Lists of mathematics topics

Areas of basic mathematics

These lists include topics typically taught in secondary education or in the first year of university.

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

List of topics in logic

Areas of advanced mathematics

See also Areas of mathematics.

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

Algebra

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

Outline of algebra

List of abstract algebra topics

List of algebraic structures

List of Boolean algebra topics

List of category theory topics

List of commutative algebra topics

List of homological algebra topics

List of group theory topics

List of representation theory topics

List of linear algebra topics

List of reciprocity laws

Glossary of field theory

Glossary of group theory

Glossary of linear algebra

Glossary of ring theory

List of cohomology theories

Calculus and analysis

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

List of complex analysis topics

List of functional analysis topics

List of vector spaces in mathematics

List of integration and measure theory topics

List of harmonic analysis topics

List of Fourier analysis topics

List of multivariable calculus topics

List of q-analogs

List of real analysis topics

List of variational topics

Glossary of tensor theory

List of mathematical series

See also Dynamical systems and differential equations section below.

Geometry and topology

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

List of geometry topics

List of geometric shapes

List of curves topics

List of triangle topics

List of circle topics

List of topics related to pi

List of general topology topics

List of differential geometry topics

List of algebraic geometry topics

List of algebraic surfaces

List of algebraic topology topics

List of cohomology theories

List of geometric topology topics

List of knot theory topics

List of Lie group topics

Glossary of differential geometry and topology

Glossary of general topology

List of mathematical properties of points

Glossary of Riemannian and metric geometry

Glossary of scheme theory

Combinatorics

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

Outline of combinatorics

List of graph theory topics

Glossary of graph theory

Logic

Logic is the foundation which underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.

List of Boolean algebra topics

List of first-order theories

List of large cardinal properties

List of mathematical logic topics

Glossary of order theory

List of set theory topics

Number theory

Number theory studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.

List of algebraic number theory topics

List of number theory topics

List of recreational number theory topics

Glossary of arithmetic and Diophantine geometry

List of prime numbers—not just a table, but a list of various kinds of prime numbers (each with an accompanying table)

List of zeta functions

Dynamical systems and differential equations

A differential equation is an equation involving an unknown function and its derivatives.

In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.

List of dynamical systems and differential equations topics

List of partial differential equation topics

List of nonlinear partial differential equations

Mathematical physics

Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".¹

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

Computation

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

List of algorithm general topics

List of computability and complexity topics

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 is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed to find fundamental limits on compressing and reliably communicating data.

Signal processing is the analysis, interpretation, and manipulation of signals. Signals of interest include sound, images, biological signals such as ECG, radar signals, and many others. Processing of such signals includes filtering, storage and reconstruction, separation of information from noise, compression, and feature extraction.

List of information theory topics

List of algebraic coding theory topics

List of cryptography topics

Probability and statistics

Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics. Statistics, the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics).

List of probability topics

List of stochastic processes topics

List of probability distributions

Catalog of articles in probability theory

List of statistics topics

Outline of regression analysis

Game theory

Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics, evolutionary biology, political science, social psychology and military strategy.

Glossary of game theory

List of games in game theory

Operations research

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

List of network theory topics

List of knapsack problems

Methodology

List of graphical methods

List of mathematics-based methods

List of rules of inference

Mathematical statements

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

List of algorithms

List of axioms

List of conjectures

Erdős conjecture — a list of conjectures by Paul Erdős

Combinatorial principles

List of equations

List of formulae involving pi

List of mathematical identities

List of inequalities

List of lemmas

List of mathematical proofs

List of NP-complete problems

List of statements undecidable in ZFC

List of undecidable problems

List of theorems

List of fundamental theorems

General concepts

List of convexity topics

List of dualities

List of exceptional set concepts

List of exponential topics

List of factorial and binomial topics

List of fractal topics

List of logarithm topics

List of numeral system topics

List of order topics

List of partition topics

List of polynomial topics

List of properties of sets of reals

List of transforms

List of permutation topics

Mathematical objects

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

List of mathematical examples

List of curves

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

List of mathematical functions

List of mathematical knots and links

List of manifolds

List of mathematical shapes

List of matrices

List of numbers

List of polygons, polyhedra and polytopes

List of regular polytopes

List of simple Lie groups

List of small groups

List of special functions and eponyms

List of algebraic surfaces

List of surfaces

Table of Lie groups

Equations named after people

Scientific equations named after people

About mathematics

List of mathematical societies

List of letters used in mathematics and science

List of mathematics competitions

List of mathematics history topics

List of publications in mathematics

Mathematicians

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

List of geometers

List of logicians

List of game theorists

List of mathematicians

List of mathematical probabilists

List of statisticians

Work of particular mathematicians

List of things named after Niels Henrik Abel

List of things named after Archimedes

List of things named after Emil Artin

List of things named after Thomas Bayes

List of things named after Élie Cartan

List of things named after Augustin-Louis Cauchy

List of things named after Arthur Cayley

List of things named after Richard Dedekind

List of things named after Pierre Deligne

List of things named after Peter Gustav Lejeune Dirichlet

List of things named after Albert Einstein

List of things named after Euclid

List of things named after Leonhard Euler

List of things named after Paul Erdős

List of things named after Fibonacci

List of things named after Ferdinand Georg Frobenius

List of things named after Carl Friedrich Gauss

List of things named after Évariste Galois

List of things named after Jacques Hadamard

List of things named after Erich Hecke

List of things named after Eduard Heine

List of things named after Charles Hermite

List of things named after W. V. D. Hodge

List of things named after Carl Gustav Jacob Jacobi

List of things named after Felix Klein

List of things named after Joseph-Louis Lagrange

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 John Milnor

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 Jean-Pierre Serre

List of things named after James Joseph Sylvester

List of things named after Alfred Tarski

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 Ernst Witt

List of things named after John von Neumann

Journals

List of mathematics journals

List of mathematics education journals

Category:History of science journals

Category:Philosophy of science literature

Meta-lists

List of important publications in mathematics

List of important publications in statistics

List of mathematical theories

List of mathematics categories

Table of mathematical symbols

Table of logic symbols

Others

Lists of unsolved problems in mathematics