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수학(Mathematics)은 추상적 대상 (예를 들어, 숫자, 점, 공간, 집합, 구조, 및 게임)에 대한 표현과 추론의 연구입니다. 수학은 자연 과학, 공학, 의학, 및 사회 과학을 포함한 많은 분야에서 필수적인 도구로 전 세계적으로 사용됩니다. 수학적 지식을 다른 분야에 적용하는 것과 관련된 수학의 가지, 응용 수학은 새로운 수학적 발견의 사용을 고무하고 만들고 때때로 통계와 게임 이론과 같은 완전히 새로운 수학적 분야의 개발로 이어집니다. 수학자들은 역시 임의의 응용도 염두에 두지 않고 순수 수학, 또는 그것 자체를 위한 수학에 참여합니다. 순수 수학과 응용 수학을 구분하는 명확한 선이 없고, 순수 수학으로 시작된 것에 대한 실용적인 응용이 종종 발견됩니다. (Full article...)

Topics in mathematics

General	Foundations	Number theory	Discrete mathematics
Mathematicians History of mathematics Philosophy of mathematics Mathematical notation Mathematical beauties Mathematics education Areas of mathematics Outline of mathematics Glossary of mathematical symbols	Foundations of mathematics Mathematical logic Proof theory Gödel's incompleteness theorems Model theory Recursion theory Set theory Naive set theory Axiomatic set theory Category theory Topos theory	Number theory Algebraic number theory Analytic number theory Arithmetic Fundamental theorem of arithmetic Numbers Natural numbers Prime numbers Rational numbers Algebraic numbers	Discrete mathematics Combinatorics Combinatorial geometry Coding theory Combinatorial design Enumerative combinatorics Combinatorial optimization Graph theory Order theory Lattice theory Digital Signal Processing Theoretical computer science Computability theory Complexity theory
Algebra	Analysis	Geometry and topology	Applied mathematics
Algebra Elementary algebra Abstract algebra Group theory Ring theory Field theory Commutative algebra Geometric algebra Linear algebra Matrix theory Multilinear algebra Universal algebra Fundamental theorem of algebra	Analysis Calculus Fundamental theorem of calculus Vector calculus Geometric calculus Measure theory Real analysis Complex analysis Differential equations Ordinary differential equations Partial differential equations Integral equations Approximation theory Special functions Potential theory Harmonic analysis Fourier analysis Functional analysis Operator theory	Geometry Euclidean geometry Trigonometry Analytic geometry Non-Euclidean geometry Affine geometry Projective geometry Convex geometry Discrete geometry Algebraic geometry Differential geometry K theory Gauge theory Riemannian geometry Lie groups Topology General topology Algebraic topology Geometric topology Differential topology	Applied mathematics Mathematical modeling Mathematical physics Dynamical systems Control theory Calculus of variations Optimization Mathematical economics Game theory Mathematical finance Statistics Probability theory Stochastic processes Numerical analysis Cryptography Information theory