History of Mathematics, A: An Introduction,9780321016188

History of Mathematics, A: An Introduction

by
Edition: 2nd
ISBN13: 9780321016188
ISBN10: 0321016181
Format: Paperback
Pub. Date: 1998-01-01
Publisher(s): Addison Wesley
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Summary

One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history.

Table of Contents

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

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