhaps the simplest functions with which to do calculus. Their derivatives and indefinite integrals are given by the following rules:
item	Cauchy%27s convergence test	http://en.wikipedia.org/wiki/Cauchy%27s_convergence_test	The Cauchy convergence test is a method used to test infinite series for convergence. A series
item	Derivations of conic sections	http://en.wikipedia.org/wiki/Derivations_of_conic_sections	In mathematics, conic sections are relations which represent the equation of the curve (or curves) that result from passing a plane through two cones. These cones must be mirror images of each other across the vertex of one of the cones. Although conic sections are used very often, they are seldom derived intuitively.Contents1 Circles2 Parabolas2.1 Definitions2.2 Proof2.3 Finding the Axis of Symmetry2.4 Finding the Vertex3 Ellipses
item	Derivative %28examples%29	http://en.wikipedia.org/wiki/Derivative_%28examples%29	//[edit]Example 1Consider f(x) = 5:The derivative of a constant function is zero.[edit]Example 2Consider the graph of f(x) = 2x − 3. If the reader has an understanding of algebra and the Cartesian coordinate system, the reader should be able to independently determine that this line has a slope of 2 at every point. Using the above quotient (along with an understanding of the limit, secant, and tangent) one can determine the slope at (4,5):<img class='tex' src="http://upload.wikimedia.org/math/8/6/b/86b253a5bb62b875de94d0ff
item	Difference quotient	http://en.wikipedia.org/wiki/Difference_quotient	The primary vehicle of calculus and other higher mathematics is the function. Its "input value" is its argument, usually a point ("P") expressible on a graph. The difference between two points, themselves, is known as their Delta (ΔP), as is the difference in their function result, the particular notation being determined by the direction of formation:Forward difference:&#160; ΔF(P) = F(P + ΔP) - F(P);Central difference:&#160; δF(P) = F(P + .5ΔP)- F(P - .5ΔP);Backward difference: ∇F(P) = F(P) - F(P - ΔP).
item	Dini derivative	http://en.wikipedia.org/wiki/Dini_derivative	In mathematics, the upper Dini derivative of a continuous function,
item	Dirichlet integral	http://en.wikipedia.org/wiki/Dirichlet_integral	In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet.
item	Dynamic equations on time scales	http://en.wikipedia.org/wiki/Dynamic_equations_on_time_scales	The study of dynamic equations on time scales is an area of mathematics that tries to unify the study of differential and difference equations. It goes back to its founder Stefan Hilger in 1988, but it has recently received a lot of attention. Since much of the work is fairly recent, it is not yet clear how this compares to other approaches.[edit]
item	Evaluating sums	http://en.wikipedia.org/wiki/Evaluating_sums	In mathematics, a series is the sum of the elements of a sequence. This article mentions a few common series and how to compute their values (or prove that they do not converge).Contents1 Arithmetic series2 Geometric series3 Higher powers4 Applications of Taylor series5 See also
item	Even and odd functions	http://en.wikipedia.org/wiki/Even_and_odd_functions	In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.Contents1 Even functions2 Odd functions3 Some facts3.1 Basic properties3.2 Series3.3 Algebraic structure3.4 Harmonics4 References5 See also</
item	Extreme value	http://en.wikipedia.org/wiki/Extreme_value	The largest and the smallest element of a set are called extreme values, absolute extrema, or extreme records.
item	Extreme value theorem	http://en.wikipedia.org/wiki/Extreme_value_theorem	In calculus, the extreme value theorem states that if a function f(x) is continuous in the closed interval [a,b] then f(x) must attain its maximum and minimum value, each at least once.
item	Fa%C3%A0 di Bruno%27s formula	http://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula	//[edit]The formulaFaà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named in honor of Francesco Faà di Bruno (1825–1888), who was (in chronological order) a military officer, a mathematician, and a priest, and was beatified by the Pope a century after his death. Perhaps the most well-known form of Faà di Bruno's formula says thatwhere the sum is over all n-tuples (m1, ..., mn) satisfying the constraintSometimes, to give it a pleasing and memorable pattern, it is written in a way in which the coefficients that have the combinatorial interpretation discussed below are less explicit:<img class='tex' src="http://upload.wikimedia.org/math/2/1/f/21f285fd51bd8964bd38fbdd89d83dd4.png" alt="{d^n \over dx^n} f(g(x)) 
item	Finding the centroid	http://en.wikipedia.org/wiki/Finding_the_centroid	In mathematics, the centroid is the point at which the region/volume is equally balanced.Contents1 Finding the center of mass1.1 Prerequisites1.1.1 Moments1.2 Discrete moments in two dimensions1.3 The center of a planar lamina1.4 The center of a lamina with variable density1.5 The center of a 3-dimensional object with variable density
item	First derivative test	http://en.wikipedia.org/wiki/First_derivative_test	In calculus, a branch of mathematics, the first derivative test determines whether a given critical point of a function is a maximum, a minimum, or neither.
item	Functional integration	http://en.wikipedia.org/wiki/Functional_integration	Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations and in Feynman's approach to the quantum mechanics of particles and fields.
item	Fundamental theorem of calculus	http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus	The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. It is of such central importance in calculus that it is called the fundamental theorem for the entire field of study. This means that if a continuous function is first integrated and then differentiated, the original function is retrieved. An important consequence of this, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated. In his 2003 book (page 340), James Stewart credits the idea that led to the fundamental theorem to the English mathematician Isaac Barrow although the first known proof of the fundamental theorem was due to the Scottish mathematician James Gregory.Contents1 Intuition2 Formal statements3 Corollary
item	Gabriel%27s Horn	http://en.wikipedia.org/wiki/Gabriel%27s_Horn	Gabriel's Horn (also called Torricelli's trumpet) is a figure invented by Evangelista Torricelli which has infinite surface area, but finite volume. The name refers to the tradition identifying the archangel Gabriel with the angel who blows the horn to announce Judgement Day, associating the infinite with the divine.Illustration of left hand end of Gabriel's Horn (or Torricelli's trumpet)
item	Higher order derivative test	http://en.wikipedia.org/wiki/Higher_order_derivative_test	In mathematics, the higher order derivative test is used to find maxima, minima and points of inflection in an nth degree polynomial's curve.[edit]
item	History of calculus	http://en.wikipedia.org/wiki/History_of_calculus	//[edit]OverviewThough the origins of integral calculus are generally regarded as going no farther back than to the ancient Greeks, there is evidence that the ancient Egyptians may have harbored such knowledge amongst themselves as well (see Moscow and Rhind Mathematical Papyri). Eudoxus is generally credited with the method of exhaustion, which made it possible to compute the area and volume of regions and solids by breaking them up into recognizable shapes. Archimedes developed this method further, while also inventing heuristic methods which resemble modern day concepts somewhat. (See Archimedes on Spheres &amp; Cylinders.) It was not until the time of Newton that these methods were made obsolete.In India, the mathematician-astronomer Aryabhata in 499 used infinitesimals and expressed an astronomical problem in the form of a basic <a 
item	Hyperbolic angle	http://en.wikipedia.org/wiki/Hyperbolic_angle	A hyperbolic angle in standard position is the angle at (0,0) between the ray to (1,1) and the ray to (x,1/x) where x &gt; 1.
item	Infinitesimal	http://en.wikipedia.org/wiki/Infinitesimal	In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. A number x is an infinitesimal if and only if for every integer n, |nx| is less than 1, no matter how large n is. In that case, 1/x is larger in absolute value than any positive real number. Nonzero infinitesimals, obviously, are not real numbers, so "operations" on them are not familiar.
item	Integral %28examples%29	http://en.wikipedia.org/wiki/Integral_%28examples%29	This article is a collection of examples that you can check while reading the integral article.
item	Integration by substitution	http://en.wikipedia.org/wiki/Integration_by_substitution	In calculus, the substitution rule is a tool for finding antiderivatives and integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, the substitution rule is a relatively important tool for mathematicians. It is the counterpart to the chain rule of differentiation.Suppose f(x) is an integrable function, and φ(t) is a continuously differentiable function which is defined on the interval [a, b] and whose image (also known as range) is contained in the domain of f.Suppose the derivative φ'(t) is integrable on [a,b] andThenThe formula is best remembered using Leibniz's notation: the substitution x = φ(t) yields dx / dt = φ'(t) and thu
item	Intermediate value theorem	http://en.wikipedia.org/wiki/Intermediate_value_theorem	In analysis, the intermediate value theorem is either of two theorems of which an account is given below.Contents1 Intermediate value theorem1.1 Proof1.2 History1.3 Generalization1.4 Example of Use in Proof1.5 Converse is false2 Intermediate value theorem of integration3 External links
item	Inverse functions and differentiation	http://en.wikipedia.org/wiki/Inverse_functions_and_differentiation	In mathematics, the inverse of a function y = f(x) is a function that, in some fashion, "undoes" the effect of f (see inverse function for a formal and detailed definition). The inverse of f is denoted f - 1. The statements y=f(x) and x=f-1(y) are equivalent.
item	L%27H%C3%B4pital%27s rule	http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule	In calculus, l'Hôpital's rule (alternatively, l'Hospital's rule) uses derivatives to help compute limits with indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to a determinate form, allowing easy computation of the limit. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital, who published the rule in his book Analyse des infiniment petits pour l'intelligence des lignes courbes (1696), the first book to be written on the differential calculus. It is likely, however, that the result was originally due to Johann Bernoulli, upon whose lectures the text was largely based.Contents1 Overview1.1 Introduction1.2 Formal definition2 Examples<span class="tocnu
item	Leibniz formula for pi	http://en.wikipedia.org/wiki/Leibniz_formula_for_pi	In mathematics, Leibniz' formula for π, due to Gottfried Leibniz, states that[edit]
item	Leibniz integral rule	http://en.wikipedia.org/wiki/Leibniz_integral_rule	The Leibniz integral rule, or Leibniz formula (for differentiation of definite integrals), is
item	Leibniz notation	http://en.wikipedia.org/wiki/Leibniz_notation	In calculus, the Leibniz notation, named in honor of the 17th century German philosopher and mathematician Gottfried Wilhelm Leibniz was originally the use of dx and dy and so forth to represent "infinitely small" increments of quantities x and y, just as Δx and Δy represent finite increments of x and y respectively. According to Leibniz, the derivative of y with respect to x, which mathematicians later came to view as
item	Leibniz rule %28generalized product rule%29	http://en.wikipedia.org/wiki/Leibniz_rule_%28generalized_product_rule%29	In calculus, the Leibniz rule, named after Gottfried Leibniz, generalizes the product rule. It states that if f and g are n-times differentiable functions, then the nth derivative of the product fg is given by
item	Leibniz%27s notation for differentiation	http://en.wikipedia.org/wiki/Leibniz%27s_notation_for_differentiation	In Leibniz's notation for differentiation, the derivative of the function f(x) is written:
item	Leibniz%27s rule	http://en.wikipedia.org/wiki/Leibniz%27s_rule	At least two results in calculus are called Leibniz's rule or the Leibniz rule, in honor of Gottfried Leibniz. See:Leibniz rule (generalized product rule)Leibniz's rule (derivatives and integrals)
item	Leibniz%27s rule %28derivatives and integrals%29	http://en.wikipedia.org/wiki/Leibniz%27s_rule_%28derivatives_and_integrals%29	See Leibniz's rule, a disambiguation page, for other meanings of this term.
item	Limit of a function	http://en.wikipedia.org/wiki/Limit_of_a_function	In mathematics, the limit of a function is a fundamental concept in mathematical analysis.Rather informally, to say that a function f has limit L at a point p, is to say that we can make the value of f as close to L as we want, by taking points close enough to p. Formal definitions, first devised around the end of the 19th century, are given below.Contents1 History2 Definition2.1 Functions into a Hausdorff space2.2 Functions on metric spaces2.3 Real-valued functions2.3.1 Limit of a function at infinity2.4 Complex-valued functions2.4.1 Limit of a function at a point<a href="#Limit_o
item	Linear approximation	http://en.wikipedia.org/wiki/Linear_approximation	In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
item	Linearization	http://en.wikipedia.org/wiki/Linearization	Linearization in mathematics and its applications in general refers to finding the linear approximation to a function at a given point. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations. This method is used in fields such as engineering, physics, economics, and ecology.
item	Mean value theorem	http://en.wikipedia.org/wiki/Mean_value_theorem	In calculus, the mean value theorem states, roughly, that given a section of a smooth curve, there is a point on that section at which the derivative (slope) of the curve is equal to the "average" derivative of the section. It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.
item	Multiple integral	http://en.wikipedia.org/wiki/Multiple_integral	It may have been generated by a computer or by a translator with limited proficiency in English or the original language. Feel free to enhance the translation. For reference, the original article may appear under "Italian" in the "other languages" list.Integral as area between two curves.
item	Newton v. Leibniz calculus controversy	http://en.wikipedia.org/wiki/Newton_v._Leibniz_calculus_controversy	Isaac Newton began working on a form of the calculus in 1666. Gottfried Leibniz began working on his variant of the calculus in 1674, and in 1684 published his first paper employing it. L'Hopital published a text on Leibniz's calculus in 1696. Meanwhile, Newton did not explain his calculus in print until 1693 (in part) and 1704 (in full). While visiting London in 1676, Leibniz was shown at least one unpublished manuscript by Newton. Was this fact crucial to Leibniz's later progress on the calculus? Thus were planted the seeds of a major intellectual controversy over who first invented the calculus, one that began simmering in 1699 and that broke out in full force in 1711.Contents1 The quarrel2 Fiction3 Sources4 See also
item	Newton%27s notation for differentiation	http://en.wikipedia.org/wiki/Newton%27s_notation_for_differentiation	Newton's notation for differentiation involved placing a dash/dot over the function name, which he termed the fluxion.
item	One-sided limit	http://en.wikipedia.org/wiki/One-sided_limit	In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above. One writes either
item	Partial fractions in integration	http://en.wikipedia.org/wiki/Partial_fractions_in_integration	In integral calculus, the use of partial fractions is required to integrate the general rational function. Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of partial fractions. Each partial fraction has as its denominator a polynomial function of degree 1 or 2, or some positive integer power of such a function. If the denominator is a 1st-degree polynomial or a power of such a polynomial, then the numerator is a constant. If the denominator is a 2nd-degree polynomial or a power of such a polynomial, then the numerator is a 1st-degree polynomial.
item	Periodic function	http://en.wikipedia.org/wiki/Periodic_function	In mathematics, a periodic function is a function that repeats its values after some definite period has been added to its independent variable. Everyday examples are seen when the variable is time; for instance the hands of a clock or the phases of the moon show periodic behaviour. Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period.
item	Perron%27s formula	http://en.wikipedia.org/wiki/Perron%27s_formula	In mathematics, and more particularly in analytic number theory, Perron's formula is a formula of Oskar Perron to calculate the sum of an arithmetical function, by means of an inverse Mellin transform.Contents1 Statement2 Proof3 Examples4 References
item	Piecewise	http://en.wikipedia.org/wiki/Piecewise	In mathematics, a function f(x) of a real number variable x is defined piecewise, if f(x) is given by different expressions on various intervals. An example is given by the Heaviside step function. The term piecewise is also used as an adverb to describe a property of a piecewise function that holds on each interval but may not hold on the whole function.A piecewise-continuous function given by two different quadratic functions to the left and to the right of x0.
item	Popcorn function	http://en.wikipedia.org/wiki/Popcorn_function	The popcorn function, also known as Thomae's function, Dirichlet's function, the raindrop function, or the ruler function, is the real-valued function f(x) defined as follows:
item	Quasi-continuous function	http://en.wikipedia.org/wiki/Quasi-continuous_function	In math, a quasi-continuous function is a function in which it is continuous only for a limited range of input values. This mathematical analysis-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Quasi-continuous_function"			Categories: Mathematical analysis stubs | Calculus														
item	Radius of convergence	http://en.wikipedia.org/wiki/Radius_of_convergence	In mathematics, the radius of convergence of a power series is a non-negative quantity— either a real number or +∞—that represents a range (within the radius) in which the function will converge.
item	Rectangle method	http://en.wikipedia.org/wiki/Rectangle_method	In integral calculus, the rectangle method uses an approximation to a definite integral, made by finding the area of a series of rectangles.
item	Reflection formula	http://en.wikipedia.org/wiki/Reflection_formula	In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a-x) and f(x). Its is a spcial case of a functional equation, and it is very common in the literature to refer to use the term "functional equation" when "reflection formula" is meant.
item	Related rates	http://en.wikipedia.org/wiki/Related_rates	In differential calculus, related rates problems involve ratios of derivatives of two or more related variables that are changing with respect to time.For example, suppose x and y are both differential functions of time t and are related by the equationand you are supposed to find dy/dt when x = 3, given that dx/dt = 2 when x = 3.First, differentiate both sides of the equation with respect to t:Next, apply the chain rule:Finally, substitute 3 for x and 2 for dx/dt:Basically,[edit]ExamplesThe radius of a circle is increasing at 2 cm/s. Find the rate at which a) it's increasing.<img class='tex' src="http://upload.wikimedia.org/math
item	Rolle%27s theorem	http://en.wikipedia.org/wiki/Rolle%27s_theorem	In calculus, Rolle's theorem states that if a function f is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), and f(a) = f(b) then there is some number c in the open interval (a,b) such thatf '(c) = 0.
item	Root test	http://en.wikipedia.org/wiki/Root_test	In mathematics, the root test is a test for the convergence of an infinite series. It is particularly useful in connection with power series. It was developed first by Cauchy and so is sometimes known as the Cauchy root test or Cauchy's radical test. The root test is defined as:,
item	Series %28mathematics%29	http://en.wikipedia.org/wiki/Series_%28mathematics%29	In mathematics, a series is often represented as the sum of a sequence of terms. That is, a series is represented as a list of numbers with addition operations between them, e.g,1 + 2 + 3 + 4 + 5 + ...
