History of Mathematics, A

Part I. Ancient Mathematics

 

1. Egypt and Mesopotamia

1.1 Egypt

1.2 Mesopotamia

 

2. The Beginnings of Mathematics in Greece

2.1 The Earliest Greek Mathematics

2.2 The Time of Plato

2.3 Aristotle

 

3. Euclid

3.1 Introduction to the Elements

3.2 Book I and the Pythagorean Theorem

3.3 Book II and Geometric Algebra

3.4 Circles and the Pentagon

3.5 Ratio and Proportion

3.6 Number Theory

3.7 Irrational Magnitudes

3.8 Solid Geometry and the Method of Exhaustion

3.9 Euclid’s Data

 

4. Archimedes and Apollonius

4.1 Archimedes and Physics

4.2 Archimedes and Numerical Calculations

4.3 Archimedes and Geometry

4.4 Conic Sections Before Apollonius

4.5 The Conics of Apollonius

 

5. Mathematical Methods in Hellenistic Times

5.1 Astronomy Before Ptolemy

5.2 Ptolemy and The Almagest

5.3 Practical Mathematics

 

6. The Final Chapter of Greek Mathematics

6.1 Nichomachus and Elementary Number Theory

6.2 Diophantus and Greek Algebra

6.3 Pappus and Analysis

 

Part II. Medieval Mathematics

 

7. Ancient and Medieval China

7.1 Introduction to Mathematics in China

7.2 Calculations

7.3 Geometry

7.4 Solving Equations

7.5 Indeterminate Analysis

7.6 Transmission to and from China

 

8. Ancient and Medieval India

8.1 Introduction to Mathematics in India

8.2 Calculations

8.3 Geometry

8.4 Equation Solving

8.5 Indeterminate Analysis

8.6 Combinatorics

8.7 Trigonometry

8.8 Transmission to and from India

 

9. The Mathematics of Islam

9.1 Introduction to Mathematics in Islam

9.2 Decimal Arithmetic

9.3 Algebra

9.4 Combinatorics

9.5 Geometry

9.6 Trigonometry

9.7 Transmission of Islamic Mathematics

 

10. Medieval Europe

10.1 Introduction to the Mathematics of Medieval Europe

10.2 Geometry and Trigonometry

10.3 Combinatorics

10.4 Medieval Algebra

10.5 The Mathematics of Kinematics

 

11. Mathematics Elsewhere

11.1 Mathematics at the Turn of the Fourteenth Century

11.2 Mathematics in America, Africa, and the Pacific

 

Part III. Early Modern Mathematics

 

12. Algebra in the Renaissance

12.1 The Italian Abacists

12.2 Algebra in France, Germany, England, and Portugal

12.3 The Solution of the Cubic Equation

12.4 Viete, Algebraic Symbolism, and Analysis

12.5 Simon Stevin and Decimal Analysis

 

13. Mathematical Methods in the Renaissance

13.1 Perspective

13.2 Navigation and Geography

13.3 Astronomy and Trigonometry

13.4 Logarithms

13.5 Kinematics

 

14. Geometry, Algebra and Probability in the Seventeenth Century

14.1 The Theory of Equations

14.2 Analytic Geometry

14.3 Elementary Probability

14.4 Number Theory

14.5 Projective Geometry

 

15. The Beginnings of Calculus

15.1 Tangents and Extrema

15.2 Areas and Volumes

15.3 Rectification of Curves and the Fundamental Theorem

 

16. Newton and Leibniz

16.1 Isaac Newton

16.2 Gottfried Wilhelm Leibniz

16.3 First Calculus Texts

 

Part IV. Modern Mathematics

 

17. Analysis in the Eighteenth Century

17.1 Differential Equations

17.2 The Calculus of Several Variables

17.3 Calculus Texts

17.4 The Foundations of Calculus

 

18. Probability and Statistics in