The history of mathematics: A brief course (2013)


Part I. What is Mathematics?

Chapter 1. Mathematics and its History

Chapter 2. Proto-mathematics

Part II. The Middle East, 2000–1500 BCE

Chapter 3. Overview of Mesopotamian Mathematics

Chapter 4. Computations in Ancient Mesopotamia

Chapter 5. Geometry in Mesopotamia

Chapter 6. Egyptian Numerals and Arithmetic

Chapter 7. Algebra and Geometry in Ancient Egypt

Part III. Greek Mathematics From 500 BCE to 500 CE

Chapter 8. An Overview of Ancient Greek Mathematics

Chapter 9. Greek Number Theory

Chapter 10. Fifth-Century Greek Geometry

Chapter 11. Athenian Mathematics I: The Classical Problems

Chapter 12. Athenian Mathematics II: Plato and Aristotle

Chapter 13. Euclid of Alexandria

Chapter 14. Archimedes of Syracuse

Chapter 15. Apollonius of Perga

Chapter 16. Hellenistic and Roman Geometry

Chapter 17. Ptolemy's Geography and Astronomy

Part IV. India, China, and Japan 500 BCE-1700 CE

Chapter 18. Pappus and the Later Commentators

Chapter 19. Overview of Mathematics in India

Chapter 20. From the Vedas to Aryabhata I

Chapter 21. Brahmagupta, the Kuttaka, and Bhaskara II

Chapter 22. Early Classics of Chinese Mathematics

Chapter 23. Later Chinese Algebra and Geometry

Chapter 24. Traditional Japanese Mathematics

Part V. Islamic Mathematics, 800-1500

Chapter 25. Overview of Islamic Mathematics

Chapter 26. Islamic Number Theory and Algebra

Chapter 27. Islamic Geometry

Part VI. European Mathematics, 500-1900

Chapter 28. Medieval and Early Modern Europe

Chapter 29. European Mathematics: 1200-1500

Chapter 30. Sixteenth-Century Algebra

Chapter 31. Renaissance Art and Geometry

Chapter 32. The Calculus Before Newton and Leibniz

Chapter 33. Newton and Leibniz

Chapter 34. Consolidation of the Calculus

Part VII. Special Topics

Chapter 35. Women Mathematicians

Chapter 36. Probability

Chapter 37. Algebra from 1600 to 1850

Chapter 38. Projective and Algebraic Geometry and Topology

Chapter 39. Differential Geometry

Chapter 40. Non-Euclidean Geometry

Chapter 41. Complex Analysis

Chapter 42. Real Numbers, Series, and Integrals

Chapter 43. Foundations of Real Analysis

Chapter 44. Set Theory

Chapter 45. Logic