item	Slope field	http://en.wikipedia.org/wiki/Slope_field	In mathematics, a slope field is a graphical tool to qualitatively visualize, or aid in numerical approximation of, solutions to differential equations.Contents1 Definition2 General application3 See also4 External links5 References
item	Taylor%27s theorem	http://en.wikipedia.org/wiki/Taylor%27s_theorem	In calculus, Taylor's theorem, named after the mathematician Brook Taylor, who stated it in 1712, gives the approximation of a differentiable function near a point by a polynomial whose coefficients depend only on the derivatives of the function at that point. This result was first discovered 41 years earlier in 1671 by James Gregory.Contents1 Taylor's theorem in one variable2 Taylor's theorem for several variables3 Proof: Taylor's theorem in one variable4 Proof: several variables5 External links
item	Time scale calculus	http://en.wikipedia.org/wiki/Time_scale_calculus	In mathematics, time scale calculus is a unification of the theory of difference equations and standard calculus. Discovered in 1988 by the German mathematician Stefan Hilger, it has applications in any field that requires simultaneous modelling of discrete and continuous data.[edit]
item	Tractrice	http://en.wikipedia.org/wiki/Tractrice	The tractrice is a curve, first introduced by Claude Perrault in 1670, and later studied by Sir Isaac Newton (1676) and Christian Huygens(1692).[edit]
item	Tractrix	http://en.wikipedia.org/wiki/Tractrix	Tractrix (from the Latin verb trahere `pull, drag') is the curve along which a small object (tractens) moves when pulled on a horizontal plane with a piece of thread by a puller (tractendus) which moves rectilinearly, it is therefore a curve of pursuit.Tractrix with object initially at (4,0)Contents1 Mathematical derivation2 Properties3 See also4 External links
item	Uniform convergence	http://en.wikipedia.org/wiki/Uniform_convergence	In mathematical analysis, a sequence { fn } of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does not depend on x. This notion is used because several important properties of the functions fn, such as continuity, differentiability and Riemann integrability, are only transferred to the limit f if the convergence is uniform.Contents1 Definition and comparison with pointwise convergence2 Topological reformulation3 Theorems4 Generalizations5 History6 Reference<span class="tocnumb
item	Vi%C3%A8te formula	http://en.wikipedia.org/wiki/Vi%C3%A8te_formula	In mathematics, the Viète formula is the following infinite product type representation of the mathematical constant π:
item	Abelian category	http://en.wikipedia.org/wiki/Abelian_category	In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have nice properties. The motivating prototype example of an abelian category is the category of abelian groups, Ab.Contents1 Definitions2 Examples3 Elementary properties4 Related concepts5 History6 References
item	Abstract nonsense	http://en.wikipedia.org/wiki/Abstract_nonsense	Abstract nonsense is a popular term used by mathematicians to describe certain kinds of arguments and concepts in category theory. This term is believed to have been coined by the mathematician Norman Steenrod, himself one of the developers of the categorical point of view. This term is used by practitioners as an indication of mathematical sophistication or coolness rather than as a derogatory designation.
item	Additive category	http://en.wikipedia.org/wiki/Additive_category	In mathematics, specifically in category theory, an additive category is a preadditive category C such that any finitely many objects A1,...,An of C have a biproduct A1 ⊕ ··· ⊕ An in C.
item	Auto magma object	http://en.wikipedia.org/wiki/Auto_magma_object	In mathematics, a magma in a category, or magma object, can be defined in a category with a cartesian product. This is the 'internal' form of definition of a binary operation in a category.
item	Axiomatizable class	http://en.wikipedia.org/wiki/Axiomatizable_class	In mathematics, an axiomatizable class is a class of mathematical structures which are all models of a fixed set of sentences in formal (typically first-order) logic.
item	Biproduct	http://en.wikipedia.org/wiki/Biproduct	In category theory and its applications to mathematics, a biproduct is a generalisation of the notion of direct sum that makes sense in any preadditive category.[edit]
item	Cartesian closed category	http://en.wikipedia.org/wiki/Cartesian_closed_category	In category theory, a category is cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming. For generalizations of this notion to monoidal categories, see closed monoidal category.Contents1 Definition2 Examples3 Applications4 Equational theory
item	Cartesian morphism	http://en.wikipedia.org/wiki/Cartesian_morphism	In mathematics, in particular in category theory, given a functorp&#160;: E → B
item	Pierre Cartier	http://en.wikipedia.org/wiki/Pierre_Cartier	Pierre Cartier (born in Sedan, France in 1932) is a mathematician - more specifically, a category theorist.
item	Catamorphism	http://en.wikipedia.org/wiki/Catamorphism	The concept of a catamorphism is grounded in category theory, and has been applied to functional programming. The term comes from Greek κατα- (downwards, according to) + morphism, the latter from Greek μορφή (form, shape).Contents1 Catamorphisms in functional programming1.1 Example2 Catamorphisms in category theory2.1 The general case2.2 Properties2.3 Notation
item	Categories for the Working Mathematician	http://en.wikipedia.org/wiki/Categories_for_the_Working_Mathematician	Categories for the Working Mathematician is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. It was first published in 1971, and is based on his lectures on the subject given at the University of Chicago, the Australian National University, Bowdoin College, and Tulane University. It is widely regarded as the premier introduction to the subject.[edit]
item	Categorification	http://en.wikipedia.org/wiki/Categorification	In mathematics, categorification refers to the process of replacing set-theoretic theorems by category-theoretic analogues. Categorification, when done successfully, replaces sets by categories, functions with functors, and equations by natural isomorphisms of functors satisfying additional properties. The term was coined by Louis Crane.
item	Characterizations of the category of topological spaces	http://en.wikipedia.org/wiki/Characterizations_of_the_category_of_topological_spaces	In mathematics, a topological space is usually defined in terms of open sets. However, there are many equivalent characterizations of the category of topological spaces. Each of these definitions provides a new way of thinking about topological concepts, and many of these have led to further lines of inquiry and generalisation.Contents1 Definitions2 Definition via open sets3 Definition via closed sets4 Definition via closure operators5 Definition via interior operators6 Definition via neighbourhoods7 Definition via convergence8 <span class="toc
item	Chu space	http://en.wikipedia.org/wiki/Chu_space	Chu spaces generalize the notion of topological space by dropping the requirements that the set of open sets be closed under union and finite intersection, that the open sets be extensional, and that the membership predicate (of points in open sets) be two-valued. The definition of continuous function remains unchanged other than having to be worded carefully to continue to make sense after these generalizations.Contents1 Definition2 Categorical structure3 Variants4 Universality5 References6 External links
item	Class %28set theory%29	http://en.wikipedia.org/wiki/Class_%28set_theory%29	In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Some classes are sets (for instance, the class of all integers that are even), but others are not (for instance, the class of all ordinal numbers or the class of all sets). A class that is not a set is called a proper class.
item	Closed category	http://en.wikipedia.org/wiki/Closed_category	In mathematics, a closed category can be defined as a category V with an internal homomorphism functor , left Yoneda natural arrows  and a fixed object I of V such that there is a natural isomorphism  and a natural transformation [edit]
item	Coequalizer	http://en.wikipedia.org/wiki/Coequalizer	In mathematics, a coequalizer (or coequaliser) is a generalization of a quotient by an equivalence relation to objects in an arbitrary category. It is the categorical construction dual to the equalizer (hence the name).Contents1 Definition2 Examples3 Special cases4 See also
item	Cokernel	http://en.wikipedia.org/wiki/Cokernel	In mathematics, the cokernel of a morphism f&#160;: X → Y (e.g. a homomorphism between groups or a bounded linear operator between Hilbert spaces) is an object Q and a morphism q&#160;: Y → Q such that the composition q f is zero, and furthermore Q is, in a sense, the "most general" object with this property. Often the map q is understood, and Q itself is called the cokernel of f.
item	Comma category	http://en.wikipedia.org/wiki/Comma_category	A comma category (also sometimes called a slice category) is a construction in category theory, a branch of mathematics. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, they become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere, although the technique did not become generally known until many years later. Today, it has become particularly important to mathematicians, because several important mathematical concepts can be treated as comma categories. There are also certain guarantees about the existence of limits and colimits in the context of comma categories. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. Although standard notation has changed, the use of a comma as an operator being potentially confusing, the name persists.Contents1 Definition1.1 General form1.2 Category of objects under A<spa
item	Commutative diagram	http://en.wikipedia.org/wiki/Commutative_diagram	In mathematics, especially the many applications of category theory, a commutative diagram is a diagram of objects and morphisms such that, when picking two objects, one can follow any path through the diagram and obtain the same result by composition.
item	Concrete category	http://en.wikipedia.org/wiki/Concrete_category	In mathematics, a concrete category is a category in which, roughly speaking, all objects are sets possibly carrying some additional structure, all morphisms are functions between those sets, and the composition of morphisms is the composition of functions. The prototypical concrete category is Set, the category of sets and functions.
item	Connected category	http://en.wikipedia.org/wiki/Connected_category	In category theory, a branch of mathematics, a connected category is a category in which, for every two objects, there is at least one morphism connecting them.
item	Coproduct	http://en.wikipedia.org/wiki/Coproduct	In category theory, the coproduct, or categorical sum, is the category-theoretic construction which subsumes the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "most general" object to which each object in the family admits a morphism. It is the category-theoretic dual notion to the categorical product, which means the definition is the same as the product but with all arrows reversed. Despite this innocuous-looking change in the name and notation, coproducts can be dramatically different from products.Contents1 Definition2 Examples3 Discussion4 See also
item	Derived functor	http://en.wikipedia.org/wiki/Derived_functor	In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. (It is not related in any way to the derivatives of calculus.)Contents1 Motivation2 Construction and first properties3 Variations4 Applications5 Naturality6 Generalization
item	Descent %28category theory%29	http://en.wikipedia.org/wiki/Descent_%28category_theory%29	In mathematics, the idea of descent has come to stand for a very general idea, extending the intuitive idea of 'gluing' in topology. Since the topologists' glue is actually the use of equivalence relations on topological spaces, the theory starts with some ideas on identification.
item	Diagonal functor	http://en.wikipedia.org/wiki/Diagonal_functor	In category theory, for any object a in any category C where the product a×a exists, there exists the diagonal morphism δa: a → a×a, satisfying πkδa = ida for k=1,2, where πk is the canonical projection morphism to the k-th component. The existence of this morphism is a consequence of the universal property which characterizes the product (up to isomorphism). The restriction to binary products here is for ease of notation; diagonal morphisms exist similarly for arbitrary products. The image of a diagonal morphism in the category of sets, as a subset of the Cartesian product, is a relation on the domain, namely equality.
item	Dinatural transformation	http://en.wikipedia.org/wiki/Dinatural_transformation	In category theory, a dinatural transformation α between two functors,
item	Direct limit	http://en.wikipedia.org/wiki/Direct_limit	In mathematics, the direct limit (also called the inductive limit) is a general method of taking limits of "directed families of objects". We will first give the definition for algebraic structures like groups and modules, and then the general definition which can be used in any category.Contents1 Formal definition1.1 Algebraic objects1.2 General definition2 Examples3 Related constructions and generalizations
item	Discrete category	http://en.wikipedia.org/wiki/Discrete_category	In mathematics, especially category theory, a discrete category is a category whose only morphisms are the identity morphisms. It is the simplest kind of category. Specifically a category C is discrete ifMorC(X, X) = {idX} for all objects XMorC(X, Y) = ∅ for all objects X ≠ Y
item	Dual %28category theory%29	http://en.wikipedia.org/wiki/Dual_%28category_theory%29	In category theory, an abstract branch of mathematics, the dual category or opposite category Cop of a category C is the category formed by reversing all the morphisms of C. That is, we take Cop to be the category with objects that are those of C, but with the morphisms from X to Y in Cop being the morphisms from Y to X in C. Hence, the dual category of the dual category of a category is the original category itself.
item	Eckmann-Hilton argument	http://en.wikipedia.org/wiki/Eckmann-Hilton_argument	In mathematics, the Eckmann-Hilton argument (or Eckmann-Hilton principle or Eckmann-Hilton theorem) is an argument about monoid structures on a set where one is a homomorphism for the other. Given this, the structures can be shown to coincide, and the resulting monoid demonstrated to be commutative. This can then be used to prove the commutativity of the higher homotopy groups.[edit]
item	End %28category theory%29	http://en.wikipedia.org/wiki/End_%28category_theory%29	In category theory, an end of a functor  is a universal dinatural transformation from an object e of X to S.
item	Endomorphism	http://en.wikipedia.org/wiki/Endomorphism	In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself. So, for example, an endomorphism of a vector space V is a linear map f&#160;: V → V and an endomorphism of a group G is a group homomorphism f&#160;: G → G, etc. In general, we can talk about endomorphisms in any category.
item	Endomorphism ring	http://en.wikipedia.org/wiki/Endomorphism_ring	In abstract algebra, one associates to certain objects a ring, the object's endomorphism ring, which encodes several internal properties of the object.
item	Enriched category	http://en.wikipedia.org/wiki/Enriched_category	In category theory and its applications to mathematics, an enriched category is a category whose hom-sets are replaced by objects from some other category, in a well-behaved manner.Contents1 Definition2 Examples3 A property4 Enriched functors5 References6 External links
item	Epimorphism	http://en.wikipedia.org/wiki/Epimorphism	In category theory an epimorphism (also called an epic morphism or an epi) is a morphism f&#160;: X → Y which is "right-cancellable" in the following sense:g1&#160;o&#160;f = g2&#160;o&#160;f implies g1 = g2 for all morphisms g1, g2&#160;: Y → Z.
item	Equaliser	http://en.wikipedia.org/wiki/Equaliser	In mathematics, an equaliser, or equalizer, is a set of arguments where two or more functions have equal values. An equaliser is the solution set of an equation. In certain contexts, a difference kernel is the equaliser of exactly two functions.Contents1 Definitions2 Difference kernels3 In category theory4 See also
item	Essentially surjective functor	http://en.wikipedia.org/wiki/Essentially_surjective_functor	In category theory, a functor  is essentially surjective when each object d of D is isomorphic to an object of the form Fc for some object c of C.Retrieved from "http://en.wikipedia.org/wiki/Essentially_surjective_functor"			Category: Category theory																Views						 Article				 Discussion				 Edit this page				 History						Personal tools									<a href="/w/index.php?title=Special:Userlogin&
item	Exact functor	http://en.wikipedia.org/wiki/Exact_functor	In homological algebra, an exact functor is one which preserves exact sequences. Formally, let C and D be abelian categories, and let F:C→D be a functor. Let 0→A→B→C→0 be a short exact sequence. We say that F ishalf-exact if F(A)→F(B)→F(C) is exact (There is also similar notion of topological half-exact functor) .left-exact if 0→F(A)→F(B)→F(C) is exact.right-exact if F(A)→F(B)→F(C)→0 is exact.exact if 0→F(A)→F(B)→F(C)→0 is exact.
item	Exponential object	http://en.wikipedia.org/wiki/Exponential_object	In mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories[edit]
item	F-algebra	http://en.wikipedia.org/wiki/F-algebra	In mathematics, specifically in category theory, an F-algebra for an endofunctor
item	F-coalgebra	http://en.wikipedia.org/wiki/F-coalgebra	In mathematics, specifically in category theory, an F-coalgebra for an endofunctor
item	Fibrant object	http://en.wikipedia.org/wiki/Fibrant_object	In mathematics, specifically in homotopy theory in the context of a model category M, a fibrant object A of M is an object that has a fibration to the terminal object of the category.[edit]
item	Fibration	http://en.wikipedia.org/wiki/Fibration	In algebraic topology, a fibration is a continuous mappingE → B
item	Filtered category	http://en.wikipedia.org/wiki/Filtered_category	In category theory, filtered categories generalize the notion of directed set.
item	Forgetful functor	http://en.wikipedia.org/wiki/Forgetful_functor	A forgetful functor is a type of functor in mathematics. The nomenclature is suggestive of such a functor's behaviour: given some object with structure as input, some or all of the object's structure or properties is 'forgotten' in the output. For an algebraic structure of a given signature, this may be expressed by curtailing the signature in some way: the new signature is an edited form of the old one. If the signature is left as an empty list, the functor is simply to take the underlying set of a structure; this is in fact the most common case.
item	Full and faithful functors	http://en.wikipedia.org/wiki/Full_and_faithful_functors	In category theory, a faithful functor (resp. a full functor) is a functor which is injective (resp. surjective) when restricted to each set of morphisms with a given source and target.
item	Functor	http://en.wikipedia.org/wiki/Functor	In category theory, a functor is a special type of mapping between categories. Functors can be thought of as morphisms in the category of small categories.
item	Functor category	http://en.wikipedia.org/wiki/Functor_category	In category theory, a branch of mathematics, the functors between two given categories can themselves be turned into a category; the morphisms in this functor category are natural transformations between functors. Functor categories are of interest for two main reasons:many commonly occurring categories are (disguised) functor categories, so any statement proved for general functor categories is widely applicable;a standard construction embeds a given category in a functor category; the functor category has much nicer properties than the original category, allowing to perform certain operations that were not available in the original setting.[edit]
item	Glossary of category theory	http://en.wikipedia.org/wiki/Glossary_of_category_theory	This is a glossary of properties and concepts in category theory in mathematics.Contents1 A category A is said to be:2 A morphism f in a category is said to be:3 A functor F is said to be:4 An object A a category is said to be:
item	Graded category	http://en.wikipedia.org/wiki/Graded_category	A graded category is a mathematical concept.
item	Grothendieck universe	http://en.wikipedia.org/wiki/Grothendieck_universe	In mathematics, a Grothendieck universe is a set U with the following properties:If x is an element of U and if y is an element of x, then y is also an element of U.If x and y are both elements of U, then {x,y} is an element of U.If x is an element of U, then P(x) is also an element of U. (P(x) is the power set of x.)If  is a family of elements of U, and if I is an element of U, then the union  is an element of U.
item	Grothendieck%27s Galois theory	http://en.wikipedia.org/wiki/Grothendieck%27s_Galois_theory	In mathematics, Grothendieck's Galois theory is a highly abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry. It provides, in the classical setting of field theory, an alternative perspective to that of Emil Artin, whose treatment from about 1930 became standard.
item	Grothendieck%27s relative point of view	http://en.wikipedia.org/wiki/Grothendieck%27s_relative_point_of_view	Grothendieck's relative point of view is a heuristic applied in certain abstract mathematical situations, with a rough meaning of taking for consideration families of 'objects' explicitly depending on parameters, as the basic field of study, rather than a single such object. It is named for Alexander Grothendieck, who made extensive use of it in treating foundational aspects of algebraic geometry. Outside that field, it has been influential particularly on category theory and categorical logic.
