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Tables of Contents for A History of Mathematics
Chapter/Section Title
Page #
Page Count
Preface
ix
PART ONE Mathematics Before the Sixth Century
1
191
CHAPTER 1 Ancient Mathematics
1
45
1.1 Ancient Civilizations
2
2
1.2 Counting
4
4
1.3 Arithmetic Computations
8
6
1.4 Linear Equations
14
5
1.5 Elementary Geometry
19
6
1.6 Astronomical Calculations
25
2
1.7 Square Roots
27
3
1.8 The Pythagorean Theorem
30
5
1.9 Quadratic Equations
35
11
CHAPTER 2 The Beginnings of Mathematics in Greece
46
56
2.1 The Earliest Greek Mathematics
47
5
2.2 The Time of Plato
52
2
2.3 Aristotle
54
4
2.4 Euclid and the Elements
58
37
2.5 Euclid's Other Works
95
7
CHAPTER 3 Archimedes and Apollonius
102
33
3.1 Archimedes and Physics
103
5
3.2 Archimedes and Numerical Calculations
108
3
3.3 Archimedes and Geometry
111
5
3.4 Conics Before Apollonius
116
1
3.5 The Conics of Apollonius
117
18
CHAPTER 4 Mathematical Methods in Hellenistic Times
135
33
4.1 Astronomy Before Ptolemy
136
9
4.2 Ptolemy and the Almagest
145
11
4.3 Practical Mathematics
156
12
CHAPTER 5 The Final Chapters of Greek Mathematics
168
24
5.1 Nicomachus and Elementary Number Theory
171
2
5.2 Diophantus and Greek Algebra
173
10
5.3 Pappus and Analysis
183
9
PART TWO Medieval Mathematics: 500-1400
192
150
CHAPTER 6 Medieval China and India
192
46
6.1 Introduction to Medieval Chinese Mathematics
192
1
6.2 The Mathematics of Surveying and Astronomy
193
4
6.3 Indeterminate Analysis
197
5
6.4 Solving Equations
202
8
6.5 Introduction to the Mathematics of Medieval India
210
2
6.6 Indian Trigonometry
212
6
6.7 Indian Indeterminate Analysis
218
7
6.8 Algebra and Combinatorics
225
5
6.9 The Hindu-Arabic Decimal Place-Value System
230
8
CHAPTER 7 The Mathematics of Islam
238
50
7.1 Decimal Arithmetic
240
3
7.2 Algebra
243
20
7.3 Combinatorics
263
5
7.4 Geometry
268
6
7.5 Trigonometry
274
14
CHAPTER 8 Mathematics in Medieval Europe
288
54
8.1 Geometry and Trigonometry
292
8
8.2 Combinatorics
300
7
8.3 Medieval Algebra
307
7
8.4 The Mathematics of Kinematics
314
13
INTERCHAPTER Mathematics Around the World
327
15
1.1 Mathematics at the Turn of the Fourteenth Century
327
5
1.2 Mathematics in America, Africa, and the Pacific
332
10
PART THREE Early Modern Mathematics: 1400-1700
342
202
CHAPTER 9 Algebra in the Renaissance
342
43
9.1 The Italian Abacists
343
5
9.2 Algebra in France, Germany, England, and Portugal
348
10
9.3 The Solution of the Cubic Equation
358
9
9.4 The Work of Viete and Stevin
367
18
CHAPTER 10 Mathematical Methods in the Renaissance
385
46
10.1 Perspective
389
4
10.2 Geography and Navigation
393
5
10.3 Astronomy and Trigonometry
398
18
10.4 Logarithms
416
4
10.5 Kinematics
420
11
CHAPTER 11 Geometry, Algebra, and Probability in the Seventeenth Century
431
37
11.1 Analytic Geometry
432
13
11.2 The Theory of Equations
445
3
11.3 Elementary Probability
448
10
11.4 Number Theory
458
2
11.5 Projective Geometry
460
8
CHAPTER 12 The Beginnings of Calculus
468
76
12.1 Tangents and Extrema
469
6
12.2 Areas and Volumes
475
17
12.3 Power Series
492
4
12.4 Rectification of Curves and the Fundamental Theorem
496
7
12.5 Isaac Newton
503
19
12.6 Gottfried Wilhelm Leibniz
522
10
12.7 First Calculus Texts
532
12
PART FOUR Modern Mathematics: 1700-2000
544
313
CHAPTER 13 Analysis in the Eighteenth Century
544
52
13.1 Differential Equations
545
15
13.2 Calculus Texts
560
14
13.3 Multiple Integration
574
4
13.4 Partial Differential Equations: The Wave Equation
578
4
13.5 The Foundations of Calculus
582
14
CHAPTER 14 Probability, Algebra, and Geometry in the Eighteenth Century
596
54
14.1 Probability
597
13
14.2 Algebra and Number Theory
610
11
14.3 Geometry
621
16
14.4 The French Revolution and Mathematics Education
637
3
14.5 Mathematics in the Americas
640
10
CHAPTER 15 Algebra in the Nineteenth Century
650
54
15.1 Number Theory
652
10
15.2 Solving Algebraic Equations
662
8
15.3 Groups and Fields-The Beginning of Structure
670
7
15.4 Symbolic Algebra
677
10
15.5 Matrices and Systems of Linear Equations
687
17
CHAPTER 16 Analysis in the Nineteenth Century
704
62
16.1 Rigor in Analysis
706
23
16.2 The Arithmetization of Analysis
729
8
16.3 Complex Analysis
737
9
16.4 Vector Analysis
746
7
16.5 Probability and Statistics
753
13
CHAPTER 17 Geometry in the Nineteenth Century
766
39
17.1 Differential Geometry
768
4
17.2 Non-Euclidean Geometry
772
13
17.3 Projective Geometry
785
7
17.4 Geometry in N Dimensions
792
5
17.5 The Foundations of Geometry
797
8
CHAPTER 18 Aspects of the Twentieth Century
805
52
18.1 Set Theory: Problems and Paradoxes
807
7
18.2 Topology
814
8
18.3 New Ideas in Algebra
822
12
18.4 Computers and Applications
834
23
ANSWERS TO SELECTED PROBLEMS
857
6
GENERAL REFERENCES IN THE HISTORY OF MATHEMATICS
863
INDEX AND PRONUNCIATION GUIDE
I-1