Lists of mathematics topics cover a variety of topics related to

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables. They also cover equations named after people, societies, mathematicians, journals, and meta-lists. The purpose of this list is ''not'' similar to that of the

Mathematics Subject Classification The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme collaboratively produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH. ...

formulated by the American Mathematical Society. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, ''

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

'' and '' Zentralblatt MATH''. This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage.

Basic mathematics

This branch is typically taught in secondary education or in the first year of university. *

Outline of arithmetic Arithmetic is an elementary branch of mathematics that is widely used for tasks ranging from simple day-to-day counting to advanced science and business calculations. Essence of arithmetic *Elementary arithmetic * Decimal arithmetic *Decimal po ...

Outline of discrete mathematics Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such a ...

* List of calculus topics * List of geometry topics **

Outline of geometry Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Classical branches * Geometry — * Analytic geomet ...

List of trigonometry topics Trigonometry is a branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena ...

***

Outline of trigonometry Trigonometry is a branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena ...

*** List of trigonometric identities *

List of logarithmic identities In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes. Trivial identities : Explanations By definition, we know that: :\color \log \color ...

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, see list of integrals. ''Note:'' ''x'' > 0 is assumed throughout this article, and the constant of integration ...

* List of set identities and relations * List of topics in logic

Areas of advanced mathematics

As a rough guide, this list is divided into pure and applied sections although in reality, these branches are overlapping and intertwined.

Pure mathematics

Algebra

Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called ''group''. *

Outline of algebra Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determini ...

Glossary of field theory Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring ...

* Glossary of group theory * Glossary of linear algebra * Glossary of ring theory * List of abstract algebra topics * List of algebraic structures * List of Boolean algebra topics * List of category theory topics * List of cohomology theories * List of commutative algebra topics * List of homological algebra topics *

List of group theory topics In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all b ...

List of representation theory topics This is a list of representation theory topics, by Wikipedia page. See also list of harmonic analysis topics, which is more directed towards the mathematical analysis aspects of representation theory. See also: Glossary of representation theory ...

List of linear algebra topics This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations Linear equation *System of linear equa ...

* List of reciprocity laws

Calculus and analysis

Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis evolved from calculus. *

Glossary of tensor theory This is a glossary of tensor theory. For expositions of tensor theory from different points of view, see: * Tensor * Tensor (intrinsic definition) * Application of tensor theory in engineering science For some history of the abstract theory see ...

List of complex analysis topics Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied ...

List of functional analysis topics This is a list of functional analysis topics, by Wikipedia page. See also: Glossary of functional analysis. Hilbert space Functional analysis, classic results Operator theory Banach space examples * Lp space *Hardy space *Sobolev space ...

** List of vector spaces in mathematics *

List of integration and measure theory topics {{TOCright This is a list of integration and measure theory topics, by Wikipedia page. Intuitive foundations *Length *Area *Volume *Probability *Moving average Riemann integral *Riemann sum *Riemann–Stieltjes integral *Bounded variation * Jorda ...

List of harmonic analysis topics This is a list of harmonic analysis topics. 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 p ...

List of Fourier analysis topics {{Short description, none This is a list of Fourier analysis topics. See also the list of Fourier-related transforms, and the list of harmonic analysis topics. Fourier analysis * Multiplier (Fourier analysis) * Fourier shell correlation * Pin ...

* List of mathematical series * List of multivariable calculus topics * List of q-analogs *

List of real analysis topics This is a list of articles that are considered real analysis topics. General topics Limits *Limit of a sequence **Subsequential limit – the limit of some subsequence *Limit of a function (''see List of limits for a list of limits of common fu ...

List of variational topics {{Short description, none This is a list of variational topics in from mathematics and physics. See calculus of variations for a general introduction. * Action (physics) * Averaged Lagrangian * Brachistochrone curve * Calculus of variations * Cateno ...

* See also Dynamical systems and differential equations section below.

Geometry and topology

Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension. * Glossary of differential geometry and topology *

Glossary of general topology This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also funda ...

