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Mathematical Thought From Ancient to Modern Times : Volume 1 - Morris Kline

Mathematical Thought From Ancient to Modern Times

Volume 1

Paperback

Published: 1st March 1990
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This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians 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.

"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 "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 "It's a pleasure to see such a complete and scholarly treatise of this type from the pen of a working mathematician."--Robert A. Haberstroh, The Boston Globe "I found it hard to put the book down--the bold sweep of mathematics, as a shaper of the world, and as it is shaped by world needs is balanced neatly with almost anecdotal vignettes."--New Engineer "For scope and detail there is no work which could compete with [this book]. Students or teachers in search of their mathematical heritage will find most of it in Mathematical Thought from Ancient to Modern Times."--Times Literary Supplement (London) "The most ambitious and comprehensive history in the English language of mathematics and its relations to science."--Carl Boyer, author of A History of Mathematics "We had better treasure this book on our shelf, for as far as mathematical history goes, it is the best we have."--Gian-Carlo Rota, Massachusetts Institute of Technology "A precious source of information on the history of mathematics....The book, clearly the result of a lifetime of critical research, will be appreciated by all who wish their understanding of the way our present mathematics came into being both broadened and deepened."--Dirk J. Struik, author of A Concise History of Mathematics "A masterful presentation....His narrative reveals mathematics as a living organism of man's intellect."--Philip J. Davis, Brown University "Superb! Thorough, accurate, usefully organized--the way history books should be."--School Science and Mathematics "It is not unlikely that history will establish this book as one of the great works of the twentieth century in the field of mathematics....One of a kind."--Mathematics Teacher "A remarkably readable book....There is no other book from which one can obtain a comparable understanding of the history of mathematics....Extraordinary."--American Scientist "A work of love....A magnificent, successful attempt to produce a chronological overview of the entire field of pure and applied mathematics."--Industrial Mathematics "A great and important work....Should be found in all places where the history of mathematics is dealt with or touched upon."--Centaurus "As a survey of the history of mathematics from its earliest beginnings to modern times, Kline's work is without peer."--Phillip Johnson, University of North Carolina, Charlotte "This classic work...reveals the unity behind seemingly disconnected branches of the discipline."--Science News "This is probably the most extensive and scholarly general reference book on the history of mathematics available in English....Extremely valuable."--Michael J. Dixon, California State University "The work is an excellent candidate for a school or personal library or as a textbook for a course in the history of mathematics covering the period from 3000 B.C. to A.D. 1650." --Mathematics Teacher

