Lists of mathematics topics cover a variety of topics related to 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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. 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'' 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 {{Short description, none This is a list of factorial and binomial topics in mathematics. See also binomial (disambiguation). * Abel's binomial theorem *Alternating factorial *Antichain *Beta function * Bhargava factorial *Binomial coefficient ** ...

, 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 poi ...

* Outline of discrete mathematics * 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 geo ...

** List of trigonometry topics *** Outline of trigonometry *** 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 \colo ...

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 integratio ...

* 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 Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

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 * Glossary of field theory * 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 This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions * Algebra of sets * Boolean algebra (structure) * Boolean algebra * Field of sets * Logical connective * Prop ...

* List of category theory topics *

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 ...

* List of commutative algebra topics * List of homological algebra topics * List of group theory topics *

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 * List of reciprocity laws

Calculus and analysis

Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change.

Analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

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 *

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 **

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 * Pinsk ...

List of mathematical series This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. *Here, 0^0 is taken to have the value 1 *\ denotes the fractional part of x *B_n(x) is a Bernou ...

List of multivariable calculus topics This is a list of multivariable calculus topics. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics. *Closed and exact differential forms *Contact (mathematics) *Contour integral *Contour line ...

* 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 * Cate ...

* 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 * Glossary of Riemannian and metric geometry *

Glossary of scheme theory This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometr ...

* List of algebraic geometry topics ** List of algebraic surfaces *

List of algebraic topology topics This is a list of algebraic topology topics, by Wikipedia page. See also: * Glossary of algebraic topology * topology glossary * List of topology topics * List of general topology topics *List of geometric topology topics * Publications in topology ...

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 * List of curves topics * List of differential geometry topics *

List of general topology topics This is a list of general topology topics, by Wikipedia page. Basic concepts *Topological space * Topological property *Open set, closed set **Clopen set **Closure (topology) **Boundary (topology) **Dense (topology) ** G-delta set, F-sigma set * ...

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 ...

* List of geometry topics * List of knot theory topics * List of Lie group topics * List of mathematical properties of points *

List of topology topics In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. A to ...

** List of topologies ** Topological property *

List of triangle topics This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space. It ...

Combinatorics

Combinatorics concerns the study of discrete (and usually

finite Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb Traditionally, a finite verb (from la, fīnītus, past particip ...

) 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 design Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of ''balance'' and/or ''symmetry''. These c ...

s 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 ...

'' and ''

combinatorial optimization Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combin ...

''), and finding

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

ic 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 alge ...

''). * Outline of combinatorics * Glossary of graph theory *

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 **Lea ...

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 first-order theories * List of large cardinal properties * List of mathematical logic topics *

List of set theory topics This page is a list of articles related to set theory. Articles on individual set theory topics Lists related to set theory * Glossary of set theory * List of large cardinal properties * List of properties of sets of reals * List of ...

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 ...

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 * List of recreational number theory topics * 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

Applied mathematics

Dynamical systems and differential equations

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

is an equation involving an unknown function and its derivatives. In a

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

, 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 ...

* List of nonlinear partial differential equations * 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 * List of mathematical topics in relativity * List of string theory topics * Index of wave articles

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 *

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 computer graphics and descriptive geometry topics ** List of numerical computational geometry topics *

List of computer vision topics The following outline is provided as an overview of and topical guide to computer vision: Computer vision – interdisciplinary field that deals with how computers can be made to gain high-level understanding from digital images or videos. F ...

* 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 is a branch of

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical ...

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 Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, d ...

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, storage and reconstruction, separation of information from

noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...

, 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 o ...

* List of information theory topics * List of cryptography topics

Probability and statistics

Probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

is the formalization and study of the mathematics of uncertain events or knowledge. The related field of

mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical a ...

develops statistical theory with mathematics. Statistics, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of

). * Catalog of articles in probability theory * 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 o ...

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 applic ...

is a branch of mathematics 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 Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavi ...

, political science,

social psychology Social psychology is the scientific study of how thoughts, feelings, and behaviors are influenced by the real or imagined presence of other people or by social norms. Social psychologists typically explain human behavior as a result of the re ...

and military strategy. * Glossary of game theory *

List of games in game theory Game theory studies strategic interaction between individuals in situations called games. Classes of these games have been given names. This is a list of the most commonly studied games Explanation of features Games can have several features, ...

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 *

List of rules of inference This is a list of rules of inference, logical laws that relate to mathematical formulae. Introduction Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules ...

Mathematical statements

A mathematical statement amounts to a

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

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 * List of conjectures ** List of conjectures by Paul Erdős *

Combinatorial principles In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. B ...

* List of equations * List of formulae involving pi * List of representations of e *

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 ineq ...

* List of lemmas * List of mathematical identities * List of mathematical proofs * List of theorems

General concepts

* List of convexity topics *

List of dualities Mathematics In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operat ...

* List of exceptional set concepts * List of exponential topics *

List of factorial and binomial topics {{Short description, none This is a list of factorial and binomial topics in mathematics. See also binomial (disambiguation). * Abel's binomial theorem *Alternating factorial *Antichain *Beta function * Bhargava factorial *Binomial coefficient ** ...

* List of fractal topics *

List of logarithm topics {{Short description, None This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics. * Acoustic power * Antilogarithm * Apparent magnitude * Baker's theorem * Bel * Benford's law * Binary logarithm * Bode plot ...

