# List of lists of mathematical topics

This article attempts to list all **lists** collecting articles about mathematics in Wikipedia. Some of these lists link to hundreds of articles; some link only to a few. The extremely long list of mathematical topics contains all mathematical articles in alphabetical order. This article brings together the same content organised in a manner better suited to browsing.

The purpose of this list is *not* similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, *Mathematical Reviews* and *Zentralblatt MATH*. This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics, which may surprise the reader with the diversity of their coverage.

## Contents

## Fields of mathematics

### Basic mathematics

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

- List of basic discrete mathematics topics
- List of calculus topics
- List of geometry topics
- List of topics in logic
- List of trigonometry topics

### Advanced mathematics

#### Algebra

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

- List of abstract algebra topics
- 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 linear algebra topics
- Glossary of field theory
- Glossary of group theory
- Glossary of linear algebra
- Glossary of ring theory

#### 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 studies the same subjects, but on a more rigorous level, and also topics that evolved from calculus.

- List of complex analysis topics
- List of functional analysis topics
- List of integration and measure theory topics
- List of harmonic analysis and representation theory topics
- List of multivariable calculus topics
- List of real analysis topics
- List of variational topics
- Glossary of tensor theory

#### 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 curve topics
- List of circle topics
- List of general topology topics
- List of differential geometry topics
- List of algebraic geometry topics
- List of algebraic topology topics
- 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
- Glossary of Riemannian and metric geometry
- Glossary of scheme theory

#### Discrete mathematics

Discrete mathematics concerns itself with the study of finite sets. This is in contrast with analysis and geometry, which study continua: between every two distinct points, however close together, one can always find another point.

#### 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 computability and complexity topics
- 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

### Applied mathematics

#### Computing

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 algebraic coding theory topics
- List of cryptography topics
- Lists for computational topics in geometry and graphics
- List of formal language and literal string topics
- List of network theory topics
- List of numerical analysis topics
- List of terms relating to algorithms and data structures

#### Dynamical systems

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

#### 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
- List of wave topics

#### Probability and statistics

Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of statistics concerns the mathematics and science of collecting and analyzing data.

- List of probability distributions
- List of probability topics
- List of information theory topics
- List of statistical topics
- List of stochastic processes topics

#### 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.

## Methodology

## 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
- Combinatorial principles
- List of equations
- List of fundamental theorems
- 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

## General concepts

- List of convexity topics
- List of exponential topics
- List of factorial and binomial topics
- List of fractal topics
- List of logarithmic 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

## 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 complexity classes
- List of examples in general topology
- List of finite simple groups
- List of Fourier-related transforms
- List of large cardinal properties
- List of mathematical functions [[Talk::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 algebraic surfaces
- List of surfaces
- Table of Lie groups

## 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 mathematicians
- List of probabilists
- List of statisticians

### Trivia

- List of topics named after Leonhard Euler
- List of topics named after Carl Friedrich Gauss
- List of terms based on the word cube

## Reference tables

### Integrals

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

- List of integrals
- List of integrals of arc functions
- List of integrals of exponential functions
- List of integrals of hyperbolic functions
- List of integrals of irrational functions
- List of integrals of logarithmic functions
- List of integrals of rational functions
- List of integrals of trigonometric functions

## Meta-lists

## External links and references

- 2000 Mathematics Subject Classification from the American Mathematical Society. Many research journals in mathematics ask authors to classify their papers according to this scheme; the classifications appear in the published work.

## Notes

- Template:Fnb Definition from the
*Journal of Mathematical Physics*[1].