Introduction to mathematics;
1, History of Mathematics
2. Mathematical logic and mathematical foundation
(1) Deductive Logic (also known as symbolic logic), (2) Proof Theory (also known as Metamathematics), (3) recursion theory, (4) Model Theory, (5) Axiomatic Set Theory, (6) Mathematical Basis, (7) Mathematical Logic and other basic disciplines.
3. Algebraic geometry
4. Mathematical analysis
(1) differential calculus, (2) integral calculus, (3) series theory and (4) other disciplines of mathematical analysis.
5. Non-standard analysis
6. Function theory
(1) real variable function theory, (2) simple complex variable function theory, (3) multiple complex variable function theory, (4) function approximation theory, (5) harmonic analysis, (6) complex manifold, (7) special function theory, (8) function theory and other disciplines.
7. Ordinary differential equations
(1) qualitative theory, (2) stability theory. (3) Analytical theory, (4) Other disciplines of ordinary differential equations.
8. Partial differential equations
(1) elliptic partial differential equations, (2) hyperbolic partial differential equations, (3) parabolic partial differential equations, (4) nonlinear partial differential equations and (5) other disciplines of partial differential equations.
The development history of mathematics:
1. Ancient Greek scholars regarded it as the starting point of philosophy and "the basis of learning". In addition, there is a narrow and technical meaning-"mathematical research". Even in its etymology, its adjective meaning is used to refer to mathematics whenever it is related to learning.
2. In ancient China, mathematics was called arithmetic, also called arithmetic, and finally it was changed to mathematics. Arithmetic in ancient China was one of the six arts (called "number" in the six arts).
3. Mathematics originated from the early production activities of human beings, and ancient Babylonians accumulated certain mathematical knowledge and could apply it to practical problems. As far as mathematics itself is concerned, their mathematical knowledge is only obtained through observation and experience, and there is no comprehensive conclusion and proof, but their contribution to mathematics should also be fully affirmed.
4. The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has continued to make small progress.