The History of Mathematics: A Source-Based Approach

Cover
Title page
Copyright
Contents
Acknowledgments
	Permissions & Acknowledgments
Chapter 1. Introduction
Chapter 2. Early Mathematics
	Introduction
	2.1. Early counting
	2.2. Egyptian mathematics
	2.3. Mesopotamian mathematics
	2.4. A historical case study
	2.5. Further reading
Chapter 3. Greek Mathematics: An Introduction
	Introduction
	3.1. A dialogue from Plato’s Meno
	3.2. Geometry before Plato
	3.3. Plato and Aristotle
	3.4. Euclid’s Elements
	3.5. Further reading
Chapter 4. Greek Mathematics: Proofs and Problems
	Introduction
	4.1. The development of proof
	4.2. Methods of proof
	4.3. Doubling the cube and trisecting an angle
	4.4. Squaring the circle
	4.5. Further reading
Chapter 5. Greek Mathematics: Curves
	Introduction
	5.1. Problems with curves
	5.2. Archimedes
	5.3. Conics
	5.4. Further reading
Chapter 6. Greek Mathematics: Later Years
	Introduction
	6.1. The Hellenistic world
	6.2. Ptolemy and astronomy
	6.3. Diophantus
	6.4. The commentating tradition
	6.5. Further reading
Chapter 7. Mathematics in India and China
	Introduction
	7.1. Indian mathematics
	7.2. Chinese mathematics
	7.3. Further reading
Chapter 8. Mathematics in the Islamic World
	Introduction
	8.1. The Islamic intellectual world
	8.2. Islamic algebra
	8.3. Islamic geometry
	8.4. Further reading
Chapter 9. The Mathematical Awakening of Europe
	Introduction
	9.1. Mathematics in the medieval Christian West
	9.2. The rise of the universities
	9.3. Further reading
Chapter 10. The Renaissance: Recovery and Innovation
	Introduction
	10.1. Early European mathematics
	10.2. Renaissance translators: Maurolico andCommandino
	10.3. Cubics and quartics in 16th-century Italy
	10.4. Bombelli and Viète
	10.5. Further reading
Chapter 11. The Renaissance of Mathematics in Britain
	Introduction
	11.1. Mathematics in the vernacular: Robert Recorde
	11.2. Mathematics for the Commonwealth:John Dee
	11.3. The mathematical practitioners
	11.4. Thomas Harriot
	11.5. Excellent briefe rules: Napier and Briggs
	11.6. Further reading
Chapter 12. The Astronomical Revolution
	Introduction
	12.1. The Copernican revolution
	12.2. Kepler
	12.3. The language of nature: Galileo
	12.4. Further reading
Chapter 13. European Mathematics in the Early 17th Century
	Introduction
	13.1. Algebra and analysis
	13.2. Fermat’s number theory
	13.3. Descartes
	13.4. Pappus’s locus problem
	13.5. The Cartesian challenge to Euclid
	13.6. Further reading
Chapter 14. Concluding Remarks
Chapter 15. Exercises
	Advice on tackling the exercises
	Exercises: Part A
	Exercises: Part B
	Exercises: Part C
Bibliography
Index
Back Cover