Mathematics and Its History

Cover......Page 1
Title page......Page 2
Preface......Page 6
Contents......Page 8
CHAPTER 1 The Theorem of Pythagoras......Page 10
CHAPTER 2 Greek Geometry......Page 22
CHAPTER 3 Greek Number Theory......Page 36
CHAPTER 4 Infinity in Greek Mathematics......Page 46
CHAPTER 5 Polynomial Equations......Page 57
CHAPTER 6 Analytic Geometry......Page 74
CHAPTER 7 Projective Geometry......Page 87
CHAPTER 8 Calculus......Page 109
CHAPTER 9 Infinite Series......Page 127
CHAPTER 10 The Revival of Number Theory......Page 144
CHAPTER 11 Elliptic Functions......Page 161
CHAPTER 12 Mechanics......Page 176
CHAPTER 13 Complex Numbers in Algebra......Page 197
CHAPTER 14 Complex Numbers and Curves......Page 213
CHAPTER 15 Complex Numbers and Functions......Page 229
CHAPTER 16 Differential Geometry......Page 246
CHAPTER 17 Noneuclidean Geometry......Page 264
CHAPTER 18 Group Theory......Page 284
CHAPTER 19 Topology......Page 301
CHAPTER 20 Sets, Logic, and Computation......Page 322
References......Page 342
Index......Page 372