item	Group object	http://en.wikipedia.org/wiki/Group_object	In mathematics, group objects are certain generalizations of groups which are built on more complicated structures than sets. A typical example of a group object is a topological group, a group whose underlying set is a topological space such that the group operations are continuous.Contents1 Definition2 Examples3 Group theory generalized4 See also
item	Groupoid	http://en.wikipedia.org/wiki/Groupoid	In mathematics, especially in category theory and homotopy theory, a groupoid is a concept (first developed by Heinrich Brandt in 1926) that simultaneously generalises groups, equivalence relations on sets, and actions of groups on sets. They are often used to capture information about geometrical objects such as manifolds.Contents1 Definitions2 Examples3 Relation to groups3.1 Covariance in special relativity4 Lie groupoids and Lie algebroids5 See also6 External links</li
item	Hom functor	http://en.wikipedia.org/wiki/Hom_functor	In mathematics, specifically in category theory, Hom-sets, i.e. sets of morphisms between objects, give rise to important functors to the category of sets. These functors are called Hom-functors and have numerous applications in category theory and other branches of mathematics.[edit]
item	Image %28category theory%29	http://en.wikipedia.org/wiki/Image_%28category_theory%29	Given a category C and a morphism  in C, the image of f is a monomorphism  satisfying the following universal property:There exists a morphism  such that f = hg.For any object Z with a morphism  and a monomorphism  such that f = lk, there exists a unique morphism  such that k = mg and h = lm.
item	Initial algebra	http://en.wikipedia.org/wiki/Initial_algebra	In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F.[edit]
item	Initial object	http://en.wikipedia.org/wiki/Initial_object	In mathematics, an initial object of a category C is an object I in C such that to every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object: T is terminal, if to every object X in C there exists a single morphism X → T. Initial objects are also called coterminal and terminal objects are also called final. If an object is both initial and terminal, we call it a zero object.
item	Injective cogenerator	http://en.wikipedia.org/wiki/Injective_cogenerator	In category theory, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation, and (dually) cogenerators are objects which envelope other objects as an approximation. When working with unfamiliar algebraic objects, one can use these to approximate with the more familiar.
item	Inverse limit	http://en.wikipedia.org/wiki/Inverse_limit	In mathematics, the inverse limit (also called the projective limit) is a construction which allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects. Inverse limits can be defined in any category, but we will initially only consider inverse limits of groups.Contents1 Formal definition1.1 Algebraic objects1.2 General definition2 Examples3 Related concepts and generalizations
item	Karoubi envelope	http://en.wikipedia.org/wiki/Karoubi_envelope	In mathematics the Karoubi envelope (or Cauchy completion, but that term has other meanings) of a category C is a classification of the idempotents of C, by means of an auxiliary category. It is named for the French mathematician Max Karoubi.
item	Kernel %28category theory%29	http://en.wikipedia.org/wiki/Kernel_%28category_theory%29	In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms and the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel of the morphism f&#160;: X → Y is the "most general" morphism k&#160;: K → X which, when composed with f, yields zero.
item	Limit %28category theory%29	http://en.wikipedia.org/wiki/Limit_%28category_theory%29	In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions that are used in various parts of mathematics, like products and inverse limits. Accordingly, the dual notion of a colimit, generalizes disjoint unions and direct sums. Limits and colimits have strong relationships to the categorial concepts of universal morphisms and adjoint functors.Contents1 Definition2 Examples3 Complete categories4 Continuous functors5 Colimits5.1 Creation of Limits and Co-Limits
item	Localization of a category	http://en.wikipedia.org/wiki/Localization_of_a_category	In mathematics, localization of a category consists of adding to a category inverse morphisms for some collection of morphisms, constraining them to become isomorphisms. This is formally similar to the process of localization of a ring; it in general makes objects isomorphic that were not so before. In homotopy theory, for example, there are many examples of mappings that are invertible up to homotopy; and so large classes of homotopy equivalent spaces. Calculus of fractions is another name for working in a localized category.
item	Mitchell%27s embedding theorem	http://en.wikipedia.org/wiki/Mitchell%27s_embedding_theorem	In mathematics, Mitchell's embedding theorem is an important result about abelian categories; it states that these categories, while rather abstractly defined, are all quite concrete categories of modules. This allows one to use element-wise diagram chasing proofs in arbitrary abelian categories.
item	Model category	http://en.wikipedia.org/wiki/Model_category	In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows'): 'weak equivalences', 'fibrations' and 'cofibrations'. These abstract from a conventional homotopy category, of topological spaces or of chain complexes (derived category theory). This concept was introduced in 1967 by Daniel G. Quillen.Contents1 Motivation2 Formal definition3 Example: Topological spaces4 Example: Bounded from below chain complexes of R-modules5 Example: Arbitrary chain-complexes of
item	Model structure	http://en.wikipedia.org/wiki/Model_structure	In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows'): 'weak equivalences', 'fibrations' and 'cofibrations'. These abstract from a conventional homotopy category, of topological spaces or of chain complexes (derived category theory). This concept was introduced in 1967 by Daniel G. Quillen.Contents1 Motivation2 Formal definition3 Example: Topological spaces4 Example: Bounded from below chain complexes of R-modules5 Example: Arbitrary chain-complexes of
item	Monoid	http://en.wikipedia.org/wiki/Monoid	In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element. In other words, it is a unital semigroup.Contents1 Definition2 Examples3 Properties4 Monoid homomorphisms5 Relation to category theory6 External links
item	Monoid %28category theory%29	http://en.wikipedia.org/wiki/Monoid_%28category_theory%29	In category theory, a monoid (or monoid object) (M,μ,η) in a monoidal category C is an object M together with two morphisms called multiplication,and  called unit,
item	Monomorphism	http://en.wikipedia.org/wiki/Monomorphism	In the context of abstract algebra or universal algebra, a monomorphism is simply an injective homomorphism.
item	Morphism	http://en.wikipedia.org/wiki/Morphism	In mathematics, a morphism is an abstraction of a structure-preserving mapping between two mathematical structures.
item	Multicategory	http://en.wikipedia.org/wiki/Multicategory	In mathematics (especially category theory), a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are analogous to functions, then morphisms in a multicategory are analogous to functions of several variables.[edit]
item	Natural number object	http://en.wikipedia.org/wiki/Natural_number_object	In category theory, a natural number object (nno) is an object endowed with a recursive structure similar to natural numbers. More precisely, in a category E with a terminal object (alternately, a topos), an nno N is given by:a global element z&#160;: 1 → N, andan arrow s&#160;: N → N,
item	Natural transformation	http://en.wikipedia.org/wiki/Natural_transformation	In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e. the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed this intuition can be formalized to define so called functor categories. Natural transformations are, after categories and functors, one of the most basic notions of categorical algebra and consequently appear in the majority of its applications.Contents1 Definition2 Examples2.1 A worked example2.2 Further examples3 Operations with natural transformations4 Functor categories5 Yoneda lemma<a href="#Historical_note
item	Normal morphism	http://en.wikipedia.org/wiki/Normal_morphism	In category theory and its applications to mathematics, a normal monomorphism or normal epimorphism is a particularly well-behaved type of morphism. A normal category is a category in which morphisms are normal, whenever reasonable.[edit]
item	Operad theory	http://en.wikipedia.org/wiki/Operad_theory	Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity. Operads generalize the various associativity properties already observed in algebras and coalgebras such as Lie algebras or Poisson algebras by modeling computational trees within the algebra. Algebras are to operads as group representations are to groups. Originating from work in category theory by Saunders Mac Lane, it has expanded more recently drawing upon work by Kontsevich on graph homology.
item	Pointed space	http://en.wikipedia.org/wiki/Pointed_space	In mathematics, a pointed space is a topological space X with a distinguished basepoint x0 in X. Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e. a continuous map f&#160;: X → Y such that f(x0) = y0. This is usually denotedf&#160;: (X, x0) → (Y, y0).
item	Pointless topology	http://en.wikipedia.org/wiki/Pointless_topology	In mathematics, pointless topology (also called point-free or pointfree topology) is an approach to topology which avoids the mentioning of points.Contents1 General concepts2 Categories of frames and locales3 Relation to point-set topology4 See also5 References
item	Pre-Abelian category	http://en.wikipedia.org/wiki/Pre-Abelian_category	In mathematics, specifically in category theory, a pre-Abelian category is an additive category that has all kernels and cokernels.
item	Preadditive category	http://en.wikipedia.org/wiki/Preadditive_category	In mathematics, a preadditive category is a category that is enriched over the monoidal category of abelian groups. In other words, the category C is preadditive if every hom-set Hom(A,B) in C has the structure of an abelian group, and composition of morphisms is bilinear over the integers.
item	Presheaf %28category theory%29	http://en.wikipedia.org/wiki/Presheaf_%28category_theory%29	In category theory, a V-valued presheaf F on a category C is a functor . One often simply talk of a presheaf to mean a Set-valued presheaf. Maps between presheaves are called profunctors.
item	Product %28category theory%29	http://en.wikipedia.org/wiki/Product_%28category_theory%29	In category theory, one defines products to generalize constructions such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism to each of the given objects.Contents1 Definition2 Examples3 Discussion4 Distributivity5 See also
item	Profunctor	http://en.wikipedia.org/wiki/Profunctor	In category theory, profunctors are a generalization of relations and also of bimodules.Contents1 Definition1.1 Composition of profunctors1.2 The bicategory of profunctors2 Properties2.1 Lifting functors to profunctors3 References
item	Projective object	http://en.wikipedia.org/wiki/Projective_object	In category theory, the notion of a projective object generalizes the notion of free module.
item	Pulation square	http://en.wikipedia.org/wiki/Pulation_square	In category theory, a branch of mathematics, a pulation square (also called a Doolittle diagram) is a diagram that is simultaneously a pullback square and a pushout square. It is a self-dual concept.[edit]
item	Pullback %28category theory%29	http://en.wikipedia.org/wiki/Pullback_%28category_theory%29	In category theory, a branch of mathematics, a pullback (also called a fibered product or cartesian square) is the limit of a diagram consisting of two morphisms f&#160;: X → Z and g&#160;: Y → Z with a common codomain. The pullback is often writtenP = X ×Z Y.Contents1 Universal property2 Examples3 See also4 References
item	Pushout %28category theory%29	http://en.wikipedia.org/wiki/Pushout_%28category_theory%29	In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum) is the colimit of a diagram consisting of two morphisms f&#160;: Z → X and g&#160;: Z → Y with a common domain.
item	Quotient category	http://en.wikipedia.org/wiki/Quotient_category	In mathematics, a quotient category is a category obtained from another one by identifying sets of morphisms. The notion is similar to that of a quotient group or quotient space, but in the categorical setting.Contents1 Definition2 Properties3 Examples4 See also
item	Representable functor	http://en.wikipedia.org/wiki/Representable_functor	In mathematics, especially in category theory, a representable functor is a functor of a special form from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings.
item	Samuel Eilenberg	http://en.wikipedia.org/wiki/Samuel_Eilenberg	Samuel Eilenberg (September 30, 1913-January 30, 1998) was a Polish mathematician. He was born in Warsaw, Poland and died in New York, USA where he had spent much of his career as a professor at Columbia University.
item	Sieve %28category theory%29	http://en.wikipedia.org/wiki/Sieve_%28category_theory%29	In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of open subsets of a fixed open set in topology. In a Grothendieck topology, certain sieves become categorical analogues of open covers in topology.[edit]
item	Simplicial set	http://en.wikipedia.org/wiki/Simplicial_set	In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a "well-behaved" topological space. Historically, this model arose from earlier work in combinatorial topology and in particular from the notion of simplicial complexes.Contents1 Motivation2 Formal definition3 Face and degeneracy maps4 The standard n-simplex and the simplex category5 Geometric realization6 Singular set for a space7 Homotopy theory of simplicial sets8 <span
item	Skeleton %28category theory%29	http://en.wikipedia.org/wiki/Skeleton_%28category_theory%29	In mathematics, a skeleton of a category is a subcategory which, roughly speaking, does not contain any extraneous isomorphisms. In a certain sense, the skeleton of a category is the "smallest" equivalent category which captures all "categorical properties". In fact, two categories are equivalent if and only if they have isomorphic skeletons.Contents1 Definition2 Existence and uniqueness3 Examples4 Reference
item	Small set %28category theory%29	http://en.wikipedia.org/wiki/Small_set_%28category_theory%29	In category theory, a small set is one in a fixed universe of sets (as the word universe is used in mathematics in general). Thus, the category of small sets is the category of all sets one cares to consider. This is used when one does not wish to bother with set-theoretic concerns of what is and what is not considered a set, which concerns would arise if one tried to speak of the category of "all sets".
item	Stable homotopy category	http://en.wikipedia.org/wiki/Stable_homotopy_category	In homotopy theory, the stable homotopy category can be thought to be related to the category of spaces and continuous maps in the same way that stable homotopy groups are related to (standard) homotopy groups.
item	Stack %28category theory%29	http://en.wikipedia.org/wiki/Stack_%28category_theory%29	In algebraic geometry, an algebraic stack is a concept introduced to generalize algebraic varieties, schemes, and algebraic spaces. They were originally proposed in a paper of Deligne and Mumford on the compactifications of moduli of curves; such stacks are now called Deligne-Mumford stacks. They were later generalized by Michael Artin to what is now called an Artin stack, or sometimes, confusingly, an algebraic stack.
item	Structure %28category theory%29	http://en.wikipedia.org/wiki/Structure_%28category_theory%29	In mathematics, progress often consists of recognising the same structure in different contexts - so that one method exploiting it has multiple applications. In fact this is a normal way of proceeding; in the absence of recognisable structure (which might though be hidden) problems tend to fall into the combinatorics classification of matters requiring special arguments.
item	Subcategory	http://en.wikipedia.org/wiki/Subcategory	In mathematics, a subcategory of a category C is a category S whose objects are objects in C and whose arrows  are arrows in C (with the same source and target). Intuitively, a subcategory of C is therefore a category obtained from C by "removing" objects and arrows.
item	Subfunctor	http://en.wikipedia.org/wiki/Subfunctor	In category theory, a branch of mathematics, a subfunctor is a special type of functor which is an analogue of a subset.[edit]
item	Subobject	http://en.wikipedia.org/wiki/Subobject	In category theory, there is a general definition of subobject extending the idea of subset and subgroup.
item	Talk:Model category	http://en.wikipedia.org/wiki/Talk:Model_category	Well, a category stuck on this could have saved me work; I translated the German page just now as model category. So a merge is now required. Charles Matthews 18:41, 15 October 2005 (UTC)
item	Universal property	http://en.wikipedia.org/wiki/Universal_property	In various branches of mathematics, certain constructions are frequently defined or characterised by an abstract property which requires the existence of a unique morphism under certain conditions. These properties are called universal properties. Universal properties are studied abstractly using the language of category theory.
item	User:Lethe/list of categories	http://en.wikipedia.org/wiki/User:Lethe/list_of_categories	In category theory, categories are the main object of study. The following is a list of important categories, and a glossary of named categories.Contents1 Table of categories2 Categories3 what are the abbreviated names for these categories? I could take a guess4 to be inserted4.1 specific categories4.2 classes of categories
item	Yoneda lemma	http://en.wikipedia.org/wiki/Yoneda_lemma	In mathematics, the Yoneda lemma in category theory is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation of Cayley's theorem from group theory (a group being a category with just one object). It allows the embedding of any category into a category of functors defined on that category. It also clarifies how the embedded category, of representable functors and their natural transformations, relates to the other objects in the larger functor category. It is an important tool that underlies several modern developments in algebraic geometry and representation theory.Contents1 Generalities2 Formal statement2.1 General version2.2 Proof<a href="#The_Yoneda_embed
item	Zero morphism	http://en.wikipedia.org/wiki/Zero_morphism	In category theory, a zero morphism is a special kind of "trivial" morphism. Suppose C is a category, and for any two objects X and Y in C we are given a morphism 0XY&#160;: X → Y with the following property: for any two morphism f&#160;: R → S and g&#160;: U → V we obtain a commutative diagram:
item	Lowndean Professor of Astronomy and Geometry	http://en.wikipedia.org/wiki/Lowndean_Professor_of_Astronomy_and_Geometry	The Lowndean chair of Astronomy and Geometry is one of the two major Professorships in Astronomy at Cambridge University, alongside the Plumian Professorship. It was founded in 1749 by Thomas Lowndes, an astronomer from Overton in Cheshire.
item	Rouse Ball Professor of Mathematics	http://en.wikipedia.org/wiki/Rouse_Ball_Professor_of_Mathematics	The Rouse Ball Professorship of Mathematics is one of the senior chairs in the Mathematics Department at Cambridge University. It was founded in 1927 by a bequest from the mathematician W. W. Rouse Ball.[edit]
item	Ben Bitdiddle	http://en.wikipedia.org/wiki/Ben_Bitdiddle	Ben Bitdiddle is a fictional character used most notably in the problem sets for 6.001 at MIT. He considerably predates this class, though, since he was created by Steve Ward for use in problem sets for its predecessor, 6.031, in the 1970s. He has since appeared in a large number of other locations, including other classes at MIT and at other institutions. This article about a fictional character is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/
item	Gian-Carlo Rota	http://en.wikipedia.org/wiki/Gian-Carlo_Rota	Gian-Carlo Rota (April 27, 1932 – April 18, 1999, known as Juan Carlos Rota to Spanish-speakers) was an Italian-born American mathematician and philosopher.
item	1960s	http://en.wikipedia.org/wiki/1960s	The outrageously crowded Woodstock festival epitomized the popular antiwar movement of the 60s.The 1960s decade refers to the years from 1960 to 1969, inclusive. Informally, it can also include a few years at the end of the preceding decade or the beginning of the following decade.The Sixties has also come to refer to the complex of inter-related cultural and political events which occurred in approximately that period, in Western countries, particularly Britain, France, the United States and West Germany. Social upheaval was not limited to just these nations, reaching large scale in nations such as Japan, Mexico and Cana
item	Paul Erd%C5%91s	http://en.wikipedia.org/wiki/Paul_Erd%C5%91s	Paul Erdős also Pál Erdős, in English Paul Erdos or Paul Erdös, (March 26, 1913 – September 20, 1996) was an immensely prolific (and famously eccentric) Hungarian mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory.Contents1 Biography2 Mathematical work3 Collaborations4 Erdős number5 DVD collection of his works<s
item	Enumeration	http://en.wikipedia.org/wiki/Enumeration	In mathematics and theoretical computer science, an enumeration of a set is a procedure for listing all members of the set in some definite sequence, or, equivalently, a means of assigning a unique natural number to each element of the set.
