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 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 Infrastructur ...

''. 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 * Approximating natural exponents (log base e) * Artin–Hasse exponential * Bacterial growth * Bake ...

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 **P ...

, 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 *

List of calculus topics {{Calculus This is a list of calculus topics. Limits * Limit (mathematics) * Limit of a function ** One-sided limit * Limit of a sequence * Indeterminate form * Orders of approximation * (ε, δ)-definition of limit *Continuous function Differe ...

List of geometry topics This is a list of geometry topics. Types, methodologies, and terminologies of geometry. * Absolute geometry * Affine geometry * Algebraic geometry * Analytic geometry * Archimedes' use of infinitesimals * Birational geometry * Complex geometry ...

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 *** 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 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 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 eva ...

* 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 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 A group is a set together with an associative operation which admits an identity element and such that every element has an inverse. Throughout the article, we use e to denote the identity element of a group. A C ...

Glossary of linear algebra This is a glossary of linear algebra. See also: glossary of module theory. A B C D E I L M N R S U V Z Notes References * * * ...

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 theory ...

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 this ...

List of algebraic structures In mathematics, there are many types of algebraic structures which 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 commo ...

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 * Pro ...

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 (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 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 r ...

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 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 ...

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 In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f(x) with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irr ...

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 (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 ...

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 ** 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 {{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 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 Bernoul ...

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 {{DISPLAYTITLE:List of ''q''-analogs This is a list of q-analog, ''q''-analogs in mathematics and related fields. Algebra * Iwahori–Hecke algebra * Quantum affine algebra * Quantum enveloping algebra * Quantum group Analysis * Jackson integ ...

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 f ...

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 Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

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

Topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

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 This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related: *Glossary of general topology *Glossary of algebraic topology *Glossary of Riemannian and metric geometr ...

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 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 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 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 * T ...

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 This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. Differential geometry of curves and surfaces Differential geometry of curves *List of curves topics *Frenet–Se ...

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 the ...

List of knot theory topics Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical lang ...

* List of Lie group topics *

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 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 top ...

List of topologies The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, s ...

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 spa ...

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 matrix, triangular matrices, or concretely in ...

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 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, a ...

(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, a verb form that has a subject, usually being inflected or marked ...

) 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 infin ...

''), 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 branch of mathematics, 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 axiomatically, the most significant being ...

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 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 combi ...

''), 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 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 Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

is the foundation that underlies

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

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 In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model theory and some of their properties. Preliminaries For every natural mathematical structure ...

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 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 o ...

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 Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

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 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 because the only ways ...

, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians. *

List of algebraic number theory topics This is a list of algebraic number theory topics. Basic topics These topics are basic to the field, either as prototypical examples, or as basic objects of study. *Algebraic number field **Gaussian integer, Gaussian rational **Quadratic field **C ...

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 **Par ...

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 This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of pro ...

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 o ...

—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

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 (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

, 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 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 ...

Mathematical physics

Mathematical physics Mathematical physics refers to 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 t ...

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 {{Short description, none This is a list of mathematical topics in classical mechanics, by Wikipedia page. See also list of variational topics, correspondence principle. Newtonian physics *Newton's laws of motion *Inertia, *Kinematics, rigid body ...

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 {{Short description, none This is a list of mathematical topics in relativity (physics), relativity, by Wikipedia page. Special relativity *''Foundational issues'' **principle of relativity **speed of light **faster-than-light *biquaternion *conju ...

* List of string theory topics *

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

, the study of algorithms and data structures, and in

scientific computing Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disc ...

, 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 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 (disambiguation), A ...

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 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. Fr ...

List of formal language and literal string topics {{Short description, none This is a list of formal language and literal string topics, by Wikipedia page. __TOC__ Formal languages * Abstract syntax tree * Backus-Naur form * Categorial grammar * Chomsky hierarchy * Concatenation * Context-free gra ...

List of numerical analysis topics This is a list of numerical analysis topics. General *Validated numerics * Iterative method *Rate of convergence — the speed at which a convergent sequence approaches its limit **Order of accuracy — rate at which numerical solution of differen ...

List of terms relating to algorithms and data structures The NIST ''Dictionary of Algorithms and Data Structures'' is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures. For algorithms an ...

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 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 s ...

and

Social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...

involving the quantification of

information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...

. Historically, information theory was developed to find fundamental limits on compressing and reliably

communicating Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...

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, and scientific measurements. Signal processing techniq ...

is the analysis, interpretation, and manipulation of

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...

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 ...

images An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...

