The first volume includes the emergence of Mesopotamian mathematics, Egyptian mathematics and classical Greek mathematics.

The second volume contains coordinate geometry; Mathematicization of science; The establishment of calculus; 17th century mathematics; 18th century calculus; Infinite series and so on.

The third volume comprehensively discusses the historical development of most branches of modern mathematics, focusing on the archaization of mathematical thought, and expounds the significance of mathematics and the relationship between mathematics and other natural sciences.

The fourth volume includes the basis and remainder of real numbers, geometric basis,19th century mathematics, real variable function theory, integral equation, divergent series, the emergence of abstract algebra, tensor analysis and differential geometry, mathematical basis, etc.

catalogue

4. 1 Volume 1

Chapter 1 Mathematics in Mesopotamia

1. Where did mathematics begin to appear? 2. The political history of Mesopotamia

3. Digital symbols

4. Arithmetic operation

5. Babylonian algebra

6. Babylonian geometry

7. Babylonian use of mathematics

8. Evaluation of Babylonian Mathematics

Chapter 2 Mathematics in Egypt

1. Background

2. arithmetic

3. Algebra and Geometry

4. Egyptians' use of mathematics

summary

Chapter 3 The emergence of classical Greek mathematics

1. Background

2. Historical sources

3. Several universities in the classical period

4. Ionian school

5. Pythagoras School

6. Electronic school

7. The Wise School

8. Plato school

9. eudoxus School

10. Aristotle and his school

Chapter 4 Euclid and apollonius

1. Introduction

2.2 background. Euclid is the original work.

3. Definitions and axioms in elements

4. Articles 1 to 4 of the original text

5. Part V: Proportional theory.

6. Part VI: Similarity

7. Chapters 7, 8 and 9: Number Theory

8. Chapter 10: Classification of uncommon indicators

9. Chapters 1 1, 12 and 13: solid geometry and exhaustive method.

10. Advantages and disadvantages of the original

Other mathematical works of 1 1 Euclid

12. apollonius's mathematical works

Chapter 5 Alexandria, Greece: Geometry and Triangle

1. The establishment of Alexandria

2. The characteristics of Alexander Greek mathematics

3. Archimedes' work on area and volume

4. Helen's work in area and volume

5. Some special curves

6. The establishment of trigonometry

7. Alexander's later geometric works

Chapter six Alexander: the revival of arithmetic and algebra

1. Symbols and operations of Greek arithmetic

2. The development of arithmetic and algebra as an independent discipline.

Chapter seven: The process of the formation of rational view of nature by the Greeks.