item	2-large	http://en.wikipedia.org/wiki/2-large	In the field of Ramsey theory, a branch of combinatorial mathematics, a set is 2-large when it meets the conditions for largeness when the restatement of van der Waerden's theorem is concerned only with 2-colorings. A similar definition defines k-largeness for any k. All nonempty subsets of the set of natural numbers are trivially 1-large. Every set is either large or k-large for some maximal k. This follows from two important, albeit trivially true, facts:k-largeness implies (k-1)-largeness for k&gt;1k-largeness for all k implies largeness.
item	Algebraic enumeration	http://en.wikipedia.org/wiki/Algebraic_enumeration	Algebraic enumeration is a subfield of enumeration that deals with counting algebraic objects. Algebraic properties and symmetries of the objects being counted can be taken advantage of to simplify the counting process. See also combinatorics.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Algebraic_enumeration"			Categories: Mathematics stubs | <a href
item	All-pairs testing	http://en.wikipedia.org/wiki/All-pairs_testing	All-pairs testing or pairwise testing is a combinatorial testing method that, for each pair of input parameters to a system (typically, a software algorithm) tests all possible discrete combinations of those parameters. Using carefully chosen test vectors, this can be done much faster than an exhaustive search of all combinations of all parameters, by "parallelizing" the tests of parameter pairs. The number of tests is typically O(nm), where n and m are the number of possibilities for each of the two parameters with the most choices.
item	Alternating sign matrix	http://en.wikipedia.org/wiki/Alternating_sign_matrix	In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the non-zero entries of each row begin and end with 1 and alternate in sign, and the non-zero entries of each column have the same property. These matrices arise naturally when using Dodgson condensation to compute a determinant. They are also closely related to the square ice model from statistical mechanics. They were first defined by William Mills, David Robbins, and Howard Rumsey in the former context.
item	Analytic combinatorics	http://en.wikipedia.org/wiki/Analytic_combinatorics	Analytic combinatorics is a sub-branch of combinatorics that describes combinatorial classes using generating functions, which are often analytic functions, but sometimes formal power series.
item	Antichain	http://en.wikipedia.org/wiki/Antichain	In mathematics, in the area of order theory, an antichain is a relation defined on partially ordered sets.
item	Arrangement of hyperplanes	http://en.wikipedia.org/wiki/Arrangement_of_hyperplanes	In geometry and combinatorics, an arrangement of hyperplanes is a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice. The intersection semilattice of A, written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These subspaces are called the flats of A. L(A) is partially ordered by reverse inclusion.
item	Association scheme	http://en.wikipedia.org/wiki/Association_scheme	In mathematics, association schemes are structures that appear in many different forms in the fields of combinatorics and statistics.Contents1 Definition2 Terminology3 Basic Facts4 Examples5 References
item	Bell polynomials	http://en.wikipedia.org/wiki/Bell_polynomials	//[edit]DefinitionIn combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are given bythe sum extending over all sequences j1, j2, j3, ..., jn−k+1 of non-negative integers such that[edit]Convolution identityFor sequences xn, yn, n = 1, 2, ..., define a sort of <a href="/wiki/Convolution" title="Convolu
item	Bertrand%27s ballot theorem	http://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem	In combinatorics, Bertrand's ballot theorem is the solution to the question: "In an election where one candidate receives p votes and the other q votes with p≥q, what is the probability that the first candidate will be strictly ahead of the second candidate throughout the count?" The answer is(p−q)/(p+q).
item	Bijective proof	http://en.wikipedia.org/wiki/Bijective_proof	In combinatorics, bijective proof, is a proof technique that finds a bijective function
item	Block walking	http://en.wikipedia.org/wiki/Block_walking	In mathematics, block walking is a method useful in thinking about sums of combinations graphically as a 'walk' on Pascal's triangle.Contents1 An analogous problem1.1 Brute force1.2 A smarter approach2 Back to the original problem3 Some problems
item	Bruck%E2%80%93Chowla%E2%80%93Ryser theorem	http://en.wikipedia.org/wiki/Bruck%E2%80%93Chowla%E2%80%93Ryser_theorem	The Bruck–Chowla–Ryser theorem is a result on the combinatorics of block designs. It states that if a (v; k; λ) design exists, then:k − λ is a square,
item	Bruhat%E2%80%93Tits building	http://en.wikipedia.org/wiki/Bruhat%E2%80%93Tits_building	In mathematics, a building is a combinatorial structure on which groups act; the theory of buildings was introduced by Jacques Tits and expounded in Kenneth S. Brown's excellent monograph Buildings (ISBN 0387986243).&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Bruhat%E2%80%93Tits_building"			<a href="/w/index.php?title=Special:Categories&amp;article=Bruhat%E2%80%93Tits_building" tit
item	Catalan%27s constant	http://en.wikipedia.org/wiki/Catalan%27s_constant	In mathematics, Catalan's constant K, which occasionally appears in estimates in combinatorics, is defined by
item	Combinadic	http://en.wikipedia.org/wiki/Combinadic	In mathematics, a combinadic is an ordered integer partition, or composition. Combinadics provide a lexicographical index for combinations. Applications for combinadics include software testing, sampling, quality control, and the analysis of gambling games such as Canada's national 6/49 lottery.
item	Combination	http://en.wikipedia.org/wiki/Combination	In combinatorial mathematics, a combination is an un-ordered collection of unique elements. Given S, the set of all possible unique elements, a combination is a subset of the elements of S. The order of the elements in a combination is not important (two lists with the same elements in different orders are considered to be the same combination). Also, the elements cannot be repeated in a combination (every element appears uniquely once). A k-combination (or k-subset) is a subset with k elements. The number of k-combinations (each of size k) from a set S with n elements (size n) is the binomial coefficient.
item	Combinatorial class	http://en.wikipedia.org/wiki/Combinatorial_class	In combinatorics, a combinatorial class (or simply class) is an equivalence class of sets that have the same counting sequence. Although the elements of these equivalent sets may have very different definitions and semantics, combinatorics is concerned only with the number of elements of a given size. Therefore, knowledge about one set in the class can be applied directly to other sets in the class.
item	Combinatorial design	http://en.wikipedia.org/wiki/Combinatorial_design	Combinatorial design theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties.
item	Combinatorial enumeration	http://en.wikipedia.org/wiki/Combinatorial_enumeration	Combinatorial enumeration is a subfield of enumeration that deals with the counting of objects whose symmetries do not exist or, if they exist, are combinatorial in nature. See combinatorics.This combinatorics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Combinatorial_enumeration"			Categories: Combinatorics stubs | Combinatorics																Views						 Article				 Dis
item	Combinatorial explosion	http://en.wikipedia.org/wiki/Combinatorial_explosion	In administration and computing, a combinatorial explosion is the rapidly accelerating increase in lines of communication as organizations are added in a process. (Casually described as "exponential" it is actually strictly only polynomial)
item	Combinatorial principles	http://en.wikipedia.org/wiki/Combinatorial_principles	In proving results in combinatorics several useful combinatorial rules or combinatorial principles are used. They include:Rule of sumRule of productBijective proofDouble countingPigeonhole principleInclusion-exclusion principleMethod of distinguished elementGenerating functionRecurrence relationThis combinatorics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Combinatorial_principles"			<a href="/w/index.php?title=Special:Cat
item	Combinatorial proof	http://en.wikipedia.org/wiki/Combinatorial_proof	A combinatorial proof is a method of proving a statement, usually a combinatorics identity, by counting some carefully chosen object in different ways to obtain different expressions in the statement (see also double counting). Since those expressions count the same object, they must be equal to each other and thus the statement is established.
item	Combinatorial species	http://en.wikipedia.org/wiki/Combinatorial_species	In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions. Examples of discrete structures are (finite) graphs, permutations, trees, and so on; each of these has an associated generating function which counts how many structures there are of a certain size. One goal of species theory is to be able to analyse complicated structures by describing them in terms of transformations and combinations of simpler structures. These operations correspond to equivalent manipulations of generating functions, so producing such functions for complicated structures is much easier than with other methods.
item	Constraint counting	http://en.wikipedia.org/wiki/Constraint_counting	In mathematics, constraint counting is a crude but often useful way of counting the number of free functions needed to specify a solution to a partial differential equation.Contents1 Einstein strength1.1 Linear equations1.2 General solution of initial value problem1.3 Quasilinear equations2 References
item	Covering problem	http://en.wikipedia.org/wiki/Covering_problem	In combinatorics and computer science, the covering problem is a type of general question: if a certain structure covers another, or how many structures are required to cover another?
item	Cycle decomposition	http://en.wikipedia.org/wiki/Cycle_decomposition	A cycle decomposition in mathematics may refer to one of two related concepts.In graph theory, a cycle decomposition is a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle.In combinatorics, a cycle decomposition is a way of writing a permutation as a number of disjoint cycles.This combinatorics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Cycle_decomposition"			Categories: Combinatorics | Graph theory | Combinatorics stubs</span
item	Cyclic order	http://en.wikipedia.org/wiki/Cyclic_order	In combinatorial mathematics, a cyclic order on a set X with n elements is an arrangement of X as on a clock face, for an n-hour clock. That is, rather than an order relation on X, we define on X just functions 'element immediately before' and 'element immediately following' any given x, in such a way that taking predecessors, or successors, cycles once through the elements as x(1), x(2), ..., x(n). Another way to put it is to say that we make X into the standard n-cycle directed graph on n vertices, by some matching of elements to vertices. A popular example is Rock, Paper, Scissors.
item	DIMACS	http://en.wikipedia.org/wiki/DIMACS	The Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) is a collaboration between Rutgers and Princeton Universities, and the research firms AT&amp;T, Bell Labs, Telecordia, and NEC. It was founded in 1989 with money from the National Science Foundation. Its offices are located on the Rutgers campus, and 250 members from the six institutions form its permanent members.
item	De Arte Combinatoria	http://en.wikipedia.org/wiki/De_Arte_Combinatoria	The Dissertatio de arte combinatoria was published by Gottfried Leibniz in 1666. It is a youthful work, written before the author had seriously undertaken the study of mathematics. Although it is a very original work and it provided the author the first glimpse of fame among the scholars of his time, he often regretted its publication because he considered it premature.
item	De Bruijn digraph	http://en.wikipedia.org/wiki/De_Bruijn_digraph	The vertices of the de Bruijn digraph B(n,m) are all possible words of length m − 1 chosen from an alphabet of size n.
item	De Bruijn sequence	http://en.wikipedia.org/wiki/De_Bruijn_sequence	In mathematics, especially combinatorics, a k-ary De Bruijn sequence B(k,&#160;n) of order n, named after Nicolaas Govert de Bruijn, is a cyclic sequence from a given alphabet A of size k for which every possible subsequence of length n in A is present exactly once.
item	Dickson%27s lemma	http://en.wikipedia.org/wiki/Dickson%27s_lemma	In mathematics, Dickson's lemma is a finiteness statement applying to n-tuples of natural numbers. It is a simple fact from combinatorics, which has become attributed to the American algebraist L. E. Dickson. It was certainly known earlier, for example to Gordan in his researches on invariant theory.
item	Dinitz conjecture	http://en.wikipedia.org/wiki/Dinitz_conjecture	In combinatorics, the Dinitz conjecture was a problem on the extension of arrays to partial Latin squares, posed in 1979 by Jeff Dinitz, and proven in 1994 by Fred Galvin.
item	Dividing a circle into areas	http://en.wikipedia.org/wiki/Dividing_a_circle_into_areas	In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides, in such a way as to maximise the number of areas created by the edges and diagonals, has a solution by an inductive method.Contents1 The problem2 Lemma3 Solution3.1 Inductive method3.2 Combinatorics and topology method4 References5 External links
item	Dobinski%27s formula	http://en.wikipedia.org/wiki/Dobinski%27s_formula	In combinatorial mathematics, Dobinsky's formula states that the number of partitions of a set of n members is
item	Double counting	http://en.wikipedia.org/wiki/Double_counting	This article is about double counting in combinatorics. For double counting in accounting, see double counting.Contents1 Bijective proof1.1 Example1.2 Handshaking lemma2 Probabilistic fallacy2.1 See also
item	Eight queens puzzle	http://en.wikipedia.org/wiki/Eight_queens_puzzle	
item	Equiangular lines	http://en.wikipedia.org/wiki/Equiangular_lines	In geometry, a set of lines in Euclidean space is called equiangular if every pair of lines makes the same angle.
item	Erd%C5%91s-Graham conjecture	http://en.wikipedia.org/wiki/Erd%C5%91s-Graham_conjecture	In mathematics, the Erdős-Graham conjecture in combinatorics states that there exists a constant b &gt; 0 such that for some r &gt; 0, for every r-coloring of the integers in [2, br], there is a monochromatic subset S of these integers such that
item	Exponential formula	http://en.wikipedia.org/wiki/Exponential_formula	In combinatorial mathematics, the exponential formula states that for any formal power series of the form
item	Extremal combinatorics	http://en.wikipedia.org/wiki/Extremal_combinatorics	Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vectors, sets, etc.) can be, if it has to satisfy certain restrictions.
item	Factoradic	http://en.wikipedia.org/wiki/Factoradic	In combinatorial mathematics, the factoradic is a specially constructed number. Factoradics provide a lexicographical index for permutations, so they have potential application to computer security. The idea of the factoradic is closely linked to that of the Lehmer code. Dr. James D. McCaffrey has posted an article on MSDN documenting the factoradic index for permutations with supporting code written in C#. The origins of the term 'factoradic' are obscure. In his article he acknowledges Dr. Peter Cameron of Queen Mary, University of London, as having made the original suggestion.Definition&#160;factoradic&#160;the unique factorial-based mixed radix numeral systemradix:7654321
item	Factorial	http://en.wikipedia.org/wiki/Factorial	In mathematics, the factorial of a natural number n is the product of all positive integers less than or equal to n. This is written as n! and pronounced "n factorial", or colloquially "n shriek" or "n bang". The notation n! was introduced by Christian Kramp in 1808.
item	Fibonacci word	http://en.wikipedia.org/wiki/Fibonacci_word	The Fibonacci word is a specific infinite sequence of binary digits (or symbols from any two-letter alphabet).[edit]
item	Formal power series	http://en.wikipedia.org/wiki/Formal_power_series	In mathematics, formal power series are devices that make it possible to employ much of the analytical machinery of power series in settings that do not have natural notions of convergence. They are also useful, especially in combinatorics, for providing compact representations of sequences and multisets, and for finding closed formulas for recursively defined sequences; this is known as the method of generating functions.Contents1 Informal introduction2 Formal development2.1 Two definitions of the formal power series ring2.1.1 Ring structure2.1.2 Topological structure2.2 Universal property<li 
item	Freiman%27s theorem	http://en.wikipedia.org/wiki/Freiman%27s_theorem	In mathematics, Freiman's theorem is a combinatorial result in number theory. It in a sense accounts for the approximate structure of sets of integers which contain a high proportion of their internal sums, taken two at a time.
item	Fundamental theorem of combinatorial enumeration	http://en.wikipedia.org/wiki/Fundamental_theorem_of_combinatorial_enumeration	The fundamental theorem of combinatorial enumeration is a theorem in combinatorics that solves the enumeration problem of labelled and unlabelled combinatorial classes. The unlabelled case is based on the Pólya enumeration theorem. This theorem is also known as the "folklore theorem of enumeration" and its most important application is the creation of symbolic operators, the so-called "symbolic method", that makes it possible to translate equations involving combinatorial structures directly (and automatically) into equations in the generating functions of these structures.Contents1 Classes of combinatorial structures2 The fundamental theorem of combinatorial enumeration3 The sequence operator4 The cycle operator5 The dihedral operator6 The multiset/set operator7 External links8 <span class=
item	Garden of Eden pattern	http://en.wikipedia.org/wiki/Garden_of_Eden_pattern	In the study of cellular automata, Garden of Eden patterns are configurations that cannot be reached from any other starting configuration. They are named after the biblical Garden of Eden because they have no predecessor configurations—they must be created as such.
item	Generating function	http://en.wikipedia.org/wiki/Generating_function	In mathematics a generating function is a formal power series whose coefficients encode information about a sequence an that is indexed by the natural numbers.
item	Gomory%27s theorem	http://en.wikipedia.org/wiki/Gomory%27s_theorem	Gomory's theorem is a theorem in discrete mathematics. It states the following: If you take away one black and one white square from ordinary 8×8 chessboard, it is still possible to cover the board with 2×1 dominoes.&#160;This geometry-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Gomory%27s_theorem"			Categories: Combinatorics | Geometry stubs			<!-- e
item	Graded poset	http://en.wikipedia.org/wiki/Graded_poset	A locally finite graded poset consists of a poset P along with a function , called the rank function of P. The rank function must satisfy the following properties:If x and y are both minimal elements, then ρ(x) = ρ(y).If y covers x, then ρ(y) = ρ(x) + 1.
item	Graph topology	http://en.wikipedia.org/wiki/Graph_topology	In mathematics, a graph(V,E)
item	Gray code	http://en.wikipedia.org/wiki/Gray_code	
item	Greedoid	http://en.wikipedia.org/wiki/Greedoid	In combinatorics, a greedoid is a type of set system. It rises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs and was later used by Edmonds to characterize a class of optimization problems that can be solved by greedy algorithms. Around 1980, Korte and Lovász introduced the greedoid to further generalize this characterization of greedy algorithms; hence the name greedoid. Besides mathematical optimization, greedoids have also been connected to graph theory, language theory, poset theory, and other areas of mathematics.[edit]
item	Heawood number	http://en.wikipedia.org/wiki/Heawood_number	In mathematics, the Heawood number of a surface is a certain upper bound for the maximal number of colors needed to color any graph embedded in the surface.
item	Hypergraph	http://en.wikipedia.org/wiki/Hypergraph	In mathematics, a hypergraph is a generalization of a graph, where edges can connect any number of vertices. Formally, an hypergraph is a pair (X,E) where X is a set of elements, called nodes or vertices, and a E is a set of subsets of X, called hyperedges. While graph edges are pairs of nodes, hyperedges are arbitrary sets of nodes, and can therefore contain an arbitrary number of nodes.
