Mathematical Thought From Ancient to Modern Times, Volume 2 [NOOK Book]


This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of ...
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Mathematical Thought From Ancient to Modern Times, Volume 2

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This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

Together, these volumes offer a lucid and authoritative study which demonstrates how the character of mathematics as a whole has changed over the centuries.

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Editorial Reviews

From the Publisher
"I have always had great regard for this book as the one which relates the development of modern mathematical ideas in a readable fashion."—Michael F. O'Reilly, University of Minnesota in Morris

"Outstanding scholarship and readability. One of only a couple of books available in English for in-depth historical studies at the fourth year/graduate level."—Charles V. Jones, Ball State University

"The consistently high quality of presentation, the accuracy, the readable style, and the stress on the conceptual development of mathematics make [these volumes] a most desirable reference."—Choice

"Without a doubt a book which should be in the library of every institution where mathematics is either taught or played."—The Economist

"What must be the definitive history of mathematical thought....Probably the most comprehensive account of mathematical history we have yet had."—Saturday Review

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Product Details

  • ISBN-13: 9780199840427
  • Publisher: Oxford University Press, USA
  • Publication date: 3/1/1990
  • Sold by: Barnes & Noble
  • Format: eBook
  • File size: 11 MB
  • Note: This product may take a few minutes to download.

Meet the Author

Morris Kline is Professor of Mathematics, Emeritus, at the Courant Institute of Mathematical Sciences, New York University, where he directed the Division of Electromagnetic Research for twenty years.

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Table of Contents

1 Mathematics in Mesopotamia 3
1 Where Did Mathematics Begin? 3
2 Political History in Mesopotamia 4
3 The Number Symbols 5
4 Arithmetic Operations 7
5 Babylonian Algebra 8
6 Babylonian Geometry 10
7 The Uses of Mathematics in Babylonia 11
8 Evaluation of Babylonian Mathematics 13
2 Egyptian Mathematics 15
1 Background 15
2 The Arithmetic 16
3 Algebra and Geometry 18
4 Egyptian Uses of Mathematics 21
5 Summary 22
3 The Creation of Classical Greek Mathematics 24
1 Background 24
2 The General Sources 25
3 The Major Schools of the Classical Period 27
4 The Ionian School 28
5 The Pythagoreans 28
6 The Eleatic School 34
7 The Sophist School 37
8 The Platonic School 42
9 The School of Eudoxus 48
10 Aristotle and His School 51
4 Euclid and Apollonius 56
1 Introduction 56
2 The Background of Euclid's Elements 57
3 The Definitions and Axioms of the Elements 58
4 Books I to IV of the Elements 60
5 Book V: The Theory of Proportion 68
6 Book VI: Similar Figures 73
7 Books VII, VIII, and IX: The Theory of Numbers 77
8 Book X: The Classification of Incommensurables 80
9 Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion 81
10 The Merits and Defects of the Elements 86
11 Other Mathematical Works by Euclid 88
12 The Mathematical Work of Apollonius 89
5 The Alexandrian Greek Period: Geometry and Trigonometry 101
1 The Founding of Alexandria 101
2 The Character of Alexandrian Greek Mathematics 103
3 Areas and Volumes in the Work of Archimedes 105
4 Areas and Volumes in the Work of Heron 116
5 Some Exceptional Curves 117
6 The Creation of Trigonometry 119
7 Late Alexandrian Activity in Geometry 126
6 The Alexandrian Period: The Reemergence of Arithmetic and Algebra 131
1 The Symbols and Operations of Greek Arithmetic 131
2 Arithmetic and Algebra as an Independent Development 135
7 The Greek Rationalization of Nature 145
1 The Inspiration for Greek Mathematics 145
2 The Beginnings of a Rational View of Nature 146
3 The Development of the Belief in Mathematical Design 147
4 Greek Mathematical Astronomy 154
5 Geography 160
6 Mechanics 162
7 Optics 166
8 Astrology 168
8 The Demise of the Greek World 171
1 A Review of the Greek Achievements 171
2 The Limitations of Greek Mathematics 173
3 The Problems Bequeathed by the Greeks 176
4 The Demise of the Greek Civilization 177
9 The Mathematics of the Hindus and Arabs 183
1 Early Hindu Mathematics 183
2 Hindu Arithmetic and Algebra of the Period A.D. 200-1200 184
3 Hindu Geometry and Trigonometry of the Period A.D. 200-1200 188
4 The Arabs 190
5 Arabic Arithmetic and Algebra 191
6 Arabic Geometry and Trigonometry 195
7 Mathematics circa 1300 197
10 The Medieval Period in Europe 200
1 The Beginnings of a European Civilization 200
2 The Materials Available for Learning 201
3 The Role of Mathematics in Early Medieval Europe 202
4 The Stagnation in Mathematics 203
5 The First Revival of the Greek Works 205
6 The Revival of Rationalism and Interest in Nature 206
7 Progress in Mathematics Proper 209
8 Progress in Physical Science 211
9 Summary 213
11 The Renaissance 216
1 Revolutionary Influences in Europe 216
2 The New Intellectual Outlook 218
3 The Spread of Learning 220
4 Humanistic Activity in Mathematics 221
5 The Clamor for the Reform of Science 223
6 The Rise of Empiricism 227
12 Mathematical Contributions in the Renaissance 231
1 Perspective 231
2 Geometry Proper 234
3 Algebra 236
4 Trigonometry 237
5 The Major Scientific Progress in the Renaissance 240
6 Remarks on the Renaissance 247
13 Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries 250
1 Introduction 250
2 The Status of the Number System and Arithmetic 251
3 Symbolism 259
4 The Solution of Third and Fourth Degree Equations 263
5 The Theory of Equations 270
6 The Binomial Theorem and Allied Topics 272
7 The Theory of Numbers 274
8 The Relationship of Algebra to Geometry 278
14 The Beginnings of Projective Geometry 285
1 The Rebirth of Geometry 285
2 The Problems Raised by the Work on Perspective 286
3 The Work of Desargues 288
4 The Work of Pascal and La Hire 295
5 The Emergence of New Principles 299
15 Coordinate Geometry 302
1 The Motivation for Coordinate Geometry 302
2 The Coordinate Geometry of Fermat 303
3 Rene Descartes 304
4 Descartes's Work in Coordinate Geometry 308
5 Seventeenth-Century Extensions of Coordinate Geometry 317
6 The Importance of Coordinate Geometry 321
16 The Mathematization of Science 325
1 Introduction 325
2 Descartes's Concept of Science 325
3 Galileo's Approach to Science 327
4 The Function Concept 335
17 The Creation of the Calculus 342
1 The Motivation for the Calculus 342
2 Early Seventeenth-Century Work on the Calculus 344
3 The Work of Newton 356
4 The Work of Leibniz 370
5 A Comparison of the Work of Newton and Leibniz 378
6 The Controversy over Priority 380
7 Some Immediate Additions to the Calculus 381
8 The Soundness of the Calculus 383
List of Abbreviations
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