* List of mathematical properties of points * List of numeral system topics * 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 permutatio ...

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 fa ...

* List of properties of sets of reals *

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 ...

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 algebraic surfaces *

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 (Geometr ...

* List of complex reflection groups * List of complexity classes *

List of examples in general topology {{Short description, none This is a list of useful examples in general topology, a field of mathematics. * Alexandrov topology * Cantor space * Co-kappa topology ** Cocountable topology ** Cofinite topology * Compact-open topology * Compactifica ...

List of finite simple groups 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 union ...

List of Fourier-related transforms This is a list of linear transformations of functions related to Fourier analysis. 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 t ...

* List of manifolds * List of mathematical constants * List of mathematical functions * List of mathematical knots and links * List of mathematical shapes * List of matrices * 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, spherical and hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an ''n''-sphere, Euclidean and hyperbolic spaces. A Schläfli sy ...

* List of simple Lie groups *

List of small groups The following list in mathematics contains the finite groups of small order up to group isomorphism. Counts For ''n'' = 1, 2, … the number of nonisomorphic groups of order ''n'' is : 1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, ...

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). Na ...

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 * Helicoi ...

* Table of Lie groups

Equations named after people

* Scientific equations named after people

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 *Archi ...

* 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 A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

List of logicians A logician is a person who studies logic. Some famous logicians are listed below in English alphabetical transliteration order (by surname). __NOTOC__ A * Peter Abelard (France, 1079–1142) * Wilhelm Ackermann (Germany, 1896–1962) * Sergei Ad ...

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 * Li ...

* List of mathematical probabilists *

List of statisticians This list of statisticians lists people who have made notable contributions to the theories or application of statistics, or to the related fields of probability or machine learning. Also included are actuaries and demographers. __NOTOC__ A ...

Work of particular mathematicians

* List of things named after Niels Henrik Abel * List of things named after George Airy * List of things named after Jean d'Alembert *

List of things named after Archimedes Archimedes (c. 287 BC – c. 212 BC) is the eponym of all of the things (and topics) listed below. Mathematical concepts *Archimedean absolute value *Archimedean circle * Archimedean copula *Archimedean group * Archimedean ordered field * Archi ...

* List of things named after Vladimir Arnold *

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 Stefan Banach was a Polish mathematician who made key contributions to mathematics. This article contains some of the things named in his memory. Mathematics * Banach algebra ** Amenable Banach algebra * Banach Jordan algebra ** Banach function ...

* List of things named after Thomas Bayes * 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 *

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 and ...

* List of things named after John Horton Conway * 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 This is a list of topics named after the Greek mathematician Euclid. Mathematics Number theory * Euclidean algorithm ** Extended Euclidean algorithm * Euclidean division * Euclid–Euler theorem * Euclid number * Euclid's lemma * Euclid's orc ...

List of things named after Leonhard Euler 200px, Leonhard Euler (1707–1783) In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler inclu ...

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 diamo ...

* List of things named after Carl Gustav Jacob Jacobi * List of things named after Johannes Kepler * List of things named after Felix Klein * List of things named after Joseph-Louis Lagrange * List of things named after Johann Lambert *

List of things named after Pierre-Simon Laplace This is a list of things named after Pierre-Simon Laplace Probability theory * de Moivre-Laplace theorem that approximates binomial distribution with a normal distribution * Laplace–Bayes estimator *Laplace distribution ** Laplace–Gauss dis ...

* List of things named after Adrien-Marie Legendre * List of things named after Gottfried Leibniz * 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 * List of things named after Hermann Minkowski * List of things named after John von Neumann *

List of things named after Isaac Newton This is a list of things named after Sir Isaac Newton. Science and mathematics * Newtonianism Newtonianism is a philosophical and scientific doctrine inspired by the beliefs and methods of natural philosopher Isaac Newton. While Newton's influe ...

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 * Noetheria ...

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, us ...

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 * Neopythagoreanis ...

* 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 ...

* List of things named after Issai Schur *

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 embeddin ...

* List of things named after George Gabriel Stokes * List of things named after Jean-Pierre Serre *

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 Sylves ...

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 * 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 *Explicit formulae (L-function)#Weil's explicit ...

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–We ...

* 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 the ...

Reference tables

* List of mathematical reference tables *

List of moments of inertia Moment of inertia, denoted by , measures the extent to which an object resists rotational acceleration about a particular axis, it is the rotational analogue to mass (which determines an object's resistance to ''linear'' acceleration). The momen ...

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 Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not ...

* 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 const ...

* List of integrals of inverse hyperbolic functions * List of integrals of inverse trigonometric functions *

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, see lists of integrals. Throughout this article the constant of integration In calculus, the constant of integrat ...

List of integrals of rational functions The following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form: : \frac, and \frac. which can th ...

List of integrals of trigonometric functions The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antide ...

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 *

List of important publications in mathematics This is a list of important publications in mathematics, organized by field. Some reasons why a particular publication might be regarded as important: *Topic creator – A publication that created a new topic *Breakthrough – A public ...

* List of important publications in statistics * List of mathematical theories * List of mathematics categories * List of mathematical symbols by subject *

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 sub ...

* Table of mathematical symbols

Others

Lists of unsolved problems in mathematics Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclid ...

List of order theory topics Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another. An alphabe ...

* List of topics related to π

Notes

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

External links and references

2000 Mathematics Subject Classification
from the

, 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