, 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 Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...

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 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 arise ...

compression Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression *Gas compression *Compression ratio, of a c ...

, and

feature extraction In machine learning, pattern recognition, and image processing, feature extraction starts from an initial set of measured data and builds derived values (features) intended to be informative and non-redundant, facilitating the subsequent learning a ...

. *

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 {{Short description, none This is a list of information theory topics, by Wikipedia page. * A Mathematical Theory of Communication * algorithmic information theory * arithmetic coding * channel capacity * Communication Theory of Secrecy Systems * c ...

* 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 o ...

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 an ...

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 statistical ...

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

). *

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 variable ...

List of probability topics This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the outline of probability and catalog of articles in probability theory. For distributions, see List of probab ...

List of stochastic processes topics In the mathematics of probability, a stochastic process is a random function (mathematics), function. In practical applications, the domain over which the function is defined is a time interval (''time series'') or a region of space (''random field ...

List of probability distributions Many probability distributions that are important in theory or applications have been given specific names. Discrete distributions With finite support * The Bernoulli distribution, which takes value 1 with probability ''p'' and value 0 with pr ...

List of statistics topics 0–9 * 1.96 *2SLS (two-stage least squares) redirects to instrumental variable *3SLS – see three-stage least squares *68–95–99.7 rule *100-year flood A *A priori probability *Abductive reasoning *Absolute deviation *Absolute risk red ...

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

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 Political science is the scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of political activities, political thought, political behavior, and associated constitutions and la ...

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 r ...

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 *

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 Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve deci ...

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 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 * Closeness ...

Methodology

List of graphical methods This is a list of graphical methods with a mathematical basis. Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization. There is also a list of computer graphics and descriptive geometry topics. Simple ...

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 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 The following is a list of well-known algorithms along with one-line descriptions for each. Automated planning Combinatorial algorithms General combinatorial algorithms * Brent's algorithm: finds a cycle in function value iterations using on ...

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 The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered monetary rewards for solving them. Unsolved * The Erdős–Gyárfás co ...

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. Bij ...

List of equations This is a list of equations, by Wikipedia page under appropriate bands of maths, science and engineering. Eponymous equations Mathematics * Cauchy–Riemann equations * Chapman–Kolmogorov equation * Maurer–Cartan equation * Pell's equat ...

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 conti ...

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 A list of articles with mathematical proofs: Theorems of which articles are primarily devoted to proving them *Bertrand's postulate and Proof of Bertrand's postulate, a proof *Estimation of covariance matrices *Fermat's little theorem and Proofs ...

List of theorems 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 ...

General concepts

List of convexity topics This is a list of convexity topics, by Wikipedia page. * Alpha blending - the process of combining a translucent foreground color with a background color, thereby producing a new blended color. This is a convex combination of two colors allowing fo ...

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 operati ...

* 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 * Approximating natural exponents (log base e) * Artin–Hasse exponential * Bacterial growth * Bake ...

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 **P ...

* 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 (unit), Bel * Benford's law * Binary logarithm * ...

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 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 alphabet ...

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 {{Short description, none This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem ...

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 This is a list of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics. Many of these classes have a 'co' partner which consists of the complement ...

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 * Compactificatio ...

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 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, ''S ...

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 exa ...

List of mathematical functions In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed ...

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 Following is a list of some mathematically well-defined shapes. Algebraic curves *Cubic plane curve *Quartic plane curve Rational curves Degree 2 *Conic sections *Unit circle *Unit hyperbola Degree 3 *Folium of Descartes *Cissoid of Diocles * ...

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 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 cu ...

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 In mathematics, a simple Lie group is a connected non-abelian Lie group ''G'' which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symme ...

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 *

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 :''This list is about the meanings of the letters used in mathematics, science and engineering. SI units are indicated in parentheses. For the Unicode blocksee Mathematical Alphanumeric Symbols.'' Latin and Greek letters are used in mathematics ...

List of mathematical societies This article provides a list of mathematical societies by country. International mathematical societies * African Mathematical Union * Circolo Matematico di Palermo * European Mathematical Society * Foundations of Computational Mathematics * Inter ...

List of mathematics competitions Mathematics competitions or mathematical olympiads are competitive events where participants complete a math test. These tests may require multiple choice or numeric answers, or a detailed written solution or proof. International mathematics compe ...

* List of mathematics history topics *

List of 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 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

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, structure, space, models, and change. History On ...

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 natural phenomena. This is in contrast to experimental physics, which uses experim ...

