Branch of mathematics
1. History of Mathematics
2. Mathematical logic and mathematical foundation
A: deductive logic (also called symbolic logic), B: proof theory (also called meta-mathematics), C: recursion theory, D: model theory, E: axiomatic set theory, F: mathematical basis, G: mathematical basis of mathematical logic and other disciplines.
3. Number theory
A: Elementary number theory, B: Analytic number theory, C: Algebraic number theory, D: Transcendental number theory, E: Diophantine approximation, F: Geometry of numbers, G: Probability number theory, H: Computational number theory, I: Other disciplines of number theory.
4. algebra
A: Linear Algebra, B: Group Theory, C: Field Theory, D: Lie Group, E: Lie Algebra, F:KAC- Moody Algebra, G: Ring Theory (including commutative ring and commutative algebra, associative ring and associative algebra, non-associative ring and non-associative algebra, etc.), H: Module Theory, I: Lattice Theory, J: Pan-Algebra Theory.
5. Algebraic geometry
6. Geometry
A: Basic Geometry, B: Euclidean Geometry, C: Non-Euclidean Geometry (including Riemannian Geometry, etc.). ), d: geometry of sphere, e: vector and tensor analysis, f: affine geometry, g: projective geometry, h: differential geometry, I: fractional geometry, j: computational geometry, and k: other geometric disciplines.
7. Topology
A: point set topology, B: algebraic topology, C: homotopy theory, D: low-dimensional topology, E: homology theory, F: dimension theory, G: lattice topology, H: fiber bundle theory, I: geometric topology, J: singularity theory, K: differential topology, L: other disciplines of topology.
8. Mathematical analysis
A: differential calculus, B: integral calculus, C: series theory, D: other disciplines of mathematical analysis.
9. Non-standard analysis
10. Function theory
A: real variable function theory, B: simple complex variable function theory, C: multiple complex variable function theory, D: function approximation theory, E: harmonic analysis, F: complex manifold, G: special function theory, H: function theory and other disciplines.
1 1. Ordinary differential equation
A: qualitative theory, b: stability theory. C: analytic theory, D: other disciplines of ordinary differential equations.
12. Partial differential equation
A: elliptic partial differential equations, b: hyperbolic partial differential equations, c: parabolic partial differential equations, d: nonlinear partial differential equations, e: other disciplines of partial differential equations.
13. Power system
A: differential dynamic systems, B: topological dynamic systems, C: complex dynamic systems, D: other disciplines of dynamic systems.
14. Integral equation
15. Functional analysis
A: linear operator theory, B: variational method, C: topological linear space, D: Hilbert space, E: function space, F: Banach space, G: operator algebra H: measure and integration, I: generalized function theory, J: nonlinear functional analysis, K: functional analysis and other disciplines.
16. Computational Mathematics
A: interpolation method and approximation theory, B: numerical solution of ordinary differential equations, C: numerical solution of partial differential equations, D: numerical solution of integral equations, E: numerical algebra, F: discretization method of continuous problems, G: random numerical experiments, H: error analysis, I: other disciplines of computational mathematics.
Probability theory.
A: geometric probability, b: probability distribution, c: limit theory, d: random process (including normal process and stationary process, point process, etc. ), e: Markov process, f: stochastic analysis, g: martingale theory, h: applied probability theory (specifically applied to related disciplines), I: probability theory of other disciplines.
18.？ mathematical statistics
A: Sampling theory (including sampling distribution, sampling survey, etc. ), b: hypothesis testing, c: nonparametric statistics, d: analysis of variance, e: correlation regression analysis, f: statistical inference, g: Bayesian statistics (including parameter estimation, etc. ), H: experimental design, I: multivariate analysis, J: statistical decision theory, K: time series analysis, etc.
19. applied statistical mathematics
A: statistical quality control, B: reliability mathematics, C: insurance mathematics, D: statistical simulation.
20.？ Other disciplines of applied statistical mathematics
2 1. operational research
A: linear programming, b: nonlinear programming, c: dynamic programming, d: combinatorial optimization, e: parametric programming, f: integer programming, g: stochastic programming, h: queuing theory, I: game theory (also known as game theory), j: inventory theory, k: decision theory, l: search theory, m: graph theory, n.
22. Combinatorial Mathematics
23. Fuzzy mathematics
24. Quantum Mathematics
25. Applied Mathematics (specially applied to related disciplines)
26. Other disciplines of mathematics