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Pure mathematics

Mathematical logic and Foundations of mathematics

Intuitionistic logic

Modal logic

Model theory

Proof theory

Recursion theory

Set theory

Algebra (outline)

Associative algebra

Category theory

Topos theory

Differential algebra

Field theory

Group theory

Group representation

Homological algebra


Lattice theory (Order theory)

Lie algebra

Linear algebra (Vector space)

Multilinear algebra

Non-associative algebra

Representation theory

Ring theory

Commutative algebra

Noncommutative algebra

Universal algebra


Complex analysis

Functional analysis

Operator theory

Harmonic analysis

Fourier analysis

Non-standard analysis

Ordinary differential equations

p-adic analysis

Partial differential equations

Real analysis

Calculus (outline)

Probability theory

Ergodic theory

Measure theory

Integral geometry

Stochastic process

Geometry (outline) and Topology

Affine geometry

Algebraic geometry

Algebraic topology

Convex geometry

Differential topology

Discrete geometry

Finite geometry

Galois geometry

General topology

Geometric topology

Integral geometry

Noncommutative geometry

Non-Euclidean geometry

Projective geometry

Number theory

Algebraic number theory

Analytic number theory

Arithmetic combinatorics

Geometric number theory


Applied mathematics


Approximation theory

Combinatorics (outline)

Coding theory


Dynamical systems

Chaos theory

Fractal geometry

Game theory

Graph theory

Information theory

Mathematical physics

Quantum field theory

Quantum gravity

String theory

Quantum mechanics

Statistical mechanics

Numerical analysis

Operations research

Assignment problem

Decision analysis

Dynamic programming

Inventory theory

Linear programming

Mathematical optimization

Optimal maintenance

Real options analysis


Stochastic processes

Systems analysis

Statistics (outline)

Actuarial science



Mathematical statistics

Data visualization

Theory of computation

Computational complexity theory