Mathematics: the study of patterns and relationships using abstract structures and logical reasoning.
Quantity
- numbers
- arithmetic
- operation
- measurement
Structure
- algebra
- abstract algebra
- linear algebra
- number theory
Space
- geometry
- algebraic geometry
- trigonometry
- differential geometry
- fractal geometry
- topology
Change
- calculus
- dynamical systems
- analysis
Foundations
- category theory
- set theory
- type theory
- information theory
Mathematical logic
- model theory
- proof theory
- computability theory
- computational complexity theory
Discrete mathematics
- combinatorics
- graph theory
- order theory
Applied mathematics
- numerical analysis
- optimization
- operations research
- statistics
- control theory
- game theory
- cryptography