Glossary of Riemannian and metric geometry This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following articles may also be useful; they either contain specialised vocabulary or provid ...

* Glossary of scheme theory *

List of algebraic geometry topics This is a list of algebraic geometry topics, by Wikipedia page. Classical topics in projective geometry *Affine space *Projective space *Projective line, cross-ratio *Projective plane **Line at infinity **Complex projective plane *Complex projecti ...

List of algebraic surfaces This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. Kodaira dimension −∞ Rational surfaces * Projective plane Qu ...

* List of algebraic topology topics ** List of cohomology theories *

List of circle topics This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like "inner circle" or "circular reasoning" in ...

List of topics related to pi A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

List of curves topics This is an alphabetical index of articles related to curves used in mathematics. * Acnode * Algebraic curve * Arc * Asymptote * Asymptotic curve * Barbier's theorem * Bézier curve * Bézout's theorem * Birch and Swinnerton-Dyer conjecture * Bi ...

* List of differential geometry topics * List of general topology topics *

List of geometric shapes Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools. Mathematics * List of mathematical shapes * List of two- ...

List of geometric topology topics This is a list of geometric topology topics, by Wikipedia page. See also: *topology glossary *List of topology topics *List of general topology topics *List of algebraic topology topics * Publications in topology Low-dimensional topology Knot the ...

* List of geometry topics * List of knot theory topics *

List of Lie group topics This is a list of Lie group topics, by Wikipedia page. Examples ''See Table of Lie groups for a list'' *General linear group, special linear group ** SL2(R) ** SL2(C) *Unitary group, special unitary group **SU(2) **SU(3) *Orthogonal group, specia ...

List of mathematical properties of points In mathematics, the following appear: * Algebraic point * Associated point * Base point * Closed point * Divisor point * Embedded point * Extreme point * Fermat point * Fixed point (mathematics), Fixed point * Focus (optics), Focal point * Geome ...

* List of topology topics ** List of topologies ** Topological property * List of triangle topics

Combinatorics

Combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

concerns the study of discrete (and usually finite) objects. Aspects include "counting" the objects satisfying certain criteria ('' enumerative combinatorics''), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in '' combinatorial designs and matroid theory''), finding "largest", "smallest", or "optimal" objects (''

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 ce ...

'' and '' combinatorial optimization''), and finding algebraic structures these objects may have (''

algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algeb ...

''). *

Outline of combinatorics Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Essence of combinatorics * Matroid * Greedoid * Ramsey theory ** Van der Waerden's theorem ** Hales–Jewett theorem ** Umbral calc ...

Glossary of graph theory This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B ...

List of graph theory topics This is a list of graph theory topics, by Wikipedia page. See glossary of graph theory terms for basic terminology Examples and types of graphs Graph coloring Paths and cycles Trees Terminology *Node **Child node **Parent node **Leaf ...

Logic

Logic is the foundation that underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof. * List of Boolean algebra topics * List of first-order theories *

List of large cardinal properties This page includes a list of cardinals with large cardinal properties. 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 g ...

List of mathematical logic topics This is a list of mathematical logic topics, by Wikipedia page. For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics for more theory of algorithms. Working foundations * ...

* List of set theory topics *

Glossary of order theory This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be ...

Number theory

The branch of mathematics deals with the properties and relationships of numbers, especially positive integers. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians. * List of algebraic number theory topics *

List of number theory topics {{Short description, none This is a list of number theory topics, by Wikipedia page. See also: *List of recreational number theory topics * Topics in cryptography Divisibility *Composite number **Highly composite number *Even and odd numbers **Pa ...

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. See list o ...

* Glossary of arithmetic and Diophantine geometry * List of prime numbers—not just a table, but a list of various ''kinds'' of prime numbers (each with an accompanying table) *

List of zeta functions In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function : \zeta(s) = \sum_^\infty \frac 1 . Zeta functions include: * Airy zeta function, related to the zeros of the Airy function * A ...

Applied mathematics

Dynamical systems and differential equations

A differential equation is an equation involving an unknown function and its derivatives. In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems. *

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. Dynamical systems, in general *Deterministic system (mathematics) *Linear system * P ...