Mathematics in Mesopotamiap. 3
Where Did Mathematics Begin?p. 3
Political History in Mesopotamiap. 4
The Number Symbolsp. 5
Arithmetic Operationsp. 7
Babylonian Algebrap. 8
Babylonian Geometryp. 10
The Uses of Mathematics in Babyloniap. 11
Evaluation of Babylonian Mathematicsp. 13
Egyptian Mathematicsp. 15
Backgroundp. 15
The Arithmeticp. 16
Algebra and Geometryp. 18
Egyptian Uses of Mathematicsp. 21
Summaryp. 22
The Creation of Classical Greek Mathematicsp. 24
Backgroundp. 24
The General Sourcesp. 25
The Major Schools of the Classical Periodp. 27
The Ionian Schoolp. 28
The Pythagoreansp. 28
The Eleatic Schoolp. 34
The Sophist Schoolp. 37
The Platonic Schoolp. 42
The School of Eudoxusp. 48
Aristotle and His Schoolp. 51
Euclid and Apolloniusp. 56
Introductionp. 56
The Background of Euclid's Elementsp. 57
The Definitions and Axioms of the Elementsp. 58
Books I to IV of the Elementsp. 60
Book V: The Theory of Proportionp. 68
Book VI: Similar Figuresp. 73
Books VII, VIII, and IX: The Theory of Numbersp. 77
Book X: The Classification of Incommensurablesp. 80
Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustionp. 81
The Merits and Defects of the Elementsp. 86
Other Mathematical Works by Euclidp. 88
The Mathematical Work of Apolloniusp. 89
The Alexandrian Greek Period: Geometry and Trigonometryp. 101
The Founding of Alexandriap. 101
The Character of Alexandrian Greek Mathematicsp. 103
Areas and Volumes in the Work of Archimedesp. 105
Areas and Volumes in the Work of Heronp. 116
Some Exceptional Curvesp. 117
The Creation of Trigonometryp. 119
Late Alexandrian Activity in Geometryp. 126
The Alexandrian Period: The Reemergence of Arithmetic and Algebrap. 131
The Symbols and Operations of Greek Arithmeticp. 131
Arithmetic and Algebra as an Independent Developmentp. 135
The Greek Rationalization of Naturep. 145
The Inspiration for Greek Mathematicsp. 145
The Beginnings of a Rational View of Naturep. 146
The Development of the Belief in Mathematical Designp. 147
Greek Mathematical Astronomyp. 154
Geographyp. 160
Mechanicsp. 162
Opticsp. 166
Astrologyp. 168
The Demise of the Greek Worldp. 171
A Review of the Greek Achievementsp. 171
The Limitations of Greek Mathematicsp. 173
The Problems Bequeathed by the Greeksp. 176
The Demise of the Greek Civilizationp. 177
The Mathematics of the Hindus and Arabsp. 183
Early Hindu Mathematicsp. 183
Hindu Arithmetic and Algebra of the Period A.D. 200-1200p. 184
Hindu Geometry and Trigonometry of the Period A.D. 200-1200p. 188
The Arabsp. 190
Arabic Arithmetic and Algebrap. 191
Arabic Geometry and Trigonometryp. 195
Mathematics circa 1300p. 197
The Medieval Period in Europep. 200
The Beginnings of a European Civilizationp. 200
The Materials Available for Learningp. 201
The Role of Mathematics in Early Medieval Europep. 202
The Stagnation in Mathematicsp. 203
The First Revival of the Greek Worksp. 205
The Revival of Rationalism and Interest in Naturep. 206
Progress in Mathematics Properp. 209
Progress in Physical Sciencep. 211
Summaryp. 213
The Renaissancep. 216
Revolutionary Influences in Europep. 216
The New Intellectual Outlookp. 218
The Spread of Learningp. 220
Humanistic Activity in Mathematicsp. 221
The Clamor for the Reform of Sciencep. 223
The Rise of Empiricismp. 227
Mathematical Contributions in the Renaissancep. 231
Perspectivep. 231
Geometry Properp. 234
Algebrap. 236
Trigonometryp. 237
The Major Scientific Progress in the Renaissancep. 240
Remarks on the Renaissancep. 247
Arithmetic and Algebra in the Sixteenth and Seventeenth Centuriesp. 250
Introductionp. 250
The Status of the Number System and Arithmeticp. 251
Symbolismp. 259
The Solution of Third and Fourth Degree Equationsp. 263
The Theory of Equationsp. 270
The Binomial Theorem and Allied Topicsp. 272
The Theory of Numbersp. 274
The Relationship of Algebra to Geometryp. 278
The Beginnings of Projective Geometryp. 285
The Rebirth of Geometryp. 285
The Problems Raised by the Work on Perspectivep. 286
The Work of Desarguesp. 288
The Work of Pascal and La Hirep. 295
The Emergence of New Principlesp. 299
Coordinate Geometryp. 302
The Motivation for Coordinate Geometryp. 302
The Coordinate Geometry of Fermatp. 303
Rene Descartesp. 304
Descartes's Work in Coordinate Geometryp. 308
Seventeenth-Century Extensions of Coordinate Geometryp. 317
The Importance of Coordinate Geometryp. 321
The Mathematization of Sciencep. 325
Introductionp. 325
Descartes's Concept of Sciencep. 325
Galileo's Approach to Sciencep. 327
The Function Conceptp. 335
The Creation of the Calculusp. 342
The Motivation for the Calculusp. 342
Early Seventeenth-Century Work on the Calculusp. 344
The Work of Newtonp. 356
The Work of Leibnizp. 370
A Comparison of the Work of Newton and Leibnizp. 378
The Controversy over Priorityp. 380
Some Immediate Additions to the Calculusp. 381
The Soundness of the Calculusp. 383
List of Abbreviations
Index
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780195061352
ISBN-10: 0195061357
Series: Mathematical Thought from Ancient to Modern Times : Book 1
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 390
Published: 1st March 1990
Publisher: Oxford University Press Inc
Country of Publication: US
Dimensions (cm): 23.3 x 15.9  x 2.2
Weight (kg): 0.63