The History of Mathematics A Brief Course

ROGER L. COOKE, PhD, is Williams Professor of Mathematics at the University of Vermont. His research interests include the history of mathematics and Fourier analysis, and he has taught a general introduction to the history and development of mathematics for many years.

Preface xxi

Changes From the Second Edition xxii

Elementary Texts on the History of Mathematics xxiii

Part 1. What is Mathematics? 1

Chapter 1. Mathematics and its History 3

Chapter 2. Proto-mathematics 15

Part 2. The Middle East, 2000-1500 BCE 27

Chapter 3. Overview of Mesopotamian Mathematics 29

Chapter 4. Computations in Ancient Mesopotamia 39

Chapter 5. Geometry in Mesopotamia 47

Chapter 6. Egyptian Numerals and Arithmetic  57

Chapter 7. Algebra and Geometry in Ancient Egypt 67

Part 3. Greek Mathematics From 500 BCE to 500 CE 79

Chapter 8. An Overview of Ancient Greek Mathematics 81

Chapter 9. Greek Number Theory 93

Chapter 10. Fifth-Century Greek Geometry 105

Chapter 11. Athenian Mathematics I: The Classical Problems  117

Chapter 12. Athenian Mathametics II: Plato and Aristotle 131

Chapter 13. Euclid of Alexandria 143

Chapter 14. Archimedes of Syracuse 151

Chapter 15. Apollonius of Perga 163

Chapter 16. Hellenistic and Roman Geometry 173

Chapter 17. Ptolemy’s Geography and Astronomy 181

Chapter 18. Pappus and the Later Commentators 195

Part 4. India, China, and Japan 500 BCE-1700 CE 205

Chapter 19. Overview of Mathematics in India 207

Chapter 20. From the Vedas to Aryabhata I 217

Chapter 21. Brahmagupta, the Kuttaka, and Bhaskara II 231

Chapter 22. Early Classics of Chinese Mathematics 243

Chapter 23. Later Chinese Algebra and Geometry 259

Chapter 24. Traditional Japanese Mathematics 271

Part 5. Islamic Mathematics, 800-1500 285

Chapter 25. Overview of Islamic Mathematics 287

Chapter 26. Islamic Number Theory and Algebra 297

Chapter 27. Islamic Geometry 307

Part 6. European Mathematics, 500-1900 317

Chapter 28. Medieval and Early Modern Europe 319

Chapter 29. European Mathematics: 1200-1500 331

Chapter 30. Sixteenth-Century Algebra 345

Chapter 31. Renaissance Art and Geometry 355

Chapter 32. The Calculus Before Newton and Leibniz 365

Chapter 33. Newton and Leibniz 379

Chapter 34. Consolidation of the Calculus 393

Part 7. Special Topics 407

Chapter 35. Women Mathematicians 411

Chapter 36. Probability 423

Chapter 37. Algebra from 1600 to 1850 439

Chapter 38. Projective and Algebraic Geometry and Topology 453

Chapter 39. Differential Geometry 469

Chapter 40. Non-Euclidean Geometry 485

Chapter 41. Complex Analysis 499

Chapter 42. Real Numbers, Series, and Integrals 515

Chapter 43. Foundations of Real Analysis 525

Chapter 44. Set Theory 537

Chapter 45. Logic 547

Literature 563

Subject Index 581

Name Index 609

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