List Of Mathematical Theories

This is a list of mathematical theories. {{columns-list, colwidth=20em, *

Algebraic K-theory Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense ...

Almgren–Pitts min-max theory In mathematics, the Almgren–Pitts min-max theory (named after Frederick J. Almgren, Jr. and his student Jon T. Pitts) is an analogue of Morse theory for hypersurfaces. The theory started with the efforts for generalizing George David Birkhoff's ...

Approximation theory In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...

Asymptotic theory In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as bec ...

Automata theory Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματο� ...

Bifurcation theory Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. ...

Braid theory A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair. The simplest and most common version is a flat, solid, three-strande ...

Brill–Noether theory In algebraic geometry, Brill–Noether theory, introduced by , is the study of special divisors, certain divisors on a curve that determine more compatible functions than would be predicted. In classical language, special divisors move on the cur ...

* Catastrophe theory *

Category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

Chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...

Character theory In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about ...

Choquet theory In mathematics, Choquet theory, named after Gustave Choquet, is an area of functional analysis and convex analysis concerned with measures which have support on the extreme points of a convex set ''C''. Roughly speaking, every vector of ''C'' sho ...

Class field theory In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credit ...

Coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are stud ...

Cohomology theory In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...

* Complexity theory *

Computation theory In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., ...

Control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

* Deformation theory *

Dimension theory In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...

* Distribution theory *

Elimination theory Elimination may refer to: Science and medicine *Elimination reaction, an organic reaction in which two functional groups split to form an organic product *Bodily waste elimination, discharging feces, urine, or foreign substances from the body ...

Extremal graph theory Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local ...

* Field theory *

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...

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 ...

Graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

Grothendieck's Galois theory In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry. It provides, in ...

Group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

* Hodge theory * Homology theory * Homotopy theory *

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 ...

Invariant theory Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descri ...

K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, ...

Knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

L-theory In mathematics, algebraic ''L''-theory is the ''K''-theory of quadratic forms; the term was coined by C. T. C. Wall, with ''L'' being used as the letter after ''K''. Algebraic ''L''-theory, also known as "Hermitian ''K''-theory", is important in ...

Local class field theory In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite res ...

M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...

Matrix theory In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begi ...

Measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...

Model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...

Morse theory In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiabl ...

Module theory In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of ''module'' generalizes also the notion of abelian group, since the abelian groups are exactly the mo ...

* Network theory *

Nevanlinna theory In the mathematical field of complex analysis, Nevanlinna theory is part of the theory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna. Hermann Weyl called it "one of the few great mathematical events of (the twentieth) century ...

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� ...

Obstruction theory In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. In the original work of Stiefel and Whitney, characteristic classes were defined as obstructions to the ex ...

Operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators ...

Optimization theory Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

Order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...

Percolation theory In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnecte ...

Perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...

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 ...

Proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four correspo ...

Quantum theory Quantum theory may refer to: Science *Quantum mechanics, a major field of physics *Old quantum theory, predating modern quantum mechanics * Quantum field theory, an area of quantum mechanics that includes: ** Quantum electrodynamics ** Quantum ...

* Queue theory *

Recursion theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since e ...

Relational theory Relationalism is any theoretical position that gives importance to the relational nature of things. For relationalism, things exist and function only as relational entities. Relationalism may be contrasted with relationism, which tends to emphasize ...

Representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

Ring theory In algebra, ring theory is the study of rings— algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their re ...

Scheme theory In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations ''x'' = 0 and ''x''2 = 0 define the same algebraic variety but different sc ...

Seiberg–Witten theory In theoretical physics, Seiberg–Witten theory is a theory that determines an exact low-energy effective action (for massless degrees of freedom) of a \mathcal = 2 supersymmetric gauge theory—namely the metric of the moduli space of vacua. ...

Semigroup theory In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy ...

Set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

Sheaf theory In mathematics, a sheaf is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could ...

Singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...

Spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result ...

String theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...

* Sturm-Liouville theory *

Surgery theory In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by . Milnor called this technique ''surgery'', while And ...

Theory of equations In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an ...

Topos theory In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notio ...

Transcendental number theory Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways. Transcendence ...

Twistor theory In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic are ...

Type theory In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundat ...

* Universal theory

Theories A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be ...