item	Incidence algebra	http://en.wikipedia.org/wiki/Incidence_algebra	In order theory, a field of mathematics, a locally finite partially ordered set is one for which every closed interval[a, b] = {x&#160;: a ≤ x ≤ b}
item	Incidence structure	http://en.wikipedia.org/wiki/Incidence_structure	In mathematics, particularly in combinatorics, an incidence structure is a triple
item	Inclusion-exclusion principle	http://en.wikipedia.org/wiki/Inclusion-exclusion_principle	In combinatorial mathematics, the inclusion-exclusion principle states that if A1, ..., An are finite sets, then
item	Independence system	http://en.wikipedia.org/wiki/Independence_system	In mathematics, an independence system is a finitary matroid. The term was introduced by Richard Rado in the 1940s in connection with transversal theory, before the name matroid became well known.This combinatorics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Independence_system"			Categories: Combinatorics stubs | Combinatorics																Views						 Arti
item	Kakeya needle problem	http://en.wikipedia.org/wiki/Kakeya_needle_problem	In mathematics, the Kakeya needle problem asks whether there is a minimum area of a region D in the plane, in which a needle can be turned through 360°. This question was first posed by Soichi Kakeya (1886-1947), a Japanese mathematician who worked mainly in mathematical analysis. In 1917 he asked this question, about convex sets.
item	Kruskal%E2%80%93Katona theorem	http://en.wikipedia.org/wiki/Kruskal%E2%80%93Katona_theorem	The Kruskal–Katona theorem is a combinatorial theorem about uniform hypergraphs. It can be used to derive facts about abstract simplicial complexes. It is named for Joseph Kruskal and Gyula Katona.
item	Labelled enumeration theorem	http://en.wikipedia.org/wiki/Labelled_enumeration_theorem	The labelled enumeration theorem is the counterpart of the Pólya enumeration theorem for the labelled case, where we have a set of labelled objects given by an exponential generating function (EGF) g(z) which are being distributed into n slots and a permutation group G which permutes the slots, thus creating equivalence classes of configurations. There is a special re-labelling operation that re-labels the objects in the slots, assigning labels from 1 to k, where k is the total number of nodes, i.e. the sum of the number of nodes of the individual objects. The EGF G(z) of the number of different configurations under this re-labelling process is given by[edit]
item	Lagrange reversion theorem	http://en.wikipedia.org/wiki/Lagrange_reversion_theorem	In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions.
item	Laver table	http://en.wikipedia.org/wiki/Laver_table	In mathematics, Laver tables (named after mathematician Richard Laver, who discovered them towards the end of the 1980s in connection with his works on set theory) are tables of numbers that have certain properties.Contents1 Definition2 Periodicity3 References4 Further reading
item	Littlewood-Offord problem	http://en.wikipedia.org/wiki/Littlewood-Offord_problem	In mathematics, the Littlewood-Offord problem is the combinatorial question in geometry of describing usefully the distribution of the subsums made out of vectorsv1, v2, ..., vn,
item	Longest increasing subsequence problem	http://en.wikipedia.org/wiki/Longest_increasing_subsequence_problem	The longest increasing subsequence problem is to find the longest increasing subsequence of a given sequence. It also reduces to a graph theory problem of finding the longest path in a directed acyclic graph.Contents1 Overview2 Techniques2.1 Longest common subsequence2.2 Dynamic programming3 External links
item	Longest-common subsequence problem	http://en.wikipedia.org/wiki/Longest-common_subsequence_problem	To meet Wikipedia's quality standards, this article or section may require cleanup.Please discuss this issue on the talk page, or replace this tag with a more specific message. Editing help is available.This article has been tagged since November 2005.
item	Lottery Mathematics	http://en.wikipedia.org/wiki/Lottery_Mathematics	This article discusses the way to calculate various probabilities in a lottery game in which one selects 6 numbers from 49, and hopes that as many of those 6 as possible match the 6 that are randomly selected from the same pool of 49 numbers in the "draw".Contents1 Calculation explained in choosing 6 from 6 of 492 Odds of getting other scores in choosing 6 from 493 Powerballs And Bonus Balls4 See also5 External links
item	Lov%C3%A1sz local lemma	http://en.wikipedia.org/wiki/Lov%C3%A1sz_local_lemma	In statistics, if a large number of events are all independent of one another, than there is still a positive (possibly small) probability that none of the events will occur. The Lovász local lemma (proved in 1975 by László Lovász and Paul Erdős) allows one to relax the independence condition slightly: as long as the events are "mostly" independent from one another and aren't individually too likely, than there will still be a positive probability that none of them occur. It is most commonly used in the probabilistic method, in particular to give existence proofs.
item	Lubell-Yamamoto-Meshalkin inequality	http://en.wikipedia.org/wiki/Lubell-Yamamoto-Meshalkin_inequality	In combinatorial mathematics, the Lubell-Yamamoto-Meshalkin inequality, more commonly known as the LYM inequality, is an inequality proved by Lubell (1966), Yamamoto (1954), and Meshalkin (1963).
item	Marriage theorem	http://en.wikipedia.org/wiki/Marriage_theorem	In mathematics, the marriage theorem (1935), usually credited to mathematician Philip Hall, is a combinatorial result that gives the condition allowing the selection of a distinct element from each of a collection of subsets.
item	Method of distinguished element	http://en.wikipedia.org/wiki/Method_of_distinguished_element	In enumerative combinatorial mathematics, identities are sometimes established by arguments that rely on singling out one "distinguished element" of a set.[edit]
item	Moreau%27s necklace-counting function	http://en.wikipedia.org/wiki/Moreau%27s_necklace-counting_function	In combinatorial mathematics, Moreau's necklace-counting function
item	Multi-index notation	http://en.wikipedia.org/wiki/Multi-index_notation	The notion of multi-indices simplifies formulae used in the multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an array of indices.
item	Multiplicities of entries in Pascal%27s triangle	http://en.wikipedia.org/wiki/Multiplicities_of_entries_in_Pascal%27s_triangle	In combinatorial mathematics, it is clear that the only number that appears infinitely many times in Pascal's triangle is 1.Contents1 Preliminary computations2 Results and questions2.1 Do any numbers appear exactly five times in Pascal's triangle?2.2 Singmaster's conjecture3 See also4 References5 External links
item	M%C3%B6bius inversion formula	http://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula	The classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius. It was later generalized to other "Möbius inversion formulas"; see incidence algebra. The classic version states that if g(n) and f(n) are arithmetic functions satisfying
item	N-cube	http://en.wikipedia.org/wiki/N-cube	In mathematics, an n-cube is a set of natural numbers that are sums of the form:
item	Natural density	http://en.wikipedia.org/wiki/Natural_density	In mathematics, a sequencea1, a2, ... , an,
item	Ordered partition of a set	http://en.wikipedia.org/wiki/Ordered_partition_of_a_set	In combinatorial mathematics, an ordered partition O of a set S is a sequenceA1, A2, A3, ..., An
item	Partition %28number theory%29	http://en.wikipedia.org/wiki/Partition_%28number_theory%29	In number theory, a partition of a positive integer n is a way of writing n as a sum of positive integers. Two sums which only differ in the order of their summands are considered to be the same partition; if order matters then the sum becomes a composition. A summand in a partition is also called a part. The number of partitions of n is given by the partition function p(n).Contents1 Examples2 Partition function3 Intermediate function4 Generating function5 Table of values6 Rademacher's series7 Congruences8 Restricted partitions<li class="t
item	Partition of a set	http://en.wikipedia.org/wiki/Partition_of_a_set	In mathematics, a partition of a set X is a division of X into non-overlapping "parts" or "blocks" or "cells" that cover all of X. More formally, these "cells" are both collectively exhaustive and mutually exclusive with respect to the set being partitioned.Contents1 Definition2 Examples3 Partitions and equivalence relations4 Partial ordering of the lattice of partitions5 Noncrossing partitions6 The number of partitions7 See also
item	Pascal%27s rule	http://en.wikipedia.org/wiki/Pascal%27s_rule	In mathematics, Pascal's rule is a combinatorial identity about binomial coefficients. It states that for any natural number n we have
item	Percolation theory	http://en.wikipedia.org/wiki/Percolation_theory	In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.Contents1 Introduction2 The subcritical and supercritical phases3 The critical phase4 The different models5 Conjectures6 References
item	Perfect ruler	http://en.wikipedia.org/wiki/Perfect_ruler	A perfect ruler of length n is a ruler with a subset of the integer markings  that appear on a regular ruler. The defining criterion of this subset is that there exists an m such that any positive integer  can be expressed uniquely as a difference k = ai − aj for some i,j. This is referred to as an m-perfect ruler.
item	Permanent is sharp-P-complete	http://en.wikipedia.org/wiki/Permanent_is_sharp-P-complete	This page gives a mathematical proof that computing the permanent of a 01-matrix is #P-complete. The proof given here follows Ben-Dor and Halevi (1993). The first proof of this fact was given by Leslie Valiant (1979).
item	Permutations and combinations	http://en.wikipedia.org/wiki/Permutations_and_combinations	This article is an elementary introduction to permutations and combinations in combinatorial mathematics.Contents1 Combinations2 Permutations2.1 Repetitions3 Summary of formulae3.1 Permutation with repetition3.2 Permutation without repetition3.3 Combination without repetition3.4 Combination with repetition4 See also5 External links
item	Pigeonhole principle	http://en.wikipedia.org/wiki/Pigeonhole_principle	The pigeonhole principle, also known as Dirichlet's box principle, states that if n pigeons are put into m pigeonholes, and if n &gt; m, then at least one pigeonhole must contain more than one pigeon. Another way of stating this would be that m holes can hold at most m objects with one object to a hole; adding another object will force you to reuse one of the holes.
item	Poly-Bernoulli number	http://en.wikipedia.org/wiki/Poly-Bernoulli_number	In mathematics, poly-Bernoulli numbers, denoted as , were defined by M. Kaneko as
item	Probabilistic method	http://en.wikipedia.org/wiki/Probabilistic_method	The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is more than zero. Although the proof uses probability, the final conclusion is determined for certain, without any possible error.
item	Proizvolov%27s identity	http://en.wikipedia.org/wiki/Proizvolov%27s_identity	The following defines Proizvolov's identity.
item	Pr%C3%BCfer sequence	http://en.wikipedia.org/wiki/Pr%C3%BCfer_sequence	In combinatorial mathematics, the Prüfer sequence (or Prüfer code) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree on n vertices has length n&#160;−&#160;2, and can be generated by a simple iterative algorithm. Prüfer sequences were first used by Heinz Prüfer to prove Cayley's formula in 1918.Contents1 Algorithm2 Example3 Application4 References5 External links
item	P%C3%B3lya enumeration theorem	http://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem	The Pólya enumeration theorem (also known as PET) is a theorem in combinatorics. Suppose you have a set of n slots and a set of objects being distributed into these slots and a generating function f(x, y, ...) of the objects by weight. Furthermore there is a permutation group G acting on the slots that creates equivalence classes of filled slot configurations (two configurations are equivalent if one may be obtained from the other by a permutation from G). Then the generating function of the equivalence classes by weight, where the weight of a configuration is the sum of the weights of the objects in the slots, is obtained by evaluating the cycle index Z(G) of G i.e.
item	Questorial	http://en.wikipedia.org/wiki/Questorial	In mathematics, the questorial of a natural number n is the division of all positive integers less than n, starting off with n. This is written as n? and pronounced "n questorial". The notation n? was introduced under the student alias of Dave Manari in 1988 at the University of Pretoria, South Africa.
item	Random permutation statistics	http://en.wikipedia.org/wiki/Random_permutation_statistics	The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating functions.
item	Rule of product	http://en.wikipedia.org/wiki/Rule_of_product	In combinatorics, the rule of product is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the idea that if we have a ways of doing something and b ways of doing another thing, then there are a&#160;·&#160;b ways of performing both actions.
item	Rule of sum	http://en.wikipedia.org/wiki/Rule_of_sum	In combinatorics, the rule of sum is a basic counting principle. Stated simply, it is the idea that if we have a ways of doing something and b ways of doing another thing and we can not do both at the same time, then there are a&#160;+&#160;b ways to choose one of the actions.
item	Set packing	http://en.wikipedia.org/wiki/Set_packing	Set packing is an NP-complete problem in combinatorics, and was one of Karp's 21 NP-complete problems.
item	Shortest common supersequence	http://en.wikipedia.org/wiki/Shortest_common_supersequence	This shortest common supersequence problem is closely related to the lcs (longest-common subsequence problem. Again, assume that two sequences X = &lt; x1,...,xm &gt; and Y = &lt; y1,...,yn &gt; are given.   A sequence U = &lt; u1,...,uk &gt; is a common supersequence of X and Y if U is a supersequence of both X and Y. 
item	Sieve theory	http://en.wikipedia.org/wiki/Sieve_theory	Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The primordial example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the primordial example of a sieve is the sieve of Eratosthenes, or the more general Legendre sieve. The direct attack on prime numbers using these methods soon reaches apparently insuperable obstacles, in the way of the accumulation of error terms. In one of the major strands of number theory in the twentieth century, ways were found of avoiding some of the difficulties of a frontal attack with a naive idea of what sieving should be.
item	Sim %28pencil game%29	http://en.wikipedia.org/wiki/Sim_%28pencil_game%29	The game of Sim is played by two players, Red and Blue, on a board consisting of six dots ('vertices'). Each dot is connected to each other with a line.
item	Small set %28combinatorics%29	http://en.wikipedia.org/wiki/Small_set_%28combinatorics%29	In combinatorics, a small set of positive integers
item	Sparse matrix	http://en.wikipedia.org/wiki/Sparse_matrix	In the mathematical subfield of numerical analysis a sparse matrix is a matrix populated primarily with zeros.
item	Sperner%27s lemma	http://en.wikipedia.org/wiki/Sperner%27s_lemma	In combinatorial mathematics, Sperner's lemma states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors. The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points, in root-finding algorithms, and are applied in fair division algorithms.
item	Squarefree word	http://en.wikipedia.org/wiki/Squarefree_word	A squarefree word is a word that does not contain any subword twice in a row. There exist infinite squarefree words in any alphabet with three or more symbols, as proved by Axel Thue. To build an infinite squarefree word in the alphabet {a, b, c}, start with the word w1 = a and obtain the word wi + 1 by replacing each a in w1 with abcba, each b with bcacb, and each cabac. Each word contains the previous, allowing us to construct an infinite squarefree word abcbabcacbcabacbcacbabcba...
item	Stable marriage problem	http://en.wikipedia.org/wiki/Stable_marriage_problem	In mathematics, the stable marriage problem (SMP) is as follows:Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, marry the men and women off such that there are no two people of opposite sex who would both rather have each other than their current partners. If there are no such people, all the marriages are "stable".Contents1 Solution2 Algorithm3 Gale-Shapley pairing4 Applications5 Similar problems6 Observations7 Further reading
item	Stanley%27s reciprocity theorem	http://en.wikipedia.org/wiki/Stanley%27s_reciprocity_theorem	In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any "rational cone" and the generating function of the cone's interior.
item	Star product	http://en.wikipedia.org/wiki/Star_product	The star product of two graded posets  and , where P has a unique maximal element  and Q has a unique minimal element , is the poset P * Q on the set . We define the partial order  by  if and only if:1. , and ;2. , and ; or3. <img class='tex' src="http://upload.wikimedia.org/math/b/2/0/b20c65
item	Sturmian word	http://en.wikipedia.org/wiki/Sturmian_word	In mathematics, a Sturmian word is a certain kind of infinite word.Contents1 Definition2 Discussion3 History4 References
item	Sum-free sequence	http://en.wikipedia.org/wiki/Sum-free_sequence	In mathematics, a sum-free sequence is an increasing positive integer sequence
item	Symbolic combinatorics	http://en.wikipedia.org/wiki/Symbolic_combinatorics	Symbolic combinatorics is a technique of analytic combinatorics (a sub-branch of combinatorics) that uses symbolic representations of combinatorial classes to derive their generating functions.Contents1 Procedure2 Combinatorial sum3 Unlabelled structures3.1 Product3.2 Sequence3.3 Set3.4 Multiset3.5 Other elementary constructions3.6 Examples4 Labelled structures<span class="tocnumber"
item	Szemer%C3%A9di%27s theorem	http://en.wikipedia.org/wiki/Szemer%C3%A9di%27s_theorem	In mathematics, Szemerédi's theorem states that a set of natural numbers of upper asymptotic density &gt; 0 contains finite arithmetic progressions, of any length k we may ask for. This generalizes the statement of van der Waerden's theorem. It was conjectured by Paul Erdős and Paul Turán in 1936.[1]
item	Theory of relations	http://en.wikipedia.org/wiki/Theory_of_relations	The theory of relations treats the subject matter of relations in its combinatorial aspect, as distinguished from, though related to, its more properly logical study on one side and its more generally mathematical study on another.
item	Thue-Morse sequence	http://en.wikipedia.org/wiki/Thue-Morse_sequence	In mathematics and its applications, the Thue-Morse sequence, or Prouhet-Thue-Morse sequence, is a certain binary sequence whose initial segments alternate (in a certain sense).
item	Transversal	http://en.wikipedia.org/wiki/Transversal	Given a collection C of disjoint sets, a transversal is a set containing exactly one member of each of them. In case that the original sets are not disjoint, there are several variations. One variation is that there is a bijection f from the transversal to C such that x is an element of f(x) for each x in the transversal. Another is merely that the transversal must have non-empty intersection with each set in C.
item	Twelvefold way	http://en.wikipedia.org/wiki/Twelvefold_way	In combinatorics, a branch of mathematics, the Twelvefold Way provides a unified framework for counting permutations, combinations and partitions.
item	Two-graph	http://en.wikipedia.org/wiki/Two-graph	In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set X, such that every (unordered) quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups.
item	Umbral calculus	http://en.wikipedia.org/wiki/Umbral_calculus	In mathematics, before the 1970s, the term umbral calculus was understood to mean the surprising similarities between otherwise unrelated polynomial equations, and certain shadowy techniques that can be used to 'prove' them. These techniques were introduced in the 19th century and are sometimes called Blissard's symbolic method, and sometimes attributed to James Joseph Sylvester, who used the technique extensively, or to Edouard Lucas.
