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I. Early Western Mathematics. 1. Origins. 2. Ancient Egyptian Mathematics. 3. Mesopotamia. 4. The Early Greeks. 5. The Euclidean Synthesis. 6. Archimedes and Apollonius. 7. Hellenistic Mathematical Science. 8. Mathematics in the Roman Empire -- II. Other Mathematical Traditions. 9. The Mathematics of the Hindus. 10. Chinese Mathematics. 11. Korea and Japan. 12. Islamic Mathematics -- III. Modern Mathematics. 13. Medieval Europe. 14. The Renaissance. 15. The Calculus. 16. Seventeenth-Century Mathematics. 17. Beyond the Calculus. 18. Modern Mathematical Science. 19. Contemporary Mathematics