List of nonlinear partial differential equations See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations See also List of nonlinear partial differential equations and List of linear ordinary differential ...

* List of partial differential equation topics

Mathematical physics

Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". * List of mathematical topics in classical mechanics *

List of mathematical topics in quantum theory {{Short description, List article 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, list of quantum-mechanical systems with analytical solutions. Mat ...

* List of mathematical topics in relativity *

List of string theory topics This is a list of string theory topics. String theory * Strings * Nambu–Goto action * Polyakov action * Bosonic string theory * Superstring theory ** Type I string ** Type II string *** Type IIA string theory *** Type IIB string theory ** H ...

Index of wave articles This is a list of Wave topics. 0–9 *21 cm line A *Abbe prism *Absorption spectroscopy *Absorption spectrum *Absorption wavemeter *Acoustic wave *Acoustic wave equation *Acoustics *Acousto-optic effect *Acousto-optic modulator *Acousto- ...

Theory of computation

The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science, and engineering. *

List of algorithm general topics This is a list of algorithm general topics. * Analysis of algorithms * Ant colony algorithm * Approximation algorithm * Best and worst cases * Big O notation * Combinatorial search * Competitive analysis (online algorithm), Competitive analysis * ...

List of computability and complexity topics This is a list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with what can be computed, in principle. Computational complexity theory deals with how hard computa ...

* Lists for computational topics in geometry and graphics **

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 mathematics, discrete entities and hence the methods of their solution are mostly the ...

List of computer graphics and descriptive geometry topics This is a list of computer graphics and descriptive geometry topics, by article name. * 2D computer graphics * 2D geometric model * 3D computer graphics * 3D projection * Alpha compositing * Anisotropic filtering * Anti-aliasing * Axis-aligned ...

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 ...

* List of computer vision topics * List of formal language and literal string topics * List of numerical analysis topics * List of terms relating to algorithms and data structures

Information theory and signal processing

Information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

is a branch of applied mathematics and Social science involving the quantification of information. Historically, information theory was developed to find fundamental limits on compressing and reliably communicating data. Signal processing is the analysis, interpretation, and manipulation of signals. Signals of interest include sound, images, biological signals such as

ECG Electrocardiography is the process of producing an electrocardiogram (ECG or EKG), a recording of the heart's electrical activity. It is an electrogram of the heart which is a graph of voltage versus time of the electrical activity of the hear ...

, radar signals, and many others. Processing of such signals includes

filtering Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component tha ...

, storage and reconstruction, separation of information from noise, compression, and feature extraction. *

List of algebraic coding theory topics This is a list of algebraic coding theory topics. {, , valign="top" , * ARQ * Adler-32 * BCH code * BCJR algorithm * Belief propagation * Berger code * Berlekamp–Massey algorithm * Binary Golay code * Bipolar violation * CRHF * Casting ou ...

* List of information theory topics * List of cryptography topics

Probability and statistics

Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics.

Statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics). *

Catalog of articles in probability theory This page lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles are marked here by a code of the form (X:Y), which refers to number of random variab ...

* List of probability topics * List of stochastic processes topics * List of probability distributions * List of statistics topics *

Outline of regression analysis The following outline is provided as an overview of and topical guide to regression analysis: Regression analysis – use of statistical techniques for learning about the relationship between one or more dependent variables (''Y'') and one ...

Game theory

Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

is a branch of

that uses

models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics, anthropology , political science, social psychology and

military strategy Military strategy is a set of ideas implemented by military organizations to pursue desired strategic goals. Derived from the Greek word '' strategos'', the term strategy, when it appeared in use during the 18th century, was seen in its narrow s ...

. *

Glossary of game theory Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject. Definitions of a game Notational conventions ; Real numbers : \mathbb . ; The s ...

* List of games in game theory

Operations research

Operations research is the study and use of mathematical models, statistics, and algorithms to aid in decision-making, typically with the goal of improving or optimizing the performance of real-world systems. *

List of knapsack problems The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special cases and generalizations have been examined. Common to all versions are a set of ''n'' items, w ...

