Paperback
Published: 1st March 1990
ISBN: 9780195061352
Number Of Pages: 390
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 Mesopotamia | p. 3 |
Where Did Mathematics Begin? | p. 3 |
Political History in Mesopotamia | p. 4 |
The Number Symbols | p. 5 |
Arithmetic Operations | p. 7 |
Babylonian Algebra | p. 8 |
Babylonian Geometry | p. 10 |
The Uses of Mathematics in Babylonia | p. 11 |
Evaluation of Babylonian Mathematics | p. 13 |
Egyptian Mathematics | p. 15 |
Background | p. 15 |
The Arithmetic | p. 16 |
Algebra and Geometry | p. 18 |
Egyptian Uses of Mathematics | p. 21 |
Summary | p. 22 |
The Creation of Classical Greek Mathematics | p. 24 |
Background | p. 24 |
The General Sources | p. 25 |
The Major Schools of the Classical Period | p. 27 |
The Ionian School | p. 28 |
The Pythagoreans | p. 28 |
The Eleatic School | p. 34 |
The Sophist School | p. 37 |
The Platonic School | p. 42 |
The School of Eudoxus | p. 48 |
Aristotle and His School | p. 51 |
Euclid and Apollonius | p. 56 |
Introduction | p. 56 |
The Background of Euclid's Elements | p. 57 |
The Definitions and Axioms of the Elements | p. 58 |
Books I to IV of the Elements | p. 60 |
Book V: The Theory of Proportion | p. 68 |
Book VI: Similar Figures | p. 73 |
Books VII, VIII, and IX: The Theory of Numbers | p. 77 |
Book X: The Classification of Incommensurables | p. 80 |
Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion | p. 81 |
The Merits and Defects of the Elements | p. 86 |
Other Mathematical Works by Euclid | p. 88 |
The Mathematical Work of Apollonius | p. 89 |
The Alexandrian Greek Period: Geometry and Trigonometry | p. 101 |
The Founding of Alexandria | p. 101 |
The Character of Alexandrian Greek Mathematics | p. 103 |
Areas and Volumes in the Work of Archimedes | p. 105 |
Areas and Volumes in the Work of Heron | p. 116 |
Some Exceptional Curves | p. 117 |
The Creation of Trigonometry | p. 119 |
Late Alexandrian Activity in Geometry | p. 126 |
The Alexandrian Period: The Reemergence of Arithmetic and Algebra | p. 131 |
The Symbols and Operations of Greek Arithmetic | p. 131 |
Arithmetic and Algebra as an Independent Development | p. 135 |
The Greek Rationalization of Nature | p. 145 |
The Inspiration for Greek Mathematics | p. 145 |
The Beginnings of a Rational View of Nature | p. 146 |
The Development of the Belief in Mathematical Design | p. 147 |
Greek Mathematical Astronomy | p. 154 |
Geography | p. 160 |
Mechanics | p. 162 |
Optics | p. 166 |
Astrology | p. 168 |
The Demise of the Greek World | p. 171 |
A Review of the Greek Achievements | p. 171 |
The Limitations of Greek Mathematics | p. 173 |
The Problems Bequeathed by the Greeks | p. 176 |
The Demise of the Greek Civilization | p. 177 |
The Mathematics of the Hindus and Arabs | p. 183 |
Early Hindu Mathematics | p. 183 |
Hindu Arithmetic and Algebra of the Period A.D. 200-1200 | p. 184 |
Hindu Geometry and Trigonometry of the Period A.D. 200-1200 | p. 188 |
The Arabs | p. 190 |
Arabic Arithmetic and Algebra | p. 191 |
Arabic Geometry and Trigonometry | p. 195 |
Mathematics