Mathematics? [shùxué]

discipline

This entry is polysemous, with a total of 7 meanings

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mathematics or maths, which in English comes from the Greek, "máthēma"; Often abbreviated as "math"), it is a discipline that studies concepts such as quantity, structure, change, space, and information, and is a kind of formal science from a certain point of view. Mathematicians and philosophers have a range of opinions about the exact scope and definition of mathematics.

Mathematics also plays an irreplaceable role in the historical development and social life of mankind, and is also an indispensable basic tool for learning and researching modern science and technology.

Chinese name

mathematics

Foreign name

Mathematics (Maths or Math for short)

Classification of Disciplines

First-level disciplines

Related Writings

Nine chapters of mathematics? Geometric primitive

Representative figures

Archimedes? Newton?? Euler? Gauss, etc

fast

navigation

History

definition

structure

space

foundation

logic

symbol

Rigour

quantity

History

correlation

Math quotes

punctuation

Discipline distribution

formula

See

Eight major problems

Branches of Mathematics

1: History of Mathematics

2: Mathematical Logic and Mathematical Foundations A; Deductive Logic (also known as Symbolic Logic) B: Proof Theory (also known as Metamathematics) C: Recursion Theory D: Model Theory E: Axiom Set Theory F: Foundations of Mathematics G: Mathematical Logic and Foundations of Mathematics 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: Number Theory Other Disciplines

4: 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 ring and commutative algebra, conjunctive ring and conjunctive algebra, unbound ring and unconjunctive algebra, etc.) h: modulo theory i: lattice theory j: panalgebra theory k: category theory l: homology algebra m: algebra k theory n: differential algebra o: algebraic coding theory p: algebra other disciplines

5: Algebraic Geometry

6: Geometry

A: Fundamentals of Geometry B: Euclidean Geometry C: Non-Euclidean Geometry (including Riemannian Geometry, etc.) D: Spherical Geometry E: Vector and Tensor Analysis F: Affine Geometry G: Projective Geometry H: Differential Geometry I: Fractional Dimensional Geometry J: Computational Geometry K: Geometry Other Disciplines

7: Topology

A: Point Set Topology B: Algebraic Topology C: Homotopy D: Low-Dimensional Topology E: Homology F: Dimensional Number Theory G: Lattice Topology H: Fiber Bundle Theory I: Geometric Topology J: Singularity Theory K: Differential Topology L: Topology Other Disciplines

8: Mathematical Analysis

A: Differential Calculus B: Integral C: Series Theory D: Mathematical Analysis Other Disciplines

9: Non-standard analysis

10: Functional theory

A: Theory of real variable functions B: Theory of single complex variable functions C: Theory of multiple complex variable functions D: Approximation of functions E: Harmonic analysis F: Complex manifold G: Theory of special functions H: Theory of functions Other disciplines

11: Ordinary differential equations

A: Qualitative Theory B: Stability Theory C: Analytical Theory D: Ordinary Differential Equations Other Disciplines

12: Partial differential equations

A: Ellipsoidal partial differential equations B: hyperbolic partial differential equations C: Parabolic partial differential equations D: Nonlinear partial differential equations E: Partial differential equationsOther disciplines

13: Power system

A: Differential dynamical system B: Topological dynamical system C: Complex dynamical system D: Other disciplines of dynamical system

14: Integral equation

15: Functional analysis

A: Linear operator theory B: Variational method C: Topological linear space D: Hilbert space E: Function space F: Barnach space G: Operator algebra H: Measure and integration I: Generalized function theory J: Nonlinear functional analysis K: Functional analysis Other disciplines

16: Computational Mathematics

A: Interpolation and approximation? B: Numerical solutions of ordinary differential equations C: Numerical solutions of partial differential equations D: Numerical solutions of integral equations E: Numerical algebra F: Discretization methods of continuous problems G: Random numerical experiments H: Error analysis I: Computational mathematics other disciplines

