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v t e Major mathematics areas
History Timeline Future Lists Glossary
Foundations	Category theory Information theory Mathematical logic Philosophy of mathematics Set theory Type theory
Algebra	Abstract Commutative Elementary Field theory Group theory Homological Linear
Analysis	Calculus Real analysis Complex analysis Differential equations Functional analysis Harmonic analysis Measure theory
Discrete	Combinatorics Discrete geometry Graph theory
Geometry	Algebraic Affine Analytic Arithmetic Complex Computational Convex Differential Discrete Euclidean Finite Information Projective
Number theory	Algebraic Analytic Arithmetic Diophantine geometry
Topology	General Algebraic Differential Geometric Homotopy theory
Applied	Engineering mathematics Mathematical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical geology Mathematical linguistics Mathematical physics Mathematical psychology Mathematical sociology Mathematical statistics Probability Statistics Systems science Control theory Game theory Operations research
Computational	Computer science Theory of computation Computational complexity theory Numerical analysis Optimization Computer algebra
Related topics	Mathematicians lists Informal mathematics Films about mathematicians Recreational mathematics Mathematics and art Mathematics education Number Large
Mathematics portal Category Commons WikiProject

v t e Number theory
Fields	Algebraic number theory (class field theory, non-abelian class field theory, Iwasawa theory, Tate's thesis, Kummer theory, ramification theory) Analytic number theory (analytic theory of $L$ -functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian geometry, $p$ -adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers Zero Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers $p$ -adic numbers ( $p$ -adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms $L$ -functions Diophantine equations Diophantine approximation Irrationality measure Simple continued fractions
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