Lists of mathematics topics cover a variety of topics related to

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. Some of these lists link to hundreds of articles; some link only to a few. The template below 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 that has collaboratively been produced by staff of, and based on the coverage of, the two major mathematical reviewing databases, Mathematical Reviews and Zen ...

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 ''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 zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

''. This list has some items that would not fit in such a classification, such as

list of exponential topics {{Short description, none This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics. * Accelerating change * Mental calculation, Approximating natural exponents (log base e) * Artin–Hasse exponential Talk:Artin–H ...

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 * Outline of discrete mathematics * List of calculus topics * List of geometry topics ** Outline of geometry ** List of trigonometry topics *** Outline of trigonometry ***

List of trigonometric identities In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involvin ...

* List of logarithmic identities ** List of integrals of logarithmic functions *

List of set identities and relations This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for ...

* 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 a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

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 determ ...

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

Glossary of group theory A group is a set together with an associative operation that admits an identity element and such that there exists an inverse for every element. Throughout this glossary, we use to denote the identity element of a group. A C ...

Glossary of linear algebra This glossary of linear algebra is a list of definitions and terms relevant to the field of linear algebra, the branch of mathematics concerned with linear equations and their representations as vector spaces. For a glossary related to the general ...

Glossary of ring theory Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. For the items in commutative algebra (the theor ...

List of abstract algebra topics Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish t ...

List of algebraic structures In mathematics, many types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting poin ...

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 * Propo ...

List of category theory topics The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of ''objec ...

List of cohomology theories This is a list of some of the ordinary and generalized cohomology theory, generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectrum (homotopy theory), spectr ...

List of commutative algebra topics Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative ...

List of homological algebra topics {{Short description, none This is a list of homological algebra topics, by Wikipedia page. Basic techniques *Cokernel *Exact sequence *Chain complex *Differential module *Five lemma *Short five lemma *Snake lemma *Nine lemma *Extension (algebra) * ...

* List of group theory topics * List of representation theory topics * List of linear algebra topics * List of reciprocity laws

Calculus and analysis

Calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

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 (38 ...

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 a ...

* List of complex analysis topics * List of functional analysis topics ** 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 * Jord ...

* List of harmonic analysis topics ** List of Fourier analysis topics *

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 Zero to the power of zero, is taken to have the value 1 *\ denotes the fractional part ...

* List of multivariable calculus topics * List of q-analogs * List of real analysis topics * List of variational topics * See also Dynamical systems and differential equations section below.

Geometry and topology

Geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

is initially the study of spatial figures like circles and cubes, though it has been generalized considerably.

Topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

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 geometry. ...

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

* List of circle topics ** List of topics related to pi * List of curves topics * List of differential geometry topics * List of general topology topics *

List of geometric shapes Lists of shapes cover different types of geometry, 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 ...

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

Topological property In topology and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms. Alternatively, a topological property is a proper class of topological space ...

* List of triangle topics

Combinatorics

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

concerns the study of

discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory * Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit * Discrete group, ...

(and usually finite) objects. Aspects include "counting" the objects satisfying certain criteria (''

enumerative combinatorics Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an inf ...

''), 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 co ...

s and

matroid In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms ...

theory''), finding "largest", "smallest", or "optimal" objects ('' extremal combinatorics'' 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 combina ...

''), and finding

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

ic structures these objects may have ('' algebraic combinatorics''). * Outline of combinatorics *

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

Logic

Logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

is the foundation that underlies

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

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 * Glossary of order theory

Number theory

The branch of mathematics deals with the properties and relationships of numbers, especially positive integers.

Number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

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 A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

, 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 A glossary (from , ''glossa''; language, speech, wording), also known as a vocabulary or clavis, is an alphabetical list of terms in a particular domain of knowledge with the definitions for those terms. Traditionally, a glossary appears at ...

List of prime numbers This is a list of articles about prime numbers. A prime number (or ''prime'') is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of ...

—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

A differential equation 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 (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

, 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 * List of nonlinear partial differential equations *

List of partial differential equation topics {{Short description, none This is a list of partial differential equation topics. General topics *Partial differential equation ** Nonlinear partial differential equation *** list of nonlinear partial differential equations * Boundary condition * ...

Mathematical physics

Mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

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 Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, the study of algorithms and data structures, and in

scientific computing Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science, and more specifically the Computer Sciences, which uses advanced computing capabilities to understand and s ...

, 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 * 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 * 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 mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

is a branch of

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

and

social science Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the ...

involving the quantification of

information Information is an Abstraction, abstract concept that refers to something which has the power Communication, to inform. At the most fundamental level, it pertains to the Interpretation (philosophy), interpretation (perhaps Interpretation (log ...

. 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 audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...

is the analysis, interpretation, and manipulation of

signal A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

s. Signals of interest include

sound In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the br ...

, images, biological signals such as ECG,

radar Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...

signals, and many others. Processing of such signals includes filtering, storage and reconstruction, separation of information from

noise Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...

, compression, and

feature extraction Feature may refer to: Computing * Feature recognition, could be a hole, pocket, or notch * Feature (computer vision), could be an edge, corner or blob * Feature (machine learning), in statistics: individual measurable properties of the phenome ...

. *

List of algebraic coding theory topics This is a list of algebraic coding theory topics. {, , valign="top" , * Automatic repeat request, ARQ * Adler-32 * Algebraic geometry code * BCH code * BCJR algorithm * Belief propagation * Berger code * Berlekamp–Massey algorithm * Binary Go ...