* List of network theory topics

Methodology

* List of graphical methods *

List of mathematics-based methods This is a list of mathematics-based methods. *Adams' method ( differential equations) *Akra–Bazzi method ( asymptotic analysis) *Bisection method (root finding) * Brent's method (root finding) *Condorcet method (voting systems) *Coombs' method ( ...

* List of rules of inference

Mathematical statements

A mathematical statement amounts to a proposition or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically. * List of algorithms *

List of axioms This is a list of axioms as that term is understood in mathematics. In epistemology, the word ''axiom'' is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system. ZF (the Zermelo ...

List of conjectures This is a list of mathematical conjectures. Open problems The following conjectures remain open. The (incomplete) column "cites" lists the number of results for a Google Scholar search for the term, in double quotes . Conjectures now proved (th ...

** List of conjectures by Paul Erdős * Combinatorial principles * List of equations *

List of formulae involving pi A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby unio ...

List of representations of e The mathematical constant can be represented in a variety of ways as a real number. Since is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a co ...

List of inequalities This article lists Wikipedia articles about named mathematical inequalities. Inequalities in pure mathematics Analysis * Agmon's inequality * Askey–Gasper inequality * Babenko–Beckner inequality * Bernoulli's inequality * Bernstein's ine ...

List of lemmas This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures. {{Expand list, date=August 2008 * Abel ...

List of mathematical identities This article lists mathematical identities, that is, ''identically true relations'' holding in mathematics. * Bézout's identity (despite its usual name, it is not, properly speaking, an identity) * Binomial inverse theorem * Binomial identity ...

* List of mathematical proofs * List of theorems

General concepts

* List of convexity topics * List of dualities * List of exceptional set concepts * List of exponential topics * List of factorial and binomial topics * List of fractal topics * List of logarithm topics *

List of numeral system topics This is a list of Wikipedia articles on topics of numeral system and "numeric representations" See also: computer numbering formats and number names. Arranged by base * Radix, radix point, mixed radix, base (mathematics) * Unary numeral syste ...

* List of order topics *

List of partition topics Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are * partition of a set or an ordered partition of a set, * partition of a graph, * partition of an integer, ...

List of permutation topics This is a list of topics on mathematical permutations. Particular kinds of permutations *Alternating permutation *Circular shift *Cyclic permutation *Derangement *Even and odd permutations—see Parity of a permutation *Josephus permutation ...

List of polynomial topics This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics. Terminology *Degree: The maximum exponents among the monomials. *Factor: An expression being multiplied. * Linear fact ...

List of properties of sets of reals {{Short description, none This article 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. Definability properties * Borel s ...

List of transforms This is a list of transforms in mathematics. Integral transforms *Abel transform *Bateman transform *Fourier transform **Short-time Fourier transform **Gabor transform *Hankel transform *Hartley transform *Hermite transform *Hilbert transform **Hi ...

Mathematical objects

Among mathematical objects are numbers, functions, sets, a great variety of things called "spaces" of one kind or another, algebraic structures such as rings, groups, or fields, and many other things. * List of mathematical examples *

List of curves This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, psychology, ecology, etc. Mathematics (Geometry) ...

* List of complex reflection groups * List of complexity classes * List of examples in general topology * List of finite simple groups *

List of Fourier-related transforms This is a list of linear transformations of function (mathematics), functions related to Fourier analysis. Such transformations Map (mathematics), map a function to a set of coefficients of basis functions, where the basis functions are trigonomet ...

* List of manifolds * List of mathematical constants * List of mathematical functions *

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. Knots Prime knots *01 knot/Unknot - a simple un-knotted closed loop *31 knot/Trefoil knot - (2,3)-torus knot, the two lo ...

* List of mathematical shapes *

List of matrices This article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called ''entries''. Matrices have a long history of both st ...

* List of numbers *

List of polygons, polyhedra and polytopes A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. Polytope ...

List of regular polytopes This article lists the regular polytopes and regular polytope compounds in Euclidean geometry, Euclidean, spherical geometry, spherical and hyperbolic geometry, hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an ' ...

