In the development of human history and social life, mathematics also plays an irreplaceable role, and it is also an indispensable basic tool for studying and studying modern science and technology.
In ancient China, mathematics was called arithmetic, also called arithmetic, and was finally changed to mathematics. Arithmetic in ancient China was one of the six arts (called "number" in the six arts).
Mathematics originated from early human production activities. The ancient Babylonians had accumulated some mathematical knowledge, which could be applied to practical problems. Judging from mathematics itself, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof. However, we should fully affirm their contribution to mathematics.
The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical classics of ancient Egypt, Mesopotamia and ancient India. Since then, its development has made small progress. But algebra and geometry at that time were still in an independent state for a long time.
Algebra can be said to be the most widely accepted "mathematics". It can be said that algebra is the first mathematics that everyone has come into contact with since childhood. Algebra, as a discipline to study numbers, is also one of the most important parts of mathematics. Geometry is the earliest branch of mathematics studied by people.
Until the Renaissance in16th century, Descartes founded analytic geometry, which linked algebra and geometry which were completely separated at that time. From then on, we can finally prove the theorem of geometry by calculation. At the same time, abstract algebraic equations can be expressed graphically, and later more subtle calculus was developed.
There are many branches of mathematics at present. French Bourbaki School, founded in 1930s, thinks that mathematics, at least pure mathematics, is a theory to study abstract structures. Structure is a deductive system based on initial concepts and axioms. They think that mathematics has three basic parent structures: algebraic structure (group, ring, field and lattice), ordered structure (partial order and total order) and topological structure (neighborhood).
Extended data:
Branch of mathematics
First, the history of mathematics
Second, mathematical logic and mathematical foundation A: deductive logic (also known as symbolic logic) B: proof theory (also known as meta-mathematics) C: recursion theory D: model theory E: axiomatic set theory F: mathematical foundation G: mathematical logic and mathematical foundation other disciplines.
Third, 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 theory H: Computational number theory I: Number theory Other disciplines
Fourth, algebra.
A: Linear Algebra B: Group Theory C: Domain Theory D: Lie Group E: Lie Algebra f:Kac-Moody Algebra G: Ring Theory (including commutative rings and commutative algebras, associative rings and associative algebras, non-associative rings and non-associative algebras, etc. H: module theory I: lattice theory J: pan-algebra theory K: category theory L: homology algebra M: algebra K: differential algebra O.
Verb (abbreviation for verb) algebraic geometry
Six, geometry
A: Geometric basis 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 K: Geometry Other Subjects.
VII. 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.
Eight, mathematical analysis
A: differential calculus B: integral calculus C: series theory D: mathematical analysis other disciplines
Nine, non-standard analysis
X. function theory
A: Theory of real variable function B: Theory of simple complex variable function C: Theory of multiple complex variable function D: Theory of function approximation E: Harmonic analysis F: Complex manifold G: Theory of special function H: Theories of other disciplines.
XI。 ordinary differential equation
A: qualitative theory B: stability theory C: analytical theory D: other disciplines of ordinary differential equations
Twelve. partial differential equation
A: elliptic PDE B: hyperbolic partial differential equations C: parabolic PDE D: nonlinear PDE E: PDE other disciplines.
Thirteen. electric power system
A: differential dynamical systems b: topological dynamical systems c: complex dynamical systems d: other disciplines of dynamical systems.
Fourteen integral equation
XV. 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 integral I: generalized function theory J: nonlinear functional analysis K: functional analysis other disciplines.
Sixteen, computational mathematics
A: interpolation method and approximation theory B: numerical solution of ordinary differential equation C: numerical solution of partial differential equation D: numerical solution of integral equation E: numerical algebra F: discretization method of continuous problems G: random numerical experiment H: error analysis I: other disciplines of computational mathematics
17. Probability theory
A: geometric probability b: probability distribution c: limit theory d: stochastic process (including normal process, 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 Other disciplines.
Eighteen, mathematical statistics
A: Sampling theory (including sampling distribution, sampling survey, etc. ) b: hypothesis test 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 L: other disciplines of mathematical statistics.
Nineteen. applied statistics
A: statistical quality control B: reliability mathematics C: insurance mathematics D: statistical simulation
Twenty, other disciplines of applied statistical mathematics
Twenty one. 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: Overall Planning Theory O: Optimization P: Operations Research Other disciplines.
Twenty-two, combinatorial mathematics?
23. Fuzzy mathematics
Twenty-four, quantum mathematics
Twenty-five, applied mathematics (specific application in related disciplines)
Twenty-six, other mathematics disciplines
References:
Baidu encyclopedia-mathematics