* List of information theory topics * List of cryptography topics

Probability and statistics

Probability theory Probability theory or probability calculus 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 expre ...

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 and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques that are commonly used in statistics inc ...

develops

statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistica ...

with mathematics.

Statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, 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

Game theory

Game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

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 , . Models can be divided int ...

to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

anthropology Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, society, societies, and linguistics, in both the present and past, including archaic humans. Social anthropology studies patterns of behav ...

political science Political science is the scientific study of politics. It is a social science dealing with systems of governance and Power (social and political), power, and the analysis of political activities, political philosophy, political thought, polit ...

social psychology Social psychology is the methodical study of how thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others. Although studying many of the same substantive topics as its counterpart in the field ...

and

military strategy Military strategy is a set of ideas implemented by military organizations to pursue desired Strategic goal (military), strategic goals. Derived from the Greek language, Greek word ''strategos'', the term strategy, when first used during the 18th ...

. * Glossary of game theory * List of games in game theory

Operations research

Operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...

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, ...

List of network theory topics Network theory is an area of applied mathematics. This page is a list of network theory topics. Network theorems * Max flow min cut theorem * Menger's theorem * Metcalfe's law Network properties * Centrality * Betweenness centrality * Closen ...

Methodology

* List of graphical methods *

List of mathematics-based methods A list is a set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of the list-maker, but ...

* List of rules of inference

Mathematical statements

A mathematical statement amounts to a

proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...

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 An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be f ...

* 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 combinatorics ...

List of equations This is a list of equations, by Wikipedia page under appropriate bands of their field. Eponymous equations The following equations are named after researchers who discovered them. Mathematics * Cauchy–Riemann equations * Chapman–Kolmog ...

* 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 ...

* List of lemmas *

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) * Binet-cauchy identity * Binomial inverse theo ...

* 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 {{Short description, none This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics. * Accelerating change * Mental calculation, Approximating natural exponents (log base e) * Artin–Hasse exponential Talk:Artin–H ...

* List of factorial and binomial topics * List of fractal topics * List of logarithm topics * List of mathematical properties of points * List of numeral system topics * List of order topics * List of partition topics * List of permutation topics * List of polynomial topics * List of properties of sets of reals *

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

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 * 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 This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see :Manifolds and its subcategories. Generic families of manifolds * Euclidean space, R''n'' * n-sphere, ''n''-sphere ...

List of mathematical constants A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. For e ...

* List of mathematical functions * List of mathematical knots and links * List of mathematical shapes * List of mathematical spaces * List of matrices *

List of numbers This is a list of notable numbers and articles about notable numbers. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical, historical or cult ...

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 in Euclidean, spherical and hyperbolic spaces. Overview This table shows a summary of regular polytope counts by rank. There are no Euclidean regular star tessellations in any number of dimensions. ...

* List of simple Lie groups *

List of small groups The following list in mathematics contains the finite groups of small order of a group, 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, ...

* List of special functions and eponyms *

List of surfaces This is a list of surface (mathematics), surfaces in mathematics. They are divided into minimal surfaces, ruled surfaces, non-orientable surfaces, quadrics, pseudospherical surfaces, algebraic surfaces, and other types of surfaces. Minimal surface ...

* 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 *

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

* List of mathematics journals

Mathematicians

Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

s 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

and

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

). * List of films about mathematicians * List of game theorists * List of geometers * List of logicians * List of mathematicians * 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. It includes the founders of statistics and others. It includes ...

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 * Arch ...

List of things named after Peter Gustav Lejeune Dirichlet The Germany, German mathematician Peter Gustav Lejeune Dirichlet (1805–1859) is the eponym of many things. Mathematics * Theorems named ''Dirichlet's theorem'': **Dirichlet's approximation theorem (diophantine approximation) **Dirichlet's ...

* 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 ...

List of things named after Leonhard Euler 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 include their own unique function, equation ...

* List of things named after Paul Erdős * 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 Joseph-Louis Lagrange Several concepts from mathematics and physics are named after the mathematician and astronomer Joseph-Louis Lagrange, as are a impact crater, crater on the Moon and :fr:Rue Lagrange, a street in Paris. Lagrangian *Lagrangian analysis *Lagrangian c ...

* List of things named after Johann Lambert * List of things named after Pierre-Simon Laplace * 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 Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution a ...

* List of things named after Emmy Noether * List of things named after Henri Poincaré * List of things named after Siméon Denis Poisson * List of things named after Pythagoras * List of things named after Srinivasa Ramanujan * List of things named after Bernhard Riemann * List of things named after Issai Schur * List of things named after Anatoliy Skorokhod *

List of things named after George Gabriel Stokes {{Short description, none George G. Stokes, Sir George Stokes (1819–1903) was an Anglo-Irish mathematical physicist whose career left a prolific body of work in mathematics and physics. Below is a collection of some of the things named after him. ...

* List of things named after Jean-Pierre Serre * List of things named after James Joseph Sylvester * List of things named after Alfred Tarski * 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 * List of things named after Hermann Weyl * List of things named after Norbert Wiener * List of things named after Ernst Witt

Reference tables

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

Integrals

In calculus, the

integral In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...

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 The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integral Indefinite integrals are antiderivative functions. A constant (the constant of integ ...

* List of integrals of hyperbolic functions * List of integrals of inverse hyperbolic functions * List of integrals of inverse trigonometric functions * List of integrals of irrational functions * List of integrals of logarithmic functions * List of integrals of rational functions * List of integrals of trigonometric functions

Journals

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

* 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 subs ...

* Table of mathematical symbols

Others

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