* List of simple Lie groups * List of small groups *

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). Name ...

List of surfaces This is a list of surfaces, by Wikipedia page. ''See also List of algebraic surfaces, List of curves, Riemann surface.'' Minimal surfaces * Catalan's minimal surface * Costa's minimal surface * Catenoid * Enneper surface * Gyroid * Helicoid * Lid ...

Table of Lie groups This article gives a table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness; compactness; the nature of the fundamental group; and whether ...

Equations named after people

Scientific equations named after people This is a list of scientific equations named after people (eponymous equations)."Reflections on the Natural History of Eponymy and Scientific Law", Donald deB. Beaver, ''Social Studies of Science'', volume 6, number 1 (February, 1976), pages 89–9 ...

About mathematics

* List of letters used in mathematics and science * List of mathematical societies * List of mathematics competitions *

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. * 1729 (anecdote) *Adequality *Archimedes Palimpsest *Archimede ...

* List of publications in mathematics *

List of mathematics journals This is a list of scientific journals covering mathematics with existing Wikipedia articles on them. Alphabetic list of titles A B C D E F G H I J K L M N O P Q R S ...

Mathematicians

Mathematicians study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science and theoretical physics). * List of game theorists * List of geometers * List of logicians *

List of mathematicians Lists of mathematicians cover notable mathematicians by nationality, ethnicity, religion, profession and other characteristics. Alphabetical lists are also available (see table to the right). Lists by nationality, ethnicity or religion * List ...

* List of mathematical probabilists * List of statisticians

Work of particular mathematicians

List of things named after Niels Henrik Abel This is the list of things named after Niels Henrik Abel (1802–1829), a Norwegian mathematician. Mathematics * Abel's binomial theorem * Abel elliptic functions * Abel equation * Abel equation of the first kind * Abel–Goncharov interpolati ...

* List of things named after George Airy * List of things named after Jean d'Alembert * List of things named after Archimedes *

List of things named after Vladimir Arnold A list of things named after Vladimir Arnold, a Russian and Soviet mathematician. *Arnold–Givental conjecture *Arnold's cat map *Arnold's rouble problem *Arnold's spectral sequence * Arnold's stability theorem *Arnold conjecture *Arnold diffusio ...

List of things named after Emil Artin {{Short description, none These are things named after Emil Artin, a mathematician. * Ankeny–Artin–Chowla congruence * Artin algebra * Artin billiards * Artin braid group * Artin character * Artin conductor * Artin's conjecture for conjectu ...

* List of things named after Stefan Banach *

List of things named after Thomas Bayes Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian () refers either to a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a followe ...

* List of things named after members of the Bernoulli family * List of things named after Jakob Bernoulli *

List of things named after Friedrich Bessel {{Short description, none This is a (partial) list of things named for Friedrich Wilhelm Bessel, a 19th-century German scholar who worked in astronomy, geodesy and mathematical sciences: Astronomy, geodesy, astronomical bodies * 1552 Bessel * Bess ...

List of things named after Élie Cartan These are things named after Élie Cartan (9 April 1869 – 6 May 1951), a French mathematician. Mathematics and physics * Cartan calculus * Cartan connection, Cartan connection applications * Cartan's criterion * Cartan decomposition * Cartan' ...

* List of things named after Augustin-Louis Cauchy *

List of things named after Arthur Cayley {{Short description, none Arthur Cayley (1821 – 1895) is the eponym of all the things listed below. * Cayley absolute * Cayley algebra * Cayley computer algebra system * Cayley diagrams – used for finding cognate linkages in mechanical eng ...

List of things named after Pafnuty Chebyshev {{Short description, none Mathematics * Chebyshev center * Chebyshev constants * Chebyshev cube root * Chebyshev distance * Chebyshev equation * Chebyshev's equioscillation theorem * Chebyshev filter, a family of analog filters in electronics an ...

