Main article: Formal sciences

Computer sciences

Main articles: Computer sciences and Outline of computer science

See also Branches of computer science and ACM Computing Classification System

Logic

Main articles: Logic and Outline of logic

  1. Mathematical logic
    1. Set theory
    2. Proof theory
    3. Model theory
    4. Recursion theory
    5. Modal logic
    6. Intuitionistic logic
  1. Philosophical logic
    1. Logical reasoning
    2. Modal logic
      1. Deontic logic
      2. Doxastic logic
  1. Logic in computer science
    1. Programming language semantics
    2. Formal methods (Formal verification)
    3. Type theory
    4. Logic programming
    5. Multi-valued logic
      1. Fuzzy logic

Mathematics

Main articles: Mathematics and Outline of mathematics

See also Branches of mathematics and AMS Mathematics Subject Classification

  1. Algebra
    1. Group theory
      1. Group representation
    2. Ring theory
      1. Commutative algebra
      2. Noncommutative algebra
    3. Field theory
    4. Linear algebra (Vector space)
    5. Multilinear algebra
    6. Lie algebra
    7. Associative algebra
    8. Non-associative algebra
    9. Universal algebra
    10. Homological algebra
    11. Differential algebra
    12. Lattice theory (Order theory)
    13. Representation theory
    14. K-theory
    15. Category theory
      1. Topos theory
  2. Analysis
    1. Real analysis
      1. Calculus
    2. Complex analysis
    3. Functional analysis
      1. Operator theory
    4. Non-standard analysis
    5. Harmonic analysis
      1. Fourier analysis
    6. p-adic analysis
    7. Ordinary differential equations
    8. Partial differential equations
  3. Probability theory
    1. Measure theory
      1. Integral geometry
    2. Ergodic theory
    3. Stochastic process
  4. Geometry and Topology
    1. General topology
    2. Algebraic topology
    3. Geometric topology
    4. Differential topology
    5. Algebraic geometry
    6. Differential geometry
    7. Projective geometry
    8. Affine geometry
    9. Non-Euclidean geometry
    10. Convex geometry
    11. Discrete geometry
    12. Integral geometry
    13. Noncommutative geometry
  1. Number theory
    1. Analytic number theory
    2. Algebraic number theory
    3. Geometric number theory
  2. Logic and Foundations of mathematics
    1. Set theory
    2. Proof theory
    3. Model theory
    4. Recursion theory
    5. Modal logic
    6. Intuitionistic logic
  3. Applied mathematics
    1. Statistics
      1. Mathematical statistics
      2. Econometrics
      3. Actuarial science
      4. Demography
    2. Approximation theory
    3. Numerical analysis
    4. Operations research
      1. Mathematical optimization
      2. Linear programming
      3. Dynamic programming
      4. Assignment problem
      5. Decision analysis
      6. Inventory theory
      7. Scheduling
      8. Real options analysis
      9. Systems analysis
      10. Stochastic processes
      11. Optimal maintenance
    5. Dynamical systems
      1. Chaos theory
      2. Fractal geometry
    6. Mathematical physics
      1. Quantum mechanics
      2. Quantum field theory
      3. Quantum gravity
        1. String theory
      4. Statistical mechanics
    7. Theory of computation
      1. Computational complexity theory
    8. Information theory
    9. Cryptography
    10. Combinatorics
      1. Coding theory
    11. Graph theory
    12. Game theory

Statistics

Main articles: Statistics and Outline of statistics

  1. Computational statistics
    1. Data mining
    2. Regression
    3. Simulation
      1. Bootstrap (statistics)
  2. Design of experiments
    1. Block design and Analysis of variance
    2. Response surface methodology
  3. Sample Survey
    1. Sampling theory
  1. Statistical modelling
    1. Biostatistics
      1. Epidemiology
    2. Multivariate analysis
      1. Structural equation model
      2. Time series
    3. Reliability theory
    4. Quality control
  2. Statistical theory
    1. Decision theory
    2. Mathematical statistics
      1. Probability
    3. Survey methodology

Systems science

Main article: Systems science

  1. Complex systems
  2. Cybernetics
  3. Control theory
    1. Control engineering
    2. Control systems
    3. Dynamical systems
  4. Operations research
  1. Systems dynamics
  2. Systems engineering
    1. Systems analysis
  3. Systems theory
    1. Developmental systems theory
    2. General systems theory
    3. Mathematical system theory