). *

List of game theorists This is a list of notable economists, mathematicians, political scientists, and computer scientists whose work has added substantially to the field of game theory. * Derek Abbott - quantum game theory and Parrondo's games * Susanne Albers - algo ...

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 * List ...

List of mathematical probabilists :''See probabilism for the followers of such a theory in theology or philosophy''. {{ProbabilityTopicsTOC This list contains only probabilists in the sense of mathematicians specializing in probability theory. :''This list is incomplete; please ad ...

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 *Archime ...

* 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 * 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 *

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 a c ...

List of things named after Richard Dedekind This is a list of things named after Richard Dedekind. Richard Dedekind (1831–1916), a mathematician, is the eponym of all of the things (and topics) listed below. *19293 Dedekind *Cantor–Dedekind axiom *Dedekind completeness *Dedekind cut *De ...

* List of things named after Pierre Deligne *

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 This is a list of things named after Albert Einstein. Scientific and mathematical concepts Technology * Einstein refrigerator * Tatung Einstein, an eight-bit home/personal computer * Einstein Observatory, the first fully imaging X-ray telescope ...

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 include ...

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 lis ...

List of things named after Pierre de Fermat This is a list of things named after Pierre de Fermat, a French amateur mathematician. *Director circle, Fermat–Apollonius circle *Fermat–Catalan conjecture *Fermat cubic *Fermat curve *Euler's theorem, Fermat–Euler theorem *Fermat number *F ...

List of things named after Fibonacci The Fibonacci numbers are the best known concept named after Leonardo of Pisa, known as Fibonacci. Among others are the following. ;Concepts in mathematics and computing ;A professional association and a scholarly journal that it publishes * The ...

List of things named after Joseph Fourier This is a list of things named after Joseph Fourier: Mathematics *Budan–Fourier theorem, see Budan's theorem * Fourier's theorem *Fourier–Motzkin elimination * Fourier algebra *Fourier division * Fourier method Analysis *Fourier analysis *F ...

* 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 * 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 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 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 *

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 Adrien-Marie Legendre (1752–1833) is the eponym of all of the things listed below. *26950 Legendre *Associated Legendre polynomials *Generalized_Fourier_series#Example_(Fourier–Legendre_series), Fourier–Legendre series *Gauss–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 * Stepped reckoner, Leibni ...

* List of things named after Sophus Lie *

List of things named after Joseph Liouville {{refimprove, date=February 2016 Several concepts from mathematics and physics are named after the French mathematician Joseph Liouville. *Euler–Liouville equation *Liouville–Arnold theorem *Liouville–Bratu–Gelfand equation * Liouville–G ...

List of things named after Andrey Markov {{Short description, none This article is a list of things named after Andrey Markov, an influential Russian mathematician. * Chebyshev–Markov–Stieltjes inequalities * Dynamics of Markovian particles * Dynamic Markov compression * Gauss–Ma ...

* 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, the philosophical principle of applying Newton's methods in a variety of fields Mathematics Physics Places Schools Artwork Other See also ...

* List of things named after Emmy Noether *

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 *

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 * 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 * List of things named after Alfred Tarski *

List of things named after Alan Turing Alan Turing (1912–1954), a pioneer computer scientist, mathematician, and philosopher, is the eponym of all of the things (and topics) listed below. *Alan Turing Building, Manchester, England *Turing School/house Varndean School Brighton,Englan ...

* List of things named after Stanislaw Ulam *

List of things named after Karl Weierstrass This is a list of things named after the German mathematician Karl Weierstrass. Mathematical concepts, theorems, and the like Named after Weierstrass and other persons Named after Weierstrass alone {{columns-list, colwidth=20em, * Weierstr ...

* List of things named after André Weil * List of things named after Hermann Weyl *

List of things named after Norbert Wiener {{Short description, none In mathematics, there are a large number of topics named in honor of Norbert Wiener (1894 – 1964). * Abstract Wiener space * Classical Wiener space * Paley–Wiener integral * Paley–Wiener theorem * Wiener algebra * W ...

* List of things named after Ernst Witt

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 In 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 i ...

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 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 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 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 integrati ...

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 antider ...

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 This is a list of notable academic journals in the field of mathematics education. C *''College Mathematics Journal'' E *''Educational Studies in Mathematics'' F *''For the Learning of Mathematics'' I *'' International Journal of Science and Ma ...

* :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 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 This is a list of important publications in statistics, 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 publicatio ...

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 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 ...

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 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. ...

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 Wikipedia outlines Lists of topics