List of things named after John Horton Conway This is a list of things named after the English mathematician John Horton Conway (1937–2020). * Conway algebra – an algebraic structure introduced by Paweł Traczyk and Józef H. Przytycki * Conway base 13 function – a function used as ...

* List of things named after Richard Dedekind * List of things named after Pierre Deligne * List of things named after Peter Gustav Lejeune Dirichlet * List of things named after Albert Einstein * List of things named after Euclid * List of things named after Leonhard Euler *

List of things named after Paul Erdős The following are named after Paul Erdős: * Paul Erdős Award of the World Federation of National Mathematics Competitions * Erdős Prize * Erdős Lectures * Erdős number * Erdős cardinal * Erdős–Nicolas number * Erdős conjecture — a li ...

* List of things named after Pierre de Fermat * List of things named after Fibonacci * List of things named after Joseph Fourier * List of things named after Erik Fredholm * List of things named after Ferdinand Georg Frobenius *

List of things named after Carl Friedrich Gauss Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

List of things named after Évariste Galois The following is a list of topics named after Évariste Galois (1811–1832), a French mathematician. Mathematics *Galois closure *Galois cohomology *Galois connection **Galois correspondence *Galois/Counter Mode *Galois covering * Galois deforma ...

* List of things named after Hermann Grassmann * List of things named after Alexander Grothendieck *

List of things named after Jacques Hadamard These are things named after Jacques Hadamard (1865–1963), a French mathematician. (For references, see the respective articles.) Theorems, lemmas, and conjectures Many of these results are sometimes called "Hadamard's theorem". * Cartan–Ha ...

List of things named after William Rowan Hamilton {{Short description, none List of things named after William Rowan Hamilton: * Cayley–Hamilton theorem * Hamilton's equations * Hamilton's principle * Hamilton–Jacobi equation ** Hamilton–Jacobi–Bellman equation, related equation in control ...

List of things named after Erich Hecke {{Short description, none These are things named after Erich Hecke, a German mathematician. * Hecke algebra ** Hecke algebra of a locally compact group **Hecke algebra of a finite group **Hecke algebra of a pair ** Hecke polynomial **Iwahori–He ...

* List of things named after Eduard Heine *

List of things named after Charles Hermite {{Short description, none Numerous things are named after the French mathematician Charles Hermite (1822–1901): Hermite * Cubic Hermite spline, a type of third-degree spline * Gauss–Hermite quadrature, an extension of Gaussian quadrature meth ...

List of things named after David Hilbert David Hilbert (1862–1943), a mathematician, is the eponym of all of the things (and topics) listed below. Mathematics and physics *Brouwer–Hilbert controversy *Einstein–Hilbert action * Einstein–Hilbert equations * Hilbert algebra * Hilbe ...

List of things named after W. V. D. Hodge These are things named after W. V. D. Hodge, a Scottish mathematician. {{incomplete-list, date=May 2013 * Hodge algebra * Hodge–Arakelov theory * Hodge bundle * Hodge conjecture * Hodge cycle * Hodge–de Rham spectral sequence * Hodge diamond ...

List of things named after Carl Gustav Jacob Jacobi These are things named after Carl Gustav Jacob Jacobi (1804–1851), a German mathematician. Jacobi Jacobian {{columns-list, colwidth=30em, * Generalized Jacobian * Intermediate Jacobian * Jacobian conjecture * Jacobian curve * Jacobian mat ...

List of things named after Johannes Kepler This is a list of things named after German mathematician and astronomer Johannes Kepler (1571 – 1630). Geometry * Kepler conjecture *Kepler triangle * Kepler–Bouwkamp constant * Kepler–Poinsot polyhedron Celestial mechanics *Kepler's la ...

* List of things named after Felix Klein *

List of things named after Joseph-Louis Lagrange Several concepts from mathematics and physics are named after the mathematician and astronomer Joseph-Louis Lagrange, as are a crater on the moon and a street in Paris. Lagrangian * Lagrangian analysis *Lagrangian coordinates * Lagrangian deri ...