item	Zarankiewicz problem	http://en.wikipedia.org/wiki/Zarankiewicz_problem	In the mathematical field of extremal graph theory, the Zarankiewicz problem asks how many edges can be added to a bipartite graph while avoiding a specific bipartite subgraph. Initially, the Polish matematician K. Zarankiewicz proposed the problem of determining the values of the function Z3(n) (defined below) for .Contents1 Definition2 Examples3 Inequalities4 Asymptotic Bounds5 See also
item	Zero-sum problem	http://en.wikipedia.org/wiki/Zero-sum_problem	In number theory, zero-sum problems are a certain class of combinatorial questions. In general, a finite abelian group G is considered. The zero-sum problem for the integer n is the following: Find the smallest integer k such that any sequence of elements of G with length k contains n terms that sum to 0.
item	American Invitational Mathematics Examination	http://en.wikipedia.org/wiki/American_Invitational_Mathematics_Examination	The AIME (or American Invitational Mathematics Examination) is a 15-question test given since 1983 to those who score above 100 on the AMC 12 high school mathematics contest (formerly known as the AHSME), and those who score above 120 on the AMC 10.
item	American Mathematics Competitions	http://en.wikipedia.org/wiki/American_Mathematics_Competitions	The American Mathematics Contest (AMC) is the first of a series of competitions in high school mathematics that determines the United States Math Team, which competes in the International Mathematical Olympiad (IMO). This team, consisting of 6 high school students, competes in the International Mathematics Olympiad (IMO), and traditionally has performed well. The United States Math Team is the only team ever to achieve a perfect score (all six members earned perfect marks) at the 1994 IMO. That team is known as the "dream team".
item	American Regions Mathematics League	http://en.wikipedia.org/wiki/American_Regions_Mathematics_League	The American Regions Mathematics League (ARML), is an annual high school mathematics team competition held simultaneously at three locations in the United States: the University of Iowa, Penn State, and Las Vegas. Past sites have included San Jose and at Duke University.
item	Asian Pacific Mathematics Olympiad	http://en.wikipedia.org/wiki/Asian_Pacific_Mathematics_Olympiad	The Asian Pacific Math Olympiad (APMO) is a regional mathematics competition which involves countries from the Pacific Rim, such as Hong Kong, Taiwan, and Malaysia. The USA also takes part in the Olympiad. Since 1989, the APMO is held in March every year.[edit]
item	Australian Mathematics Competition	http://en.wikipedia.org/wiki/Australian_Mathematics_Competition	The Australian Mathematics Competition for the Westpac Awards is a mathematics competition run by the Australian Mathematics Trust for students from year 3 up to year 12 in Australia, and their equivalent grades in other countries. Since its inception in 1976 in the Australian Capital Territory, the participation numbers have increased to around 600,000, with around 100,000 being from outside Australia, making it the world's largest mathematics competition.Contents1 History2 Format3 Syllabus4 Awards System5 Successful students6 Impact7 References
item	Balkan Mathematical Olympiad	http://en.wikipedia.org/wiki/Balkan_Mathematical_Olympiad	The Balkan Mathematical Olympiad (BMO) is an annual contest for students from one of the member countries (Balkan area). In recent years the hosts have also invited some non-member guest countries.Contents1 Member countries1.1 Albania1.2 Bosnia &amp; Herzegovina1.3 Bulgaria1.4 Cyprus1.5 Hellas1.6 Former Yugoslav Republic of Macedonia1.7 Republic of Moldova1.8 Romania1.9 Serbia &amp; Montenegro1.10 Turkey2
item	British Mathematical Olympiad	http://en.wikipedia.org/wiki/British_Mathematical_Olympiad	The British Mathematical Olympiad forms part of the selection process for the UK International Mathematics Olympiad team. There are two rounds, the BMO1 and the BMO2.[edit]
item	Cyprus Mathematical Olympiad	http://en.wikipedia.org/wiki/Cyprus_Mathematical_Olympiad	The Cyprus Mathematical Olympiad (Greek : Κυπριακή Μαθηματική Ολυμπιάδα; CMO) is a Cyprus mathematics competition for students in every grade, organized by the Cyprus Mathematical Society. There is one paper for every grade in primary school (Dhitmotiko): 4th, 5th and 6th. There is an other paper for junior high-school (Gymnasium) and an other for high-school(Lyceum).[edit]
item	ELMO	http://en.wikipedia.org/wiki/ELMO	The ELMO is a mock IMO held at the Mathematical Olympiad Program every summer, organized and run by the students. Its acronym is fixed from year to year, but each summer produces a new idea of what it stands for.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/ELMO"			Categories: Mathematics stubs | Mathematics competitions<
item	Hong Kong Mathematical High Achievers Selection Contest	http://en.wikipedia.org/wiki/Hong_Kong_Mathematical_High_Achievers_Selection_Contest	Hong Kong Mathematical High Achievers Selection Contest (HKMHASC, Traditional Chinese: 香港青少年數學精英選拔賽) is a yearly mathematics competition for students of or below Secondary 3 in Hong Kong. It is jointly organized by Po Leung Kuk and Hong Kong Association of Science and Mathematics Education since the academic year 1998-1999. Recently, there are more than 250 secondary schools participating.Contents1 Format and Scoring2 Awards and Further Training3 See also4 External links
item	Hong Kong Mathematics Olympiad	http://en.wikipedia.org/wiki/Hong_Kong_Mathematics_Olympiad	Hong Kong Mathematics Olympiad (HKMO, Traditional Chinese: 香港數學競賽) is a Mathematics Competition held in Hong Kong every year, jointly organized by the Hong Kong Institute of Education and Hong Kong Education and Manpower Bureau. At present, more than 250 secondary schools send teams of 4-6 students of or below Form 4 to enter the competition. It is made up of a Heat Event and a Final Event, which both forbide the usage of calculators and calculation assisting equipments (e.g. printed mathematical table). Though it bears the term Mathematics Olympiad, it has no relationship with the International Mathematics Olympiad.Contents1 History2 Format and Scoring in the Heat Event3 Format and Scoring in the Final Event4 See also5 External links<li class="to
item	Inter-School Mathematics Contest	http://en.wikipedia.org/wiki/Inter-School_Mathematics_Contest	The Inter-school Mathematics Contest (ISMC) is a mathematics competition organised by Hong Kong Joint School Mathematics Society, it is usually held in May every year.[edit]
item	International Mathematical Olympiad	http://en.wikipedia.org/wiki/International_Mathematical_Olympiad	The International Mathematical Olympiad (IMO) is an annual mathematical olympiad for high school students. It is the oldest of the international science olympiads.
item	International Mathematical Olympiad Preliminary Selection Contest - Hong Kong	http://en.wikipedia.org/wiki/International_Mathematical_Olympiad_Preliminary_Selection_Contest_-_Hong_Kong	The International Mathematical Olympiad Preliminary Selection Contest - Hong Kong (in Traditional Chinese: 國際數學奧林匹克香港選拔賽) is a mathematics competition held yearly in Hong Kong. It is jointly organized by Hong Kong Education and Manpower Bureau and International Mathematical Olympiad Hong Kong Committee. It aims to select Hong Kong Team members to the International Mathematical Olympiad.[edit]
item	International Mathematics Competition for University Students	http://en.wikipedia.org/wiki/International_Mathematics_Competition_for_University_Students	The International Mathematics Competition for University Students (IMC) is an annual mathematics competition open to all undergraduates reading mathematics. It is held at a different location each year, often in Eastern Europe.
item	Junior Balkan Mathematical Olympiad	http://en.wikipedia.org/wiki/Junior_Balkan_Mathematical_Olympiad	The Junior Balkan Mathematical Olympiad (BMO) is an annual contest for students under the age of 15.5 from one of the member countries (Balkan area). In recent years the hosts have also invited some non-member guest countries.Contents1 Member countries1.1 Albania1.2 Bosnia &amp; Herzegovina1.3 Bulgaria1.4 Cyprus1.5 Hellas1.6 Former Yugoslav Republic of Macedonia1.7 Republic of Moldova1.8 Romania1.9 Serbia &amp; Montenegro1.10 Turkey<s
item	List of United States regional mathematics competitions	http://en.wikipedia.org/wiki/List_of_United_States_regional_mathematics_competitions	Many math competitions in the United States have regional restrictions. Of these, most are statewide.
item	Mandelbrot Competition	http://en.wikipedia.org/wiki/Mandelbrot_Competition	Named in honor of mathematician Benoit Mandelbrot, the Mandelbrot Competition is a mathematics competition that allows high school students to compete individually and in four-person teams. It is a "correspondence competition," meaning that the competition is sent to a school's coach and students compete at their own school on a predetermined date. Individual results and team answers are then sent back to the contest coordinators. The most notable aspects of the Mandelbrot competition are the difficulty of the problems (much like American Mathematics Competition and easier American Invitational Mathematics Examination problems) and the proof-based team round. Many past medalists at the International Mathematics Olympiad first cut their teeth on the Mandelbrot Competition.
item	Math League	http://en.wikipedia.org/wiki/Math_League	Math League is a mathematics competition for elementary, middle, and high school students in the United States. The Math League was founded in 1977 by two high school mathematics teachers, Steven R. Conrad and Daniel Flegler. Math Leagues, Inc. publishes old contests through a series of books entitled Math League Press.
item	MathChallengers	http://en.wikipedia.org/wiki/MathChallengers	Mathchallengers is the former Mathcounts in British Columbia. It is open to all grade 8 and 9 students from British Columbia. The major sponsors are the Association of Professional Engineers and Geoscientists of B.C. (APEGBC),BC Hydro, and IBM Canada.Contents1 Rules1.1 Stage 11.2 Stage 21.3 Stage 31.4 Stage 42 Scoring and ranking2.1 Individual Score2.2 Team Score3 Awards and Provicial Finals4 Past Winners4.1 Indiv
item	MathCounts	http://en.wikipedia.org/wiki/MathCounts	MathCounts is a middle school math competition held in the United States. Its founding sponsors include the CNA Foundation, National Society of Professional Engineers, and the National Council of Teachers of Mathematics.A trophy from a State MathCounts competitionContents1 Subject matter2 Competition levels3 Structure<span clas
item	Mathematical Kangaroo	http://en.wikipedia.org/wiki/Mathematical_Kangaroo	Mathematical Kangaroo (also International Mathematical Kangaroo) is an international mathematical competition with more than 30 countries that take an active part. There are eleven levels of participation: from grade 2 to grade 12. The competition has a form of a multiple choice test with five choices.[edit]
item	Mathematical Olympiad Program	http://en.wikipedia.org/wiki/Mathematical_Olympiad_Program	The Mathematical Olympiad Program or MOP is an intensive summer program held at University of Nebraska-Lincoln. The main purpose of MOP, held since 1974, is to select and train the six members of the U.S. team for the IMO. Students qualify for the program by taking the USAMO; the top twelve scorers from all grades form the "black" group, which is eligible for selection to the IMO team. The approximately eighteen highest scorers among the remaining non-graduating students (i.e. non-seniors) form the "blue" group. (These colorful designations were adapted from Karate.) In 2004, the program was expanded to include approximately thirty of the highest-scoring freshmen each year, the "red" group.
item	Mathlete	http://en.wikipedia.org/wiki/Mathlete	A mathlete is a portmanteau of the words math and athlete.
item	Mikl%C3%B3s Schweitzer Competition	http://en.wikipedia.org/wiki/Mikl%C3%B3s_Schweitzer_Competition	The Miklós Schweitzer Competition (Schweitzer Miklós Matematikai Emlékverseny in Hungarian) is an annual Hungarian mathematics competition for university undergraduates, established in 1949.
item	Mu Alpha Theta National Log 1 Contest	http://en.wikipedia.org/wiki/Mu_Alpha_Theta_National_Log_1_Contest	The Mu Alpha Theta National Log 1 Contest is a free contest sponsored by Mu Alpha Theta, the national high school mathematics honor society. Although contest is free, participation is restricted to schools with active Mu Alpha Theta chapters, and specifically to students who are Mu Alpha Theta members or Associate members.Contents1 Rounds2 Awards3 Other information4 Registering for the contest5 External link
item	National Assessment %26 Testing	http://en.wikipedia.org/wiki/National_Assessment_%26_Testing	National Assessment &amp; Testing is a company that markets five different mathematics contests: The Fall Startup Event, the Ciphering Time Trials, the Team Scamble, the Four-by-Four Competition, and the Collaborative Problem Solving Contest.Contents1 Fall Startup Event2 Ciphering Time Trials3 Team Scramble4 Four-by-Four Competition5 Collaborative Problem-Solving Contest6 External link
item	New York State Mathematics League	http://en.wikipedia.org/wiki/New_York_State_Mathematics_League	The New York State Mathematics League (NYSML) competition was originally held in 1973 and has been held annually in a different location each year since. It was founded by Alfred Kalfus. The American Regions Math League competition is based on the format of the NYSML competition.[edit]
item	North Suburban Mathematics League	http://en.wikipedia.org/wiki/North_Suburban_Mathematics_League	The North Suburban Mathematics League (NSML) is an organization of 55 high school teams in the Chicago area that compete in five math contests during the school year.
item	Primary Mathematics World Contest	http://en.wikipedia.org/wiki/Primary_Mathematics_World_Contest	The Primary Mathematics World Contest or PMWC takes place every year in Hong Kong. It was first held in 1997, and is sponsored by the Po Leung Kuk organization. The competition has attracted teams from around the world. Each team consists of 4 members, all of whom must be under the age of 13 as of September 1, and must not be enrolled in a secondary institution (or the equivalent).[edit]
item	Pui Ching Invitational Mathematics Competition	http://en.wikipedia.org/wiki/Pui_Ching_Invitational_Mathematics_Competition	Pui Ching Invitational Mathematics Competiton (Traditional Chinese: 培正數學邀請賽), is held yearly by Pui Ching Middle School since 2002. It was formerly named as Pui Ching Middle School Invitational Mathematics Competition for the first three years. At present, more than 130 secondary schools send teams to participate in the competition.[edit]
item	SEAMEO Mathematics Olympiad	http://en.wikipedia.org/wiki/SEAMEO_Mathematics_Olympiad	The Southeast Asian Mathematics Olympiad, or SEA-MO, is the Regional Mathematics Competition in Southeast Asia. This competition is organised by the Southeast Asian Ministers of Education Organization Regional Centre for Education in Science and Mathematics (SEAMEO RECSAM), which bases its operations in Penang, Malaysia. Unlike the International Mathematical Olympiad, the venue for this competition is not rotated from country to country and it has been held in Penang, Malaysia since its conception. Each participating country is represented by four participants, a team leader and deputy leader. Participation in this event is strictly by invitation only. In 2005, the nine countries which participated were Brunei, Indonesia, Cambodia, Malaysia, Philippines, Singapore, Myanmar, Thailand, and Vietnam.
item	Texas Math and Science Coaches Association	http://en.wikipedia.org/wiki/Texas_Math_and_Science_Coaches_Association	The Texas Math and Science Coaches Association or TMSCA is an organization for coaches of academic University Interscholastic League teams in Texas middle schools and high schools, specifically those that compete in mathematics- and science-related tests.Contents1 Tests2 Competitions3 Grading4 Results5 External links
item	Tokutomi Mathematics Contest	http://en.wikipedia.org/wiki/Tokutomi_Mathematics_Contest	The Hokubei Mainichi, renamed the Tokutomi Mathematics Contest, is an annual mathematics contest held in the San Jose State University in California in the United States. A chance for math fanatics aged 12 to 18 to gather, the Hokubei occurs in Mid-March. It consists of two divisions, a Junior Division for grades 7-9 and a Senior Division for grades 10-12. Each division consists of twenty challenging math problems, and one tie-breaker. The tie-breaker is usually a proof.
item	Tournament of the Towns	http://en.wikipedia.org/wiki/Tournament_of_the_Towns	The Tournament of the Towns (Турнир Городов) is a mathematics contest originating from Russia. The contest was created by mathematician Nikolai Konstantinov and has participants from over 100 cities in many different countries.[edit]
item	United States of America Mathematical Olympiad	http://en.wikipedia.org/wiki/United_States_of_America_Mathematical_Olympiad	The United States of America Mathematical Olympiad (USAMO) is a prestigious high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the AMC series of contests. Top scorers on the USAMO usually represent the United States at the International Mathematical Olympiad.Contents1 Eligibility2 Participant selection process2.1 Post-20062.2 2002-20052.3 2001 and earlier2.4 Recent qualification indices3 Test format and scoring<span class="tocnumber"
item	United States of America Mathematical Talent Search	http://en.wikipedia.org/wiki/United_States_of_America_Mathematical_Talent_Search	The United States of America Mathematical Talent Search (USAMTS) is a mathematics competition open to all United States high school students. Professor George Berzsenyi initiated the contest in 1989 under joint sponsorship of the Rose-Hulman Institute of Technology and the Consortium for Mathematics and its Applications.
item	Vlaamse Wiskunde Olympiade	http://en.wikipedia.org/wiki/Vlaamse_Wiskunde_Olympiade	The Vlaamse Wiskunde Olympiade (English: Flanders Mathematics Olympiad; VWO) is a Flemish mathematics competition for students in grades 9 through 12. Two tiers of this competition exist: one for 9th- and 10th-graders, and one for 11th- and 12th-graders.[edit]
item	Computer algebra system	http://en.wikipedia.org/wiki/Computer_algebra_system	A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.Contents1 Types of expressions2 Symbolic manipulations3 Other features4 History5 Mathematics used in computer algebra systems6 See also7 References
item	Automatic differentiation	http://en.wikipedia.org/wiki/Automatic_differentiation	In mathematics and computer algebra, automatic differentiation, or AD, sometimes alternatively called algorithmic differentiation, is a method to numerically evaluate the derivative of a function specified by a computer program. Two classical ways of doing this are:symbolically differentiate the function as an expression, and evaluate it in the point; oruse finite differences.
item	Elementary function %28differential algebra%29	http://en.wikipedia.org/wiki/Elementary_function_%28differential_algebra%29	In mathematics, an elementary function is a function built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary operations (+ - × ÷). The trigonometric functions and their inverses are assumed to be included in the elementary functions by using complex variables (i = √-1) and the relations between the trigonometric functions and the exponential and logarithm functions.
