Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.
Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.
Chinese name
mathematics
Foreign name
Mathematics (mathematics or mathematics for short)
discipline classification
First-class discipline
Related works
Chapter 9 Arithmetic and Geometry
Famous mathematician
Archimedes, Newton, Euler, Gauss, etc
quick
navigate by water/air
Development history
definition
structure
space
basis
logic
sign
strict
amount
brief history
come to the point
Mathematical famous sayings
punctuate
Subject distribution
formula
see
Eight difficult problems
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.