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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Glossary of areas of mathematics | 6/7 | https://en.wikipedia.org/wiki/Glossary_of_areas_of_mathematics | reference | science, encyclopedia | 2026-05-05T07:50:22.568786+00:00 | kb-cron |
Malliavin calculus a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. Mathematical biology the mathematical modeling of biological phenomena. Mathematical chemistry the mathematical modeling of chemical phenomena. Mathematical economics the application of mathematical methods to represent theories and analyze problems in economics. Mathematical finance a field of applied mathematics, concerned with mathematical modeling of financial markets. Mathematical logic a subfield of mathematics exploring the applications of formal logic to mathematics. Mathematical optimization Mathematical physics The development of mathematical methods suitable for application to problems in physics. Mathematical psychology an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. Mathematical sciences refers to academic disciplines that are mathematical in nature, but are not considered proper subfields of mathematics. Examples include statistics, cryptography, game theory and actuarial science. Mathematical sociology the area of sociology that uses mathematics to construct social theories. Mathematical statistics the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Mathematical system theory Matrix algebra Matrix calculus Matrix theory Matroid theory Measure theory Metric geometry Microlocal analysis Model theory the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic. Modern algebra Occasionally used for abstract algebra. The term was coined by van der Waerden as the title of his book Moderne Algebra, which was renamed Algebra in the latest editions. Modern algebraic geometry the form of algebraic geometry given by Alexander Grothendieck and Jean-Pierre Serre drawing on sheaf theory. Modern invariant theory the form of invariant theory that analyses the decomposition of representations into irreducibles. Modular representation theory a part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. Module theory Molecular geometry Morse theory a part of differential topology, it analyzes the topological space of a manifold by studying differentiable functions on that manifold. Motivic cohomology Multilinear algebra an extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra. Multiplicative number theory a subfield of analytic number theory that deals with prime numbers, factorization and divisors. Multivariable calculus the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather than just one. Multiple-scale analysis
== N ==
Neutral geometry See absolute geometry. Nevanlinna theory part of complex analysis studying the value distribution of meromorphic functions. It is named after Rolf Nevanlinna Nielsen theory an area of mathematical research with its origins in fixed point topology, developed by Jakob Nielsen Non-abelian class field theory Non-classical analysis Non-Euclidean geometry Non-standard analysis Non-standard calculus Nonarchimedean dynamics also known as p-adic analysis or local arithmetic dynamics Noncommutative algebra Noncommutative algebraic geometry a direction in noncommutative geometry studying the geometric properties of formal duals of non-commutative algebraic objects. Noncommutative geometry Noncommutative harmonic analysis see representation theory Noncommutative topology Nonlinear analysis Nonlinear functional analysis Number theory a branch of pure mathematics primarily devoted to the study of the integers. Originally it was known as arithmetic or higher arithmetic. Numerical analysis Numerical linear algebra
== O ==
Operad theory a type of abstract algebra concerned with prototypical algebras. Operation research Operator K-theory Operator theory part of functional analysis studying operators. Optimal control theory a generalization of the calculus of variations. Optimal maintenance Orbifold theory Order theory a branch that investigates the intuitive notion of order using binary relations. Ordered geometry a form of geometry omitting the notion of measurement but featuring the concept of intermediacy. It is a fundamental geometry forming a common framework for affine geometry, Euclidean geometry, absolute geometry and hyperbolic geometry. Oscillation theory
== P ==
p-adic analysis a branch of number theory that deals with the analysis of functions of p-adic numbers. p-adic dynamics an application of p-adic analysis looking at p-adic differential equations. p-adic Hodge theory Parabolic geometry Paraconsistent mathematics sometimes called inconsistent mathematics, it is an attempt to develop the classical infrastructure of mathematics based on a foundation of paraconsistent logic instead of classical logic. Partition theory Perturbation theory Picard–Vessiot theory Plane geometry Point-set topology see general topology Pointless topology Poisson geometry Polyhedral combinatorics a branch within combinatorics and discrete geometry that studies the problems of describing convex polytopes. Possibility theory Potential theory Precalculus Predicative mathematics Probability theory Probabilistic combinatorics Probabilistic graph theory Probabilistic number theory Projective geometry a form of geometry that studies geometric properties that are invariant under a projective transformation. Projective differential geometry Proof theory Pseudo-Riemannian geometry generalizes Riemannian geometry to the study of pseudo-Riemannian manifolds. Pure mathematics the part of mathematics that studies entirely abstract concepts.
== Q ==
Quantum calculus a form of calculus without the notion of limits. Quantum geometry the generalization of concepts of geometry used to describe the physical phenomena of quantum physics Quaternionic analysis
== R ==