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extraordinary cohomology theory | Physics | 1 | a branch of combinatorics, it is the study of the possible sizes of a collection of finite objects given certain restrictions. |
extremal combinatorics | Physics | 1 | a branch of combinatorics, it is the study of the possible sizes of a collection of finite objects given certain restrictions. |
extremal graph theory | Physics | 1 | a branch of mathematics that studies how global properties of a graph influence local substructure. |
field theory | Physics | 1 | The branch of algebra dedicated to fields, a type of algebraic structure. |
finite geometry | Physics | 1 | a restriction of model theory to interpretations on finite structures, which have a finite universe. |
finite model theory | Physics | 1 | a restriction of model theory to interpretations on finite structures, which have a finite universe. |
finsler geometry | Physics | 1 | a branch of differential geometry whose main object of study is Finsler manifolds, a generalisation of a Riemannian manifolds. |
first order arithmetic | Physics | 1 | the study of the way general functions may be represented or approximated by sums of trigonometric functions. |
fourier analysis | Physics | 1 | the study of the way general functions may be represented or approximated by sums of trigonometric functions. |
fractal geometry | Physics | 1 | a branch of analysis that studies the possibility of taking real or complex powers of the differentiation operator. |
fractional calculus | Physics | 1 | a branch of analysis that studies the possibility of taking real or complex powers of the differentiation operator. |
fractional dynamics | Physics | 1 | investigates the behaviour of objects and systems that are described by differentiation and integration of fractional orders using methods of fractional calculus. |
fredholm theory | Physics | 1 | part of spectral theory studying integral equations. |
function theory | Physics | 1 | an ambiguous term that generally refers to mathematical analysis. |
functional analysis | Physics | 1 | a branch of mathematical analysis, the core of which is formed by the study of function spaces, which are some sort of topological vector spaces. |
functional calculus | Physics | 1 | historically the term was used synonymously with calculus of variations, but now refers to a branch of functional analysis connected with spectral theory |
fuzzy mathematics | Physics | 1 | a branch of mathematics based on fuzzy set theory and fuzzy logic. |
fuzzy measure theory | Physics | 1 | a form of set theory that studies fuzzy sets, that is sets that have degrees of membership. |
fuzzy set theory | Physics | 1 | a form of set theory that studies fuzzy sets, that is sets that have degrees of membership. |
galois cohomology | Physics | 1 | an application of homological algebra, it is the study of group cohomology of Galois modules. |
galois theory | Physics | 1 | named after Évariste Galois, it is a branch of abstract algebra providing a connection between field theory and group theory. |
galois geometry | Physics | 1 | a branch of finite geometry concerned with algebraic and analytic geometry over a Galois field. |
game theory | Physics | 1 | the study of mathematical models of strategic interaction among rational decision-makers. |
gauge theory | Physics | 1 | also known as point-set topology, it is a branch of topology studying the properties of topological spaces and structures defined on them. It differs from other branches of topology as the topological spaces do not have to be similar to manifolds. |
general topology | Physics | 1 | also known as point-set topology, it is a branch of topology studying the properties of topological spaces and structures defined on them. It differs from other branches of topology as the topological spaces do not have to be similar to manifolds. |
generalized trigonometry | Physics | 1 | developments of trigonometric methods from the application to real numbers of Euclidean geometry to any geometry or space. This includes spherical trigonometry, hyperbolic trigonometry, gyrotrigonometry, and universal hyperbolic trigonometry. |
geometric algebra | Physics | 1 | an alternative approach to classical, computational and relativistic geometry. It shows a natural correspondence between geometric entities and elements of algebra. |
geometric analysis | Physics | 1 | a discipline that uses methods from differential geometry to study partial differential equations as well as the applications to geometry. |
geometric calculus | Physics | 1 | extends the geometric algebra to include differentiation and integration. |
geometric combinatorics | Physics | 1 | a branch of combinatorics. It includes a number of subareas such as polyhedral combinatorics (the study of faces of convex polyhedra), convex geometry (the study of convex sets, in particular combinatorics of their intersections), and discrete geometry, which in turn has many applications to computational geometry. |