List of things named after Johann Lambert This article is a list of things named in the memory of the 18th century Swiss scientist Johann Heinrich Lambert: Optics * Beer–Lambert law **Beer–Lambert–Bouguer law, see above * lambert (unit) ** Foot-lambert * Lambert's cosine law * ...

* List of things named after Pierre-Simon Laplace * List of things named after Adrien-Marie Legendre *

List of things named after Gottfried Leibniz Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher and mathematician. In engineering, the following concepts are attributed to Leibniz: * Leibniz wheel, a cylinder used in a class of mechanical calculators * Leibniz calculator, a ...

* List of things named after Sophus Lie * List of things named after Joseph Liouville * List of things named after Andrey Markov *

List of things named after John Milnor {{Short description, none Things named after an American mathematician John Milnor: * Barratt–Milnor sphere * Fáry–Milnor theorem * Milnor conjecture (K-theory), Milnor conjecture in algebraic K-theory * Milnor conjecture (knot theory), Milnor ...

List of things named after Hermann Minkowski This is a list of things named after Hermann Minkowski (1864 - 1909), German mathematician: Mathematics * Brunn–Minkowski theorem * Hasse–Minkowski theorem * Hermite–Minkowski theorem * Minkowski addition * Minkowski content * Minkowski dis ...

List of things named after John von Neumann This is a list of things named after John von Neumann. John von Neumann (1903–1957), a mathematician, is the eponym of all of the things (and topics) listed below. * Birkhoff–von Neumann algorithm * Birkhoff–von Neumann theorem ** Birkhoff� ...

* List of things named after Isaac Newton *

List of things named after Emmy Noether Emmy Noether was a German mathematician who flourished in the early 20th century. This article is dedicated to the things named after her achievements. Mathematics "Noetherian" * Noetherian * Noetherian group * Noetherian module * Noetherian ...

List of things named after Henri Poincaré In physics and mathematics, a number of ideas are named after Henri Poincaré: * Euler–Poincaré characteristic * Hilbert–Poincaré series * Poincaré–Bendixson theorem * Poincaré–Birkhoff theorem * Poincaré–Birkhoff–Witt theorem, usu ...

List of things named after Siméon Denis Poisson These are things named after Siméon Denis Poisson (1781 – 1840), a French mathematician. Physics * ''Poisson’s Equations'' (thermodynamics) * ''Poisson’s Equation'' (rotational motion) * Schrödinger–Poisson equation * Vlasov–Poisson equ ...

List of things named after Pythagoras This is a list of things named after Pythagoras, the ancient Greek philosopher, mystic, mathematician, and music theorist. Philosophy and mysticism * Pythagoreanism – the system of philosophy of Pythagoras and his followers * Neopythagoreanism ...

* List of things named after Srinivasa Ramanujan *

List of things named after Bernhard Riemann The German mathematician Bernhard Riemann (1826–1866) is the eponym of many things. "Riemann" (by field) *Riemann bilinear relations * Riemann conditions *Riemann form * Riemann function *Riemann–Hurwitz formula * Riemann matrix * Riemann op ...

List of things named after Issai Schur This is a list of things named after Issai Schur. *Frobenius–Schur indicator *Herz–Schur multiplier *Jordan–Schur theorem *Lehmer–Schur algorithm *Schur algebra *Schur class *Permutation_polynomial#Schur's_conjecture, Schur's conjecture *S ...

List of things named after Anatoliy Skorokhod {{Short description, none These are things named after Anatoliy Skorokhod (1930-2011), a Ukrainian mathematician. Skorokhod * Skorokhod space * Skorokhod integral * Skorokhod problem Skorokhod's * Skorokhod's theorem: ** Skorokhod's embeddi ...

* List of things named after George Gabriel Stokes *

List of things named after Jean-Pierre Serre These are the things named after Jean-Pierre Serre, a French mathematician. *Bass–Serre theory *Serre class *Quillen–Suslin theorem (sometimes known as "Serre's Conjecture" or "Serre's problem") *Serre conjecture (number theory), Serre's Conjec ...

List of things named after James Joseph Sylvester The mathematician J. J. Sylvester was known for his ability to coin new names and new notation for mathematical objects, not based on his own name. Nevertheless, many objects and results in mathematics have come to be named after him: *The Sylvest ...