1. Enlightenment of Greek Mathematics

2. The beginning of rational view of nature

3. The development of mathematical design belief

4. Mathematical astronomy in Greece

5. Geography

……

Chapter VIII The Decline of the Greek World

Chapter 9 Mathematics in India and Arabia

Chapter 10 European Middle Ages

Chapter 1 1 Renaissance

Chapter 12 Contribution of Renaissance Mathematics

16 and 17 th century arithmetic and algebra

Chapter 14 the beginning of projective geometry

4.2 Book II

Chapter 16 Mathematicization of Science

1. Introduction 2. Descartes' view of science

3. Galileo's scientific research methods

4. Functional concept

Chapter 17 Creation of Calculus

1. Factors that promote the generation of calculus

2.65438+Calculus Work in the Early 7th Century

3. Newton's work

4. Leibniz's work

Comparison between 5.5. The work of Newton and Leibniz

6. Debate on priority

7. Some direct supplements to calculus

8. The reliability of calculus

Chapter 1817th century mathematics

1. the transformation of mathematics

2. Mathematics and Science

3. Communication between mathematicians

4. Expectation18th century

Chapter 191calculus in the 8th century

1. Introduction

2. The concept of function

3. Integration Technology and Complex Numbers

4. Elliptic integral

5. Other special functions

6. Multivariate function calculus

7. An attempt to provide rigor for calculus.

Chapter 20 Infinite series

1. Introduction

2. Early work of infinite series

3. Function expansion

4. The magical use of series

5. Trigonometric series

6. continued fraction

7. Convergence and divergence problems

1Ordinary differential equations in the 2nd chapter of the 8th century1

1. Theme

2. First order ordinary differential equation

3. Odd solutions

4. Second-order equation and Riccati equation

5. Higher-order equation

6. Series method

7. Differential equations

summary

18th century Chapter 22 Partial differential equations

18th century Chapter 23 Analytic Geometry and Differential Geometry

18th century Chapter XXIV Variational Method

18th century Chapter 25 Algebra

18th century Chapter 26 Mathematics

4.3 Book III

Chapter 27 Simple complex function

1. Introduction

2. The beginning of complex number theory 3. Geometric representation of complex numbers

4. The basis of the theory of reply number

5. The method of Wilstrass function theory.

6. Elliptic function

7. Hyperelliptic Integral and Abel Theorem

8. riemann sum multivalued function

9. Abel integral and Abel function

10. Conformal mapping

1 1. Function and Representation of Outliers

19th century Chapter 28 Partial differential equations

1. Introduction

2. Thermal equation and Fourier series

3. Closed solution; Fourier integral

4. Potential equation and Green's theorem

5. Curve coordinates

6. Wave equation and degenerate wave equation

7. System of partial differential equations

8. Existence theorem

19th century Chapter 29 Ordinary differential equations

1. Introduction

2. Series solutions and special functions

3. Sturm-Joseph Liouville theory

4. Existence theorem

5. Singularity theory

6. Automorphic function

7. Hill's work on periodic solutions of linear equations.

8. Nonlinear differential equations: qualitative theory

19th Century Chapter 30 Variational Method

1. Introduction

2. Mathematical Physics and Variational Methods

3. Mathematical extension of the variational method itself

4. Some problems in the variational method

Chapter 365438 +0 Galois Theory

1. Introduction

2. Quadratic equation

3. Abel's work in solving rooted equations

4. Galois's Solvability Theory

5. Geometric drawing problems

6. permutation group theory

Chapter 32 quaternion, vector and linear associative algebra

Algebraic basis for persistence of 1. type

2. Looking for three-dimensional "complex numbers"

3. Properties of quaternions

Calculus of 4.4. Grassmann expansion

5. From quaternion to vector

6. Linear associative algebra

Chapter 33 Determinants and Matrices

1. Introduction

2. Some new applications of determinant

3. Determinants and quadratic forms

4.[ number] matrix

19th Century Chapter 34 Number Theory

1. Introduction

……

Chapter 35 Revival of Projective Geometry

Chapter 36 Non-Euclidean Geometry

Chapter 37 Differential Geometry of Gauss and Riemann

Chapter 38 Projective Geometry and Metric Geometry

Chapter 39 Algebraic Geometry

4.4 Book IV

Chapter 40 Injection rigidity analysis 1. introduce

2. Functions and their properties

3. Derivative

4. Integral

5. Infinite series 6. Fourier series

7. Analysis status

Chapter 465438 The basis of +0 real number and remainder

1. Introduction

2. Algebraic numbers and transcendental numbers

3. Irrational number theory

4. Rational number theory

5. Other processing of real number system

6. The concept of infinite set

7. The basis of set theory

8. Overrun Cardinal Number and Overrun Ordinal Number

9. The situation of set theory in the early 20th century.

Chapter 42 Geometric Basis

Defects in 1 Euclid

2. Contribution to the foundation of projective geometry

The foundation of 3.3. Euclidean geometry

4. Some related basic work

5. Some unresolved issues

19th century Chapter 43 Mathematics

1.65438+Main features of the development in the 9th century.

2. Axiom Movement

3. Mathematics is the creation of human beings

4. The loss of truth

5. As mathematics for studying arbitrary structures

6. Compatibility issues

7. Take a look forward

Chapter 44 Theory of Real Variable Functions

1. Origin

2. Stiglitz integral

3. Early work of capacity and measurement

4. Lebesgue integral

promote

Chapter 45 Integral Equation

1. Introduction

2. The beginning of the general theory

3. Hilbert's works

4. Hilbert's direct successor

5. Popularization of theory

Chapter 46 Functional Analysis

Properties of 1. functional analysis

2. Functional theory

3. Linear functional analysis

Axiomatization of 4.4. Hilbert space

Chapter 47 Divergent series

1. Introduction

2. Informal application of divergent series

3. Formal theory of asymptotic series

Step 4 be accessible

Chapter 48 Tensor Analysis and Differential Geometry

1. the origin of tensor analysis

……

Chapter 49 The emergence of abstract algebra

Chapter 50 The Beginning of Topology

Chapter 565438 +0 Mathematical Foundation

Abbreviated list of magazine names

Personal name index

Noun index