geometric function theory | Physics | 1 | the study of geometric properties of analytic functions. |
geometric invariant theory | Physics | 1 | a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. |
geometric graph theory | Physics | 1 | a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. |
geometric group theory | Physics | 1 | the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces). |
geometric measure theory | Physics | 1 | the study of geometric properties of sets (typically in Euclidean space) through measure theory. |
geometric number theory | Physics | 1 | a branch of topology studying manifolds and mappings between them; in particular the embedding of one manifold into another. |
geometric topology | Physics | 1 | a branch of topology studying manifolds and mappings between them; in particular the embedding of one manifold into another. |
geometry | Physics | 1 | a branch of mathematics concerned with shape and the properties of space. Classically it arose as what is now known as solid geometry; this was concerning practical knowledge of length, area and volume. It was then put into an axiomatic form by Euclid, giving rise to what is now known as classical Euclidean geometry. The use of coordinates by René Descartes gave rise to Cartesian geometry enabling a more analytical approach to geometric entities. Since then many other branches have appeared including projective geometry, differential geometry, non-Euclidean geometry, Fractal geometry and algebraic geometry. Geometry also gave rise to the modern discipline of topology. |
geometry of numbers | Physics | 1 | initiated by Hermann Minkowski, it is a branch of number theory studying convex bodies and integer vectors. |
global analysis | Physics | 1 | the study of differential equations on manifolds and the relationship between differential equations and topology. |
global arithmetic dynamics | Physics | 1 | a branch of discrete mathematics devoted to the study of graphs. It has many applications in physical, biological and social systems. |
graph theory | Physics | 1 | a branch of discrete mathematics devoted to the study of graphs. It has many applications in physical, biological and social systems. |
group-character theory | Physics | 1 | the part of character theory dedicated to the study of characters of group representations. |
group representation theory | Physics | 1 | the study of algebraic structures known as groups. |
group theory | Physics | 1 | the study of algebraic structures known as groups. |
gyrotrigonometry | Physics | 1 | a form of trigonometry used in gyrovector space for hyperbolic geometry. (An analogy of the vector space in Euclidean geometry.) |
hard analysis | Physics | 1 | see classical analysis |
harmonic analysis | Physics | 1 | part of analysis concerned with the representations of functions in terms of waves. It generalizes the notions of Fourier series and Fourier transforms from the Fourier analysis. |
higher arithmetic | Physics | 1 | the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. |
higher category theory | Physics | 1 | the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. |
higher-dimensional algebra | Physics | 1 | the study of categorified structures. |
hodge theory | Physics | 1 | a method for studying the cohomology groups of a smooth manifold M using partial differential equations. |
hodge–arakelov theory | Physics | 1 | a branch of functional calculus starting with holomorphic functions. |
holomorphic functional calculus | Physics | 1 | a branch of functional calculus starting with holomorphic functions. |
homological algebra | Physics | 1 | the study of homology in general algebraic settings. |
homology theory | Physics | 1 | also known as Lobachevskian geometry or Bolyai-Lobachevskian geometry. It is a non-Euclidean geometry looking at hyperbolic space. |
homotopy theory | Physics | 1 | also known as Lobachevskian geometry or Bolyai-Lobachevskian geometry. It is a non-Euclidean geometry looking at hyperbolic space. |
hyperbolic geometry | Physics | 1 | also known as Lobachevskian geometry or Bolyai-Lobachevskian geometry. It is a non-Euclidean geometry looking at hyperbolic space. |
hyperbolic trigonometry | Physics | 1 | the study of hyperbolic triangles in hyperbolic geometry, or hyperbolic functions in Euclidean geometry. Other forms include gyrotrigonometry and universal hyperbolic trigonometry. |
hypercomplex analysis | Physics | 1 | the extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. |
ideal theory | Physics | 1 | once the precursor name for what is now known as commutative algebra; it is the theory of ideals in commutative rings. |
idempotent analysis | Physics | 1 | the study of idempotent semirings, such as the tropical semiring. |
incidence geometry | Physics | 1 | the study of relations of incidence between various geometric objects, like curves and lines. |
inconsistent mathematics | Physics | 1 | see paraconsistent mathematics. |
infinitary combinatorics | Physics | 1 | an expansion of ideas in combinatorics to account for infinite sets. |
infinitesimal analysis | Physics | 1 | once a synonym for infinitesimal calculus |
infinitesimal calculus | Physics | 1 | See calculus of infinitesimals |
information geometry | Physics | 1 | an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions. |
integral calculus | Physics | 1 | the theory of measures on a geometrical space invariant under the symmetry group of that space. |
integral geometry | Physics | 1 | the theory of measures on a geometrical space invariant under the symmetry group of that space. |
intersection theory | Physics | 1 | a branch of algebraic geometry and algebraic topology |
intuitionistic type theory | Physics | 1 | a type theory and an alternative foundation of mathematics. |
invariant theory | Physics | 1 | studies how group actions on algebraic varieties affect functions. |
inventory theory | Physics | 1 | the study of invariants preserved by a type of transformation known as inversion |
inversive geometry | Physics | 1 | the study of invariants preserved by a type of transformation known as inversion |
inversive plane geometry | Physics | 1 | inversive geometry that is limited to two dimensions |
inversive ring geometry | Physics | 1 | extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations. |
itô calculus | Physics | 1 | extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations. |
iwasawa theory | Physics | 1 | the study of objects of arithmetic interest over infinite towers of number fields. |
k-theory | Physics | 1 | originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry it is referred to as algebraic K-theory. In physics, K-theory has appeared in type II string theory. (In particular twisted K-theory.) |
k-homology | Physics | 1 | a homology theory on the category of locally compact Hausdorff spaces. |
kähler geometry | Physics | 1 | a branch of differential geometry, more specifically a union of Riemannian geometry, complex differential geometry and symplectic geometry. It is the study of Kähler manifolds. (named after Erich Kähler) |
kk-theory | Physics | 1 | a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. |
klein geometry | Physics | 1 | More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which acts as the symmetry group of the geometry. |
knot theory | Physics | 1 | part of topology dealing with knots |
kummer theory | Physics | 1 | provides a description of certain types of field extensions involving the adjunction of nth roots of elements of the base field |
l-theory | Physics | 1 | the K-theory of quadratic forms. |
large deviations theory | Physics | 1 | part of probability theory studying events of small probability (tail events). |
large sample theory | Physics | 1 | also known as asymptotic theory |
lattice theory | Physics | 1 | the study of lattices, being important in order theory and universal algebra |
lie algebra theory | Physics | 1 | geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. |
lie group theory | Physics | 1 | geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. |
lie sphere geometry | Physics | 1 | geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere. |
lie theory | Physics | 1 | a branch of algebra studying linear spaces and linear maps. It has applications in fields such as abstract algebra and functional analysis; it can be represented in analytic geometry and it is generalized in operator theory and in module theory. Sometimes matrix theory is considered a branch, although linear algebra is restricted to only finite dimensions. Extensions of the methods used belong to multilinear algebra. |
line geometry | Physics | 1 | a branch of algebra studying linear spaces and linear maps. It has applications in fields such as abstract algebra and functional analysis; it can be represented in analytic geometry and it is generalized in operator theory and in module theory. Sometimes matrix theory is considered a branch, although linear algebra is restricted to only finite dimensions. Extensions of the methods used belong to multilinear algebra. |
linear algebra | Physics | 1 | a branch of algebra studying linear spaces and linear maps. It has applications in fields such as abstract algebra and functional analysis; it can be represented in analytic geometry and it is generalized in operator theory and in module theory. Sometimes matrix theory is considered a branch, although linear algebra is restricted to only finite dimensions. Extensions of the methods used belong to multilinear algebra. |
linear functional analysis | Physics | 1 | a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. |
linear programming | Physics | 1 | a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. |
list of graphical methods | Physics | 1 | Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization. |
local algebra | Physics | 1 | a term sometimes applied to the theory of local rings. |
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