List of things named after Alfred Tarski {{Short description, none In the history of mathematics, Alfred Tarski (1901–1983) is one of the most important logicians. His name is now associated with a number of theorems and concepts in that field. Theorems * Łoś–Tarski preservation ...

* List of things named after Alan Turing *

List of things named after Stanislaw Ulam This is a (partial) list of things named after Stanislaw Ulam, a 20th-century Polish-American mathematician who also worked in physics and biological sciences: Computer science *Stan, probabilistic programming language Mathematics * Borsuk–Ulam ...

* List of things named after Karl Weierstrass *

List of things named after André Weil These are things named after André Weil (1906 – 1998), a French mathematician. *Bergman–Weil formula * Borel–Weil theorem * Chern–Weil homomorphism * Chern–Weil theory * De Rham–Weil theorem * Weil's explicit formula * Hasse-Weil bound ...

List of things named after Hermann Weyl This is a list of topics named after Hermann Weyl, the influential German mathematician from the 20th century. Mathematics and physics * Cartan–Weyl theory ** Cartan–Weyl basis * Courant–Fischer–Weyl min-max principle * De Donder–Weyl ...

* List of things named after Norbert Wiener *

List of things named after Ernst Witt {{Short description, none These are things named after Ernst Witt, a German mathematician. * Bourbaki–Witt theorem * Hall–Witt identity * Hasse–Witt matrix **Hasse–Witt invariant * Poincaré–Birkhoff–Witt theorem, usually known as th ...

Reference tables

* List of mathematical reference tables * List of moments of inertia *

Table of derivatives This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Elementary rules of differentiation Unless otherwise stated, all functions are functions of real numbers (R) that return real ...

Integrals

In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions. * Lists of integrals * List of integrals of exponential functions *

List of integrals of hyperbolic functions The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant ''a'' is assumed to be nonzero, and ''C'' denotes the constant ...

List of integrals of inverse hyperbolic functions The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals. * In all formulas the constant is assumed to be nonzero ...

List of integrals of inverse trigonometric functions The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions. For a complete list of integral formulas, see lists of integrals. * The inverse trigonometric functions are also known ...

* List of integrals of irrational functions *

* List of integrals of rational functions * List of integrals of trigonometric functions

Journals

List of mathematics journals This is a list of scientific journals covering mathematics with existing Wikipedia articles on them. Alphabetic list of titles A B C D E F G H I J K L M N O P Q R S ...

* List of mathematics education journals * :History of science journals * :Philosophy of science literature

Meta-lists

Glossary of mathematical symbols A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. ...

* List of important publications in mathematics * List of important publications in statistics *

List of mathematical theories This is a list of mathematical theories. {{columns-list, colwidth=20em, *Algebraic K-theory *Almgren–Pitts min-max theory *Approximation theory *Asymptotic theory *Automata theory *Bifurcation theory *Braid theory *Brill–Noether theory * Cat ...

* List of mathematics categories *

List of mathematical symbols by subject The following list of mathematical symbols by subject features a selection of the most common symbols used in modern mathematical notation within formulas, grouped by mathematical topic. As it is impossible to know if a complete list existing toda ...

Table of logic symbols In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subs ...

* Table of mathematical symbols

Others

* Lists of unsolved problems in mathematics * List of order theory topics *

List of topics related to π This is a list of topics related to pi (), the fundamental mathematical constant. * 2 theorem * Approximations of * Arithmetic–geometric mean *Bailey–Borwein–Plouffe formula * Basel problem *Borwein's algorithm *Buffon' ...

Notes

* : Definition from the ''Journal of Mathematical Physics'

External links and references

2000 Mathematics Subject Classification
from the American Mathematical Society, scheme authors find many mathematics research journals asking them to use to classify their submissions; those published then include these classifications.
The Mathematical Atlas

Maths Formula
{{DEFAULTSORT:mathematics topics Outlines of mathematics and logic Wikipedia outlines Lists of topics