item	Elimination theory	http://en.wikipedia.org/wiki/Elimination_theory	In algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables.
item	Gr%C3%B6bner basis	http://en.wikipedia.org/wiki/Gr%C3%B6bner_basis	In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating subset of an ideal I in a polynomial ring R. One can view it as a multivariate, non-linear generalization of:the Euclidean algorithm for computation of univariate greatest common divisors,Gaussian elimination for linear systems, andmodular arithmetic.
item	Record linkage	http://en.wikipedia.org/wiki/Record_linkage	Record linkage also known as deduplication, refers to the task of finding entries that refer to the same entity in two or more files. Record linkage is an appropriate technique when you have to join data sets that do not have a unique database key in common. A data set that have been through Record linkage is said to be linked.
item	Symbolic integration	http://en.wikipedia.org/wiki/Symbolic_integration	Symbolic integration is the application of computer software to solving problems in mathematics of find the integral of an expression, but finding an expression rather than a value.
item	Symbolic mathematics	http://en.wikipedia.org/wiki/Symbolic_mathematics	Symbolic mathematics relates to the use of computers to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols. Such a system might be used for symbolic integration or differentiation, substitution of one expression into another, simplification of an expression, etc.
item	Mathematical constants	http://en.wikipedia.org/wiki/Mathematical_constants	A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. Unlike physical constants, mathematical constants are defined independently of any physical measurement.
item	Mathematical constant	http://en.wikipedia.org/wiki/Mathematical_constant	A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. Unlike physical constants, mathematical constants are defined independently of any physical measurement.
item	Mathematical constants %28sorted by continued fraction representation%29	http://en.wikipedia.org/wiki/Mathematical_constants_%28sorted_by_continued_fraction_representation%29	This is a list of mathematical constants sorted by their representations as continued fractions:
item	Ap%C3%A9ry%27s constant	http://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant	In mathematics, Apéry's constant is a curious number that occurs in a variety of situations. It is defined as the number ζ(3),
item	Brun%27s constant	http://en.wikipedia.org/wiki/Brun%27s_constant	In 1919 Viggo Brun showed that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a mathematical constant now called Brun's constant for twin primes and usually denoted by B2 (sequence A065421 in OEIS):
item	Champernowne constant	http://en.wikipedia.org/wiki/Champernowne_constant	In mathematics, the Champernowne constant C10 is a certain real number, named after mathematician D. G. Champernowne. It is a simple number to construct, which has some important properties.Contents1 Normality2 Computations3 Transcendence4 References5 External links
item	Conic constant	http://en.wikipedia.org/wiki/Conic_constant	The conic constant is a quantity describing conic sections, and is represented by the letter K. It is given byK = −e²,
item	De Bruijn-Newman constant	http://en.wikipedia.org/wiki/De_Bruijn-Newman_constant	The de Bruijn-Newman constant, denoted by Λ, is a mathematical constant and is defined via the zeros of a certain function H(λ, z), where λ is a real parameter and z is a complex variable. H has only real zeros if and only if λ ≥ Λ. The constant is closely connected with Riemann's hypothesis on the zeros of the general Euler-Riemann's ζ-function. In brief, the Riemann hypothesis is equivalent to the conjecture that Λ ≤ 0.
item	E %28mathematical constant%29	http://en.wikipedia.org/wiki/E_%28mathematical_constant%29	The mathematical constant e is the base of the natural logarithm. It is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms. (Note: This constant is not to be confused with γ, the Euler-Mascheroni constant, which is itself sometimes called Euler's constant.) It is one of the most important numbers in mathematics, alongside the additive and multiplicative identities 0 and 1, the imaginary unit i, and π, the circumference to diameter ratio for any circle. It has a number of equivalent definitions; some of them are given below. To the 20th decimal place:e ≈ 2.71828 18284 59045 23536Contents1 History2 Definitions3 Properties<
item	Embree-Trefethen constant	http://en.wikipedia.org/wiki/Embree-Trefethen_constant	In mathematics, the Embree-Trefethen constant is a threshold value in number theory labelled β*.
item	Erd%C5%91s%E2%80%93Borwein constant	http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Borwein_constant	The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdős and Peter Borwein.
item	Euler-Mascheroni constant	http://en.wikipedia.org/wiki/Euler-Mascheroni_constant	The Euler-Mascheroni constant is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series and the natural logarithm:
item	Feigenbaum constants	http://en.wikipedia.org/wiki/Feigenbaum_constants	The Feigenbaum constants are two mathematical constants named after the mathematician Mitchell Feigenbaum. Both express ratios in a bifurcation diagram.
item	Frans%C3%A9n-Robinson constant	http://en.wikipedia.org/wiki/Frans%C3%A9n-Robinson_constant	The Fransén-Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1 / Γ(x), and the positive x axis. That is,
item	Gauss%27s constant	http://en.wikipedia.org/wiki/Gauss%27s_constant	In mathematics, Gauss's constant, denoted by G, is defined as the reciprocal of the arithmetic-geometric mean of 1 and the square root of 2:
item	Gelfond%27s constant	http://en.wikipedia.org/wiki/Gelfond%27s_constant	In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is
item	Gelfond%E2%80%93Schneider constant	http://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constant	The Gelfond–Schneider constant is
item	Glaisher-Kinkelin constant	http://en.wikipedia.org/wiki/Glaisher-Kinkelin_constant	In mathematics, the Glaisher-Kinkelin constant, typically denoted A, is a mathematical constant, related to the K-function and the Barnes G-function. It is named after mathematicians James Whitbread Lee Glaisher and Hermann Kinkelin.
item	Golden ratio	http://en.wikipedia.org/wiki/Golden_ratio	Two quantities are said to be in the golden ratio if "the whole (that is, the sum of the two parts) is to the larger part as the larger part is to the smaller part", stated mathematically as:
item	6174 %28number%29	http://en.wikipedia.org/wiki/6174_%28number%29	6174CardinalSix thousand one hundred seventy-fourOrdinalSix thousand one hundred seventy-fourthFactorizationBinary1100000011110Hexadecimal181E
item	Khinchin%27s constant	http://en.wikipedia.org/wiki/Khinchin%27s_constant	In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, the infinitely many denominators ai of the continued fraction expansion of x have an astonishing property: their geometric mean is a constant, known as Khinchin's constant, which is independent of the value of x.
item	Landau%27s constants	http://en.wikipedia.org/wiki/Landau%27s_constants	In complex analysis, Landau's constants are certain mathematical constants that describe the behaviour of holomorphic functions defined on the unit disk. Consider the set F of all those holomorphic functions f on the unit disk for which
item	Landau-Ramanujan constant	http://en.wikipedia.org/wiki/Landau-Ramanujan_constant	In mathematics, the Landau-Ramanujan constant occurs in a number theory result that the proportion of positive integers less than x which are the sum of two square numbers is, for large x, roughly proportional to
item	Lebesgue constant	http://en.wikipedia.org/wiki/Lebesgue_constant	Two kinds of constants are usually called Lebesgue constants (after Henri Lebesgue):In the process of interpolation, the Lebesgue constants (with respect to a set of nodes) measure the precision of the polynomial interpolation at those nodes in regard with the best polynomial approximation.In approximation theory, the Lebesgue constants are related to Fourier series.This is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Lebesgue_constant"			Categories: Disambiguation | <a href="/wik
item	Legendre%27s constant	http://en.wikipedia.org/wiki/Legendre%27s_constant	In mathematics, Legendre's constant is a "phantom" that does not really exist.
item	L%C3%A9vy%27s constant	http://en.wikipedia.org/wiki/L%C3%A9vy%27s_constant	In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions. In 1936 French mathematician Paul Lévy showed that the denominators qn of the convergents of the continued fraction expansions of almost all real numbers satisfy
item	Meissel-Mertens constant	http://en.wikipedia.org/wiki/Meissel-Mertens_constant	The Meissel-Mertens constant, also referred to as Mertens constant, Kronecker's constant, Hadamard-de la Vallée-Poussin constant or prime reciprocal constant, is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm:
item	Mills%27 constant	http://en.wikipedia.org/wiki/Mills%27_constant	In mathematics, it is known that there exist real positive numbers θ such that the integer part of
item	Omega constant	http://en.wikipedia.org/wiki/Omega_constant	The Omega constant is a mathematical constant defined by.
item	Particular values of the Gamma function	http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function	The Gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general.Contents1 Integers and half-integers2 General rational arguments3 Other constants4 See also5 References6 External links
item	Plastic number	http://en.wikipedia.org/wiki/Plastic_number	The plastic number or silver number is the unique real solution of the equation
item	Prouhet-Thue-Morse constant	http://en.wikipedia.org/wiki/Prouhet-Thue-Morse_constant	In mathematics and its applications, the Prouhet-Thue-Morse constant is the number τ whose binary expansion is the Prouhet-Thue-Morse sequence. That is,
item	Ramanujan-Soldner constant	http://en.wikipedia.org/wiki/Ramanujan-Soldner_constant	In mathematics, the Ramanujan-Soldner constant is a mathematical constant defined as the unique positive zero of the logarithmic integral function.
item	Sierpi%C5%84ski%27s constant	http://en.wikipedia.org/wiki/Sierpi%C5%84ski%27s_constant	The Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is by limiting the expression:
item	Silver ratio	http://en.wikipedia.org/wiki/Silver_ratio	The silver ratio is a mathematical constant. Its name is an allusion to the golden ratio.Contents1 Definition1.1 Definition as 1 plus the square root of 21.2 Definition as 2, 2, 2...2 Properties3 Silver means4 Silver rectangles5 Construction6 External link
item	Somos%27 quadratic recurrence constant	http://en.wikipedia.org/wiki/Somos%27_quadratic_recurrence_constant	In mathematics, Somos' quadratic recurrence constant is defined as the number
item	Square root of 2	http://en.wikipedia.org/wiki/Square_root_of_2	The square root of 2, , also known as Pythagoras' constant, is the positive real number which, when multiplied by itself, gives the product 2. Its numerical value approximated to 65 decimal places (sequence A002193 in OEIS) is:1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799.
item	Stieltjes constants	http://en.wikipedia.org/wiki/Stieltjes_constants	In mathematics, the Stieltjes constants are the numbers γk that occur in the Laurent series expansion of the Riemann zeta function:
item	Viswanath%27s constant	http://en.wikipedia.org/wiki/Viswanath%27s_constant	Viswanath's constant is a mathematical constant, occurring in number theory - more specifically in the study of randomized Fibonacci sequences. The value of Viswanath's constant is approximately 1.13198824.Contents1 Definition2 Explication3 Significance4 See also5 External links6 References
item	Zeta constant	http://en.wikipedia.org/wiki/Zeta_constant	In mathematics, a zeta constant is a number obtained by plugging an integer into the Riemann zeta function. This article provides a number of series identities for the zeta function for integer values.Contents1 The Riemann zeta function at 0 and 12 Positive integers2.1 Even positive integers2.2 Odd positive integers2.2.1 ζ(5)2.2.2 ζ(7)2.2.3 ζ(2n+1)3 Negative integers4 Derivatives5 References
item	Arcadia %28play%29	http://en.wikipedia.org/wiki/Arcadia_%28play%29	Arcadia is a 1994 play by Tom Stoppard about the relationship between past and present in an English country house. The play's title is a reference to the Latin phrase et in Arcadia ego which states that death is always present, even in Arcadia (a pastoral paradise).Contents1 Synopsis2 Themes3 Productions and responses4 External links
item	Dirk Niblick of the Math Brigade	http://en.wikipedia.org/wiki/Dirk_Niblick_of_the_Math_Brigade	Dirk Niblick of the Math Brigade was an animated segment on the PBS television show Square One Television.
item	Apostolos Doxiadis	http://en.wikipedia.org/wiki/Apostolos_Doxiadis	Apostolos Doxiadis (Greek: Απόστολος Δοξιάδης) (b. 1953 in Brisbane, Queensland in Australia) and raised in Greece is a Greek writer.
item	Ethnocomputing	http://en.wikipedia.org/wiki/Ethnocomputing	Ethnocomputing is the study of the interactions between computing and culture. It is carried out through theoretical analysis, empirical investigation, and design implementation. It includes research on the impact of computing on society, as well as the reverse: how cultural, historical, personal, and societal origins and surroundings cause and affect the innovation, development, diffusion, maintenance, and appropriation of computational artifacts or ideas. From the ethnocomputing perspective, no computational technology is culturally "neutral," and no cultural practice is a computational void. Instead of considering culture to be a hindrance for software engineering, culture should be seen as a resource for innovation and design.
item	Ethnomathematics	http://en.wikipedia.org/wiki/Ethnomathematics	Ethnomathematics is the study of mathematics that considers the culture in which mathematics arises. It especially focuses on the mathematics that is part of general culture, rather than formal, academic mathematics, though some ethnomathematicians study formal mathematics as an artifact of a particular culture or cultures. The goal of ethnomathematics is to contribute both to the understanding of culture and the understanding of mathematics, but mainly to the relationship between the two.Contents1 Subject matter1.1 Numerals1.2 Names for numbers1.3 Finger counting1.4 Games of skill1.5 Mathematics in folk art2 Criticism3 See also4 Further reading<span clas
item	Leonardo da Vinci	http://en.wikipedia.org/wiki/Leonardo_da_Vinci	Leonardo di ser Piero da Vinci (April 15, 1452 – May 2, 1519) was an immensely multi-talented Italian Renaissance Roman Catholic[1] polymath: architect, anatomist, sculptor, engineer, inventor, geometer, musician and painter. He has been described as the archetype of the "Renaissance man" and as a universal genius, a man infinitely curious and infinitely inventive. He is widely considered to be one of the greatest painters of all time.<div class="thumbcap
item	Mathematics and architecture	http://en.wikipedia.org/wiki/Mathematics_and_architecture	Mathematics and architecture have always enjoyed a close association with each other, not only in the sense that the latter is informed by the former, but also in that both share the search for order and beauty, the former in nature and the latter in buildings. Mathematics is indispensable to the understanding of structural concepts and calculations. It is also employed as visual ordering element or as a means to achieve harmony with the universe. Here geometry becomes the guiding principle.Golden rectangle
item	Mathematics and art	http://en.wikipedia.org/wiki/Mathematics_and_art	Mathematics and art have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid, the Parthenon, the Colosseum. The golden ratio is used in the design and layout of paintings such as The Roses of Heliogabalus. Recent studies show that the golden ratio also plays a role in the human perception of beauty in body shapes and faces.Melancholia I
item	Mathnet	http://en.wikipedia.org/wiki/Mathnet	Mathnet, a segment on Square One and spoof of Dragnet, featured detectives at the Los Angeles Police Department who solved mysteries using their mathematical skills. There were two main characters: detectives Kate Monday (Beverly Leech) and George Frankly (Joe Howard). Later on in the series, Kate Monday was replaced by Pat Tuesday (Toni DiBuono) after the show's setting moved to New York City in the third season. James Earl Jones played a recurring role as the chief Thad Green. He also briefly appears in season 4 and indicates he knows Pat Tuesday. When the duo was transferred to New York, Captain Joe Greco (Emilio Del Pozo) became their leader.
item	NUMB3RS	http://en.wikipedia.org/wiki/NUMB3RS	Numbers (NUMB3RS) is an American television show that follows FBI Special Agent Don Eppes (Rob Morrow) and his mathematical genius brother, Charlie Eppes (David Krumholtz), who develops formulae to predict the actions of various criminals. It was created by Nicolas Falacci and Cheryl Heuton, and airs on the CBS network in the US.Contents1 Introduction1.1 NUMB3RS and Mathematics2 Cast and Characters2.1 Main Characters2.2 Secondary Characters3</s
item	Possible Worlds %28play%29	http://en.wikipedia.org/wiki/Possible_Worlds_%28play%29	Possible Worlds, written by John Mighton, is an unusual play. Part murder mystery, part science-fiction, and part mathematical philosophy, it follows the multiple parallel lives of the mysterious George Barber. At the play's beginning, George is found dead, with his brain missing. Two detectives set out to uncover the truth behind his grisly death, and stumble upon several strange characters.
item	Proof %28play%29	http://en.wikipedia.org/wiki/Proof_%28play%29	Proof is a play by David Auburn. It won the 2001 Pulitzer Prize for Drama and the 2001 Tony Award for Best Play.
item	Differential equations	http://en.wikipedia.org/wiki/Differential_equations	In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. Many of the fundamental laws of physics, chemistry, biology and economics can be formulated as differential equations. The mathematical theory of differential equations has developed together with the sciences where the equations originate and where the results find application. Diverse scientific fields often give rise to identical problems in differential equations. In such cases, the mathematical theory can unify otherwise quite distinct scientific fields. A celebrated example is Fourier's theory of the conduction of heat in terms of sums of trigonometric functions Fourier series, which finds application in the propagation of sound, the propagation of electric and magnetic fields, radio waves, optics, elasticity, spectral analysis of radiation, and other scientific fields.
item	Differential equation	http://en.wikipedia.org/wiki/Differential_equation	In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. Many of the fundamental laws of physics, chemistry, biology and economics can be formulated as differential equations. The mathematical theory of differential equations has developed together with the sciences where the equations originate and where the results find application. Diverse scientific fields often give rise to identical problems in differential equations. In such cases, the mathematical theory can unify otherwise quite distinct scientific fields. A celebrated example is Fourier's theory of the conduction of heat in terms of sums of trigonometric functions Fourier series, which finds application in the propagation of sound, the propagation of electric and magnetic fields, radio waves, optics, elasticity, spectral analysis of radiation, and other scientific fields.
item	Adomian decomposition method	http://en.wikipedia.org/wiki/Adomian_decomposition_method	The Adomian decomposition method (ADM) is a non-numerical method for solving nonlinear differential equations, both ordinary and partial. The general direction of this work is towards a unified theory for Partial Differential Equations (PDE). The method was developed by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia.&#160;This mathematics-related article is a stub. You can help Wikipedia by expanding it.Retrieved from "http://en.wikipedia.org/wiki/Adomian_decomposition_method"			<a href="/w/index.php?title=Spe
item	Autonomous system %28mathematics%29	http://en.wikipedia.org/wiki/Autonomous_system_%28mathematics%29	In mathematics, an autonomous system is a system of differential equations of the form
item	Bendixson-Dulac theorem	http://en.wikipedia.org/wiki/Bendixson-Dulac_theorem	In mathematics, the Bendixson-Dulac theorem on dynamical systems states that if there exists φ(x,y)
item	Boundary condition	http://en.wikipedia.org/wiki/Boundary_condition	In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. In the problems most frequently considered, only one of the infinitely many solutions of the differential equation satisfies the boundary conditions. In a physical model simulation, the boundary conditions describe the behavior of the simulation at the edges of the simulation region.
item	Courant%E2%80%93Friedrichs%E2%80%93Lewy condition	http://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%80%93Lewy_condition	In mathematics, the Courant–Friedrichs–Lewy condition (CFL condition) is a condition for certain algorithms for solving partial differential equations to be convergent (not to be confused with numerically stable, though for an explicit it often is within a small constant factor of the stability condition). As a consequence, the time step must be less than a certain time in many explicit time-marching computer simulations, otherwise the simulation will produce wildly incorrect results. The condition is named after Richard Courant, Kurt Friedrichs and Hans Lewy who described it in their 1928 paper.
item	Covariant classical field theory	http://en.wikipedia.org/wiki/Covariant_classical_field_theory	In recent years, there has been renewed interest in covariant classical field theory. Here, dynamics are phrased in the context of a finite-dimensional space of fields at a given event in spacetime. Nowadays, it is well known that jet bundles are the correct domain for such a description. This article provides some of the geometric structure to the covariant formalism of first-order classical field theories.
item	Delay differential equation	http://en.wikipedia.org/wiki/Delay_differential_equation	In mathematics, delay differential equations (DDEs) are a type of differential equation, in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.
item	Differential Galois theory	http://en.wikipedia.org/wiki/Differential_Galois_theory	//[edit]Motivation and basic ideaIn mathematics, the antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions. The most often encountered example of such a function is exp(-x2), whose antiderivative is (up to constants) the error function, familiar from statistics. Other examples include sin(x)/x and xx.It should be realised that the notion of an elementary function is merely a matter of convention. One could choose to add the error function to the list of elementary functions, and with this new list, the antiderivative of exp(-x2) is elementary. However, no matter how long the list of so called elementary functions, there will still be functions on the list whose antiderivatives are not.The machinery of differential Galois theory allows one to determine when an elementary function does or does not have an antiderivative which can be expressed as an elementary function. Differential Galois theory is a theory based on the model of Galois theory. Whereas algebraic Galois theory studies extension
item	Differential algebraic equation	http://en.wikipedia.org/wiki/Differential_algebraic_equation	In mathematics, differential algebraic equations (DAEs) are a general form of differential equation, given in implicit form. They can be written
item	Dirichlet boundary condition	http://en.wikipedia.org/wiki/Dirichlet_boundary_condition	In mathematics, a Dirichlet boundary condition imposed on an ordinary differential equation or a partial differential equation specifies the values a solution is to take on the boundary of the domain.
item	Euler approximation	http://en.wikipedia.org/wiki/Euler_approximation	The Euler approximation is a numerical method of solving differential equations, mostly useful when the solution to a differential equation cannot be found analytically. Euler approximations are found using a recursive formula that uses slope information, given by the derivative, to approximate a value on a solution close to an initial point. It is named after the mathematician Leonhard Euler.
item	Fractional differential equation	http://en.wikipedia.org/wiki/Fractional_differential_equation	Fractional differential equations are a generalization of differential equations through the application of fractional calculus.[edit]
item	Green%27s function	http://en.wikipedia.org/wiki/Green%27s_function	In mathematics, a Green's function is a type of function used to solve inhomogeneous differential equations subject to boundary conditions. Technically, a Green's function of a linear operator L acting on distributions over a manifold M, at a point x0, is any solution of (Lf)(x) = δ(x − x0), where δ is the Dirac delta function. If the kernel of L is nontrivial, then the Green's function is not unique. However, in practice, some combination of symmetry, boundary conditions and/or other externally imposed criteria would give us a unique Green's function. Also, please note that Green's functions in general are distributions, not necessarily proper functions.
item	Hurwitz matrix	http://en.wikipedia.org/wiki/Hurwitz_matrix	In mathematics, a square matrix A is called a Hurwitz matrix if all eigenvalues of A have strictly negative real part, that is,
item	Illustration of the shooting method	http://en.wikipedia.org/wiki/Illustration_of_the_shooting_method	In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to the solution of an initial value problem. The following exposition may be clarified by this illustration of the shooting method.
item	Initial value problem	http://en.wikipedia.org/wiki/Initial_value_problem	In mathematics, an initial value problem is a statement of a differential equation together with specified value of the unknown function at a given point in the domain of the solution. Calling the given point t0 and the specified value y0, the initial value problem is
item	Jet bundle	http://en.wikipedia.org/wiki/Jet_bundle	In differential geometry, the jet bundle is a certain construction which makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to write differential equations on sections of a fiber bundle in an invariant form.
item	Lanchester%27s laws	http://en.wikipedia.org/wiki/Lanchester%27s_laws	Lanchester's laws are mathematical formulae for calculating the relative strengths of a predator/prey pair. This article is concerned with military forces.
item	Laplace transform	http://en.wikipedia.org/wiki/Laplace_transform	In mathematics, the Laplace transform is a powerful technique for analyzing linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems, to name just a few. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.
item	Lax pair	http://en.wikipedia.org/wiki/Lax_pair	In mathematics, in the theory of differential equations, a Lax pair is a pair of of time-dependent matrices that describe certain solutions of differential equations. They were developed by Peter Lax to discuss solitons in continuous media. The inverse scattering transform makes use of the Lax equations to solve a variety of the so-called exactly solvable models of physics.[edit]
item	Linear differential equation	http://en.wikipedia.org/wiki/Linear_differential_equation	In mathematics, a linear differential equation is a differential equation of the formLy = f,
item	List of solution strategies for differential equations	http://en.wikipedia.org/wiki/List_of_solution_strategies_for_differential_equations	ExactMethod of undetermined coefficientsIntegrating factorFor y' + a(x)y = b(x) let  thenMethod of variation of parametersSeparable differential equation[edit]
item	Li%C3%A9nard%27s theorem	http://en.wikipedia.org/wiki/Li%C3%A9nard%27s_theorem	In mathematics, more specifically in dynamical systems, Liénard's theorem guarantees the existence of a limit cycle for a system if it can be described in the form
item	Logistic function	http://en.wikipedia.org/wiki/Logistic_function	A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops.
item	Lotka-Volterra equation	http://en.wikipedia.org/wiki/Lotka-Volterra_equation	The Lotka-Volterra equations, also known as the predator-prey equations, are a pair of first order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey. They were proposed independently by Alfred J. Lotka in 1925 and Vito Volterra in 1926. A classic model using the equations is of the population dynamics of the lynx and the snowshoe hare, popularised due to the extensive data collected on the relative populations of the two species by the Hudson Bay company during the 19th century.Contents1 The equations2 Physical meanings of the equations2.1 Prey2.2 Predators3 Solutions to the equations4 <
item	Method of undetermined coefficients	http://en.wikipedia.org/wiki/Method_of_undetermined_coefficients	In mathematics, the method of undetermined coefficients is an approach to solving certain ordinary differential equations and recurrence relations.
item	Nash-Moser theorem	http://en.wikipedia.org/wiki/Nash-Moser_theorem	The Nash-Moser theorem, attributed to mathematicians John Forbes Nash and Jurgen Moser, uses differential calculus to solve a particularly difficult set of partial differential equations. It is a form of implicit function theorem.
item	Newmark-beta method	http://en.wikipedia.org/wiki/Newmark-beta_method	The Newmark-beta method is a method of numerical integration used to solve differential equations. It is used in finite element analysis to model dynamic systems.
item	Nullcline	http://en.wikipedia.org/wiki/Nullcline	Nullclines are encountered in two-dimensional systems of differential equationsx' = F(x,y)y' = G(x,y).
item	Shooting method	http://en.wikipedia.org/wiki/Shooting_method	In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to the solution of an initial value problem. The following exposition may be clarified by this illustration of the shooting method.
item	Singular perturbation	http://en.wikipedia.org/wiki/Singular_perturbation	Singular perturbation is a mathematical operation, which can be used on the class of linear/non-linear problems where two dynamics operating on different time scales exist. For instance, an electrically driven robot manipulator can have slower mechanical dynamics and faster electrical dynamics. In such cases, we can divide the systems into two subsystems one corresponding to faster dynamics and other corresponding to slower dynamics and then designing controllers for each one of them separately. Through singular perturbation technique, we can make these two subsystems independent of each other thereby simplifying the control problem.
item	Singular solution	http://en.wikipedia.org/wiki/Singular_solution	A singular solution ys(x) of an ordinary differential equation is a solution that is tangent to every solution from the family of general solutions. By tangent we mean that there is a point x where ys(x) = yc(x) and y's(x) = y'c(x) where yc is any general solution.
item	Stochastic differential equation	http://en.wikipedia.org/wiki/Stochastic_differential_equation	A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process.[edit]
item	Structural stability	http://en.wikipedia.org/wiki/Structural_stability	In mathematics, structural stability is an aspect of stability theory concerning whether a given function is sensitive to a small perturbation. The general idea is that a function or flow is structurally stable if any other function or flow close enough to it has similar dynamics (from the topological viewpoint, analogous to Lyapunov stability), which essentially means that the dynamics will not change under small perturbations.[edit]
item	Total derivative	http://en.wikipedia.org/wiki/Total_derivative	In mathematics, a total derivative is a combination of partial derivatives. Specifically, it may mean either of the following:a derivative which takes indirect dependencies into account;a differential operator involving the sum of all the partial derivatives with respect to all variables.[edit]
item	Template:Disambig	http://en.wikipedia.org/wiki/Template:Disambig	
item	Abelian	http://en.wikipedia.org/wiki/Abelian	Abelian, in mathematics, is used in many different definitions:
item	Adjoint	http://en.wikipedia.org/wiki/Adjoint	In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type(Ax,y) = [x, By].
item	Antisymmetric	http://en.wikipedia.org/wiki/Antisymmetric	In set theory, the adjective antisymmetric usually refers to an antisymmetric relation.
item	Big Omega function	http://en.wikipedia.org/wiki/Big_Omega_function	The notation Ω(&#160;) has two meanings in mathematics:f = Ω(g) means that the function f dominates g in some limit, see asymptotic notation.Ω(n) is the total number of prime factors of n, counting multiple factors multiple times.
item	Boundedness	http://en.wikipedia.org/wiki/Boundedness	The term bounded appears in different parts of mathematics where a notion of "size" can be given. The basic intuitive meaning common to all of them is that something is of finite size, and that this is the case if it is smaller than some other object that has a finite size. (Otherwise it is unbounded.)In topology, a subset of a metric space is bounded if it can be contained in some ball of a certain radius.In functional analysis, a subset A of a topological vector space is bounded if for every neighbourhood N of the zero vector there exists some scalar α to that A is a subset of αNA function is bounded if its range is a bounded set.A linear transformation is bounded if the image o
item	Carath%C3%A9odory%27s theorem	http://en.wikipedia.org/wiki/Carath%C3%A9odory%27s_theorem	In mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory:Carathéodory's theorem (convex hull) about the convex hulls of sets in Euclidean spaceCarathéodory's theorem (measure theory) about outer measures in measure theoryCarathéodory's extension theorem about the extension of a measure.Carathéodory's theorem (conformal mapping)Borel–Carathéodory theorem, about the boundedness of a complex analytic function.Carathéodory-Jacobi-Lie theorem, a generalization of Darboux's theorem in symplectic topology.This is a disambiguation page: a list of articles associated with the same tit
item	Cartan	http://en.wikipedia.org/wiki/Cartan	There are two well-known mathematicians with the surname Cartan:Élie Cartan orhis son, the mathematician Henri Cartan.
item	Cauchy theorem	http://en.wikipedia.org/wiki/Cauchy_theorem	In Mathematics, Augustin Louis Cauchy has his name on several theorems. These includeCauchy integral theorem or formula in complex analysisCauchy's mean value theoremCauchy's theorem in group theoryCauchy's theorem concerning differential equationsThis is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Cauchy_theorem"			Categories: Disambiguation | Mathematical disa
item	Cauchy%27s test	http://en.wikipedia.org/wiki/Cauchy%27s_test	Cauchy's test may refer to:Cauchy's root testCauchy's condensation testthe integral test for convergence, sometimes known as the Maclaurin-Cauchy test
item	Character %28mathematics%29	http://en.wikipedia.org/wiki/Character_%28mathematics%29	There are several meanings of the word character in mathematics, although all are related to the idea of using fields (most of the time the complex numbers), to study a more abstract algebraic structure.Contents1 Number-theoretic characters2 Representation characters3 Algebraic characters4 External link
item	Characteristic function	http://en.wikipedia.org/wiki/Characteristic_function	In mathematics, characteristic function can refer to any of several distinct concepts:The most common and universal usage is as a synonym for indicator function, that is the functionwhich for every subset A of X, has value 1 at points of A and 0 at points of X&#160;−&#160;A.The characteristic state function in statistical mechanics.In probability theory, the characteristic function of any probability distribution on the real line is given by the following formula, where X is any random variable with the distribution in question:where "E" means expected value. See characteristic function (probability theory).The characteristic polynomial in <a
item	Chebyshev%27s theorem	http://en.wikipedia.org/wiki/Chebyshev%27s_theorem	Chebyshev's theorem is a name given to several theorems proven by Russian mathematician Pafnuty Chebyshev:Bertrand's postulateChebyshev's inequalityRetrieved from "http://en.wikipedia.org/wiki/Chebyshev%27s_theorem"			Category: Mathematical disambiguation																Views						 Article				 Discussion				 Edit this page				 History						Personal tools									Sign in / create account						</d
item	Class	http://en.wikipedia.org/wiki/Class	Class may refer to:Appliance classes, in the electric appliance manufacturing industry.Character class, in role-playing games, or other genres such as the FPS Team FortressClass (biology), a rank used in taxonomy.Class (computer science), related to object-oriented programming.Class (education), a group of students attending a specific course or lesson, or short for a classroom.Class (film), a movie released in 1983.Class (philosophy), distinguishes between classes and types.Class (sailing), where boats of identical construction race against each other.Class (set theory), in mathematics.Class (warez), in the warez scene.Classes of US Senators.Social class, in sociology and economics.The classification of United States railroads according to revenue. See the following:Class I railroad<a href="/wiki/Class_II_railroad" title="Class II railroad"
item	Classification theorem	http://en.wikipedia.org/wiki/Classification_theorem	There exist several classification theorems in mathematics:Classification theorem of surfacesClassification of two-dimensional closed manifoldsEnriques-Kodaira classification of algebraic surfaces (complex dimension two, real dimension four)Nielsen-Thurston classification which characterizes homeomorphisms of a compact surfaceClassification of finite simple groupsArtin–Wedderburn theorem — a classification theorem for semisimple ringsThis is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Classification_theorem"			<a href="/w/index.php?title=Special:Categories&am
item	Closed form	http://en.wikipedia.org/wiki/Closed_form	In mathematics, closed form can mean:a finitary expression, rather than one involving (for example) an infinite series, or use of recursion - this meaning usually occurs in a phrase like solution in closed form and one also says closed formula;a closed differential form: see closed and exact differential forms.This is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Closed_form"			Categories: Disambiguation | Mathematical disambiguation			<!-- end c
item	Compact %28disambiguation%29	http://en.wikipedia.org/wiki/Compact_%28disambiguation%29	Compact may mean:Compact (newspaper), a broadsheet-quality newspaper printed in a tabloid format.Compact (soap opera), a 1960s British soap opera.a diplomatic contract or covenant among parties, sometimes known as a pact, treaty, or an interstate compact;A small, typically round case, usually containing one, two or all of the following: a mirror, pressed powder, and/or a powder puffCompact car[edit]
item	Completeness	http://en.wikipedia.org/wiki/Completeness	In mathematics and related technical fields, a mathematical object is complete if nothing needs to be added to it. This is made precise in various ways, several of which have a related notion of completion. It should be noted that "complete" here is just a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion". See, for example, algebraically closed field, compactification, or Gödel's incompleteness theorem.A metric space (or uniform space) is complete if every Cauchy sequence in it converges. See complete space.In functional analysis, a subset S of a topological vector space V is complete if its span is dense in V. If V is separable, it follows that any vector in V can be written as a (possibly infinite) 
item	Concave	http://en.wikipedia.org/wiki/Concave	The word concave means curving in or hollowed inward. The term is most commonly used to refer to:Concave lens, a lens with inward-curving (concave) surfaces.Concave polygon, a polygon which is not convex.Concave function, a type of function which is related to convex functions.
item	Congruent transformation	http://en.wikipedia.org/wiki/Congruent_transformation	In mathematics, a congruent transformation (or congruence transformation) is:Another term for an isometry; see congruence (geometry).A transformation of the form A → PTAP, where A and P are square matrices, P&#160;is invertible, and PT denotes the transpose of&#160;P; see congruence in linear algebra.This is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Congruent_transformation"			Categories: Disambiguation | <a href="/wiki/Category:Mathematical_disambiguation" title="
item	Conjugation	http://en.wikipedia.org/wiki/Conjugation	Conjugation may refer to:Grammatical conjugation, the modification of a verb from its basic form.Latin conjugation, Spanish conjugation and the English verb, each with complex conjugation forms.Marriage, relationship between two individuals.
item	Connected component	http://en.wikipedia.org/wiki/Connected_component	Connected components are part of topology and graph theory, two related branches of mathematics.For the graph-theoretic concept, see connected component (graph theory).For the topological concept, see connected space; see also identity component (in a topological group).This is a disambiguation page: a list of articles associated with the same title. If an internal link referred you to this page, you may wish to change the link to point directly to the intended article.Retrieved from "http://en.wikipedia.org/wiki/Connected_component"			Categories: Disambiguation | Mathematical disambiguation | <a href="/wiki/Category:Components" title="Category:Components"
item	Constructibility	http://en.wikipedia.org/wiki/Constructibility	In mathematics, there are several notions of constructibility:a point in the Euclidean plane that can be constructed with compass and straightedge. Also, any complex number associated to such a point; see constructible number.a regular polygon that can be constructed with compass and straightedge; see constructible polygon.a theorem that can be proved by const