17: Probability Theory

A: Geometric Probability B: Probability Distribution C: Limit Theory D: Stochastic Processes (including Normal Processes, Stationary Processes, Point Processes, etc.) E: Markov Processes F: Stochastic Analysis G: Martingale Theory H: Applied Probability Theory (Specific Application to Related Disciplines) I: Other Disciplines of Probability Theory

18: Mathematical Statistics

A: Sampling theory (including sampling distribution, sampling survey, etc.) B: Hypothesis testing C: Nonparametric statistics D: ANOVA 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

19: Applied Statistical Mathematics

A: Statistical Quality Control B: Reliability Mathematics C: Insurance Mathematics D: Statistical Simulation

20: Other disciplines of Applied Statistical Mathematics

21: Operations 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: Countermeasure 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: Other disciplines of operations research

22: Combinatorics

23: Fuzzy math

24: Quantum Mathematics

25: Applied Mathematics (specific application to related subjects)

26: Mathematics in other subjects

History

Mathematics (Hanyu pinyin: shùxué; Greek: μαθήματικ; English: Mathematics or Maths), which is derived from the ancient Greek μθημα (máthēma), which means learning, learning, and science. Ancient Greek scholars regarded it as the starting point of philosophy, "the foundation of learning". In addition, there is a narrower and more technical meaning - "mathematical research". Even within its etymology, its adjective meaning, which is related to learning, is used for exponentialism.

Its plural form in English, and in French + es as mathématiques, can be traced back to the Latin plural (Mathematica), translated by Cicero from the Greek plural ταμαθηματικ? (tamathēmatiká)

In ancient China, mathematics was called arithmetic, also known as arithmetic, and finally changed to mathematics.

Mathematics originated from the early production activities of human beings, the ancient Babylonians have accumulated a certain amount of mathematical knowledge since ancient times, and can apply practical problems from the perspective of mathematics itself, their mathematical knowledge is only obtained by observation and experience, without comprehensive conclusions and proofs, but it is also necessary to fully affirm their contributions to mathematics

The knowledge and application of basic mathematics is an integral part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical texts in ancient Egypt, Mesopotamia, and India, and its development has continued to progress dramatically since then, but algebra and geometry have long been in a separate state

Algebra can be the most widely accepted "mathematics", everyone can start to learn counting, the first mathematics to come into contact with is algebra, and mathematics as a discipline that studies "numbers", algebra is also one of the most important components of mathematics, geometry is the first branch of mathematics that began to be studied

It wasn't until the Renaissance in the 16th century that Descartes founded analytic geometry, linking algebra and geometry, which were completely separate at the time, and from then on, we can finally prove the theorems of geometry with calculations; At the same time, abstract algebraic equations could be represented graphically, and later more subtle calculus was developed

The Bourbachi school in France, founded in the thirties of the twentieth century, believed that mathematics, at least pure mathematics, is the study of theoretical structures of abstract structures, that is, deductive systems based on initial concepts and axioms, and they believed that mathematics has three basic parent structures: algebraic structures (groups, rings, fields, lattices...... ), order structure (partial order, full order...... ), topology (neighborhood, limit, connectivity, dimensionality...... ）[1]

Mathematics is applied in many different fields, including science, engineering, medicine, and economics, and the application of mathematics in these fields is generally referred to as applied mathematics, which sometimes provokes new mathematical discoveries and leads to the development of entirely new mathematical disciplinesMathematicians also study pure mathematics, that is, mathematics itself, without aiming for any practical application

Specifically, there are sub-fields that explore the connections between the core of mathematics and other fields: from logic and set theory (the foundations of mathematics), to empirical mathematics from different sciences (applied mathematics), to more recent studies of uncertainty (chaos and fuzzy mathematics)

In terms of verticality, the exploration of their respective fields of mathematics has also become more and more in-depth

The numbers in the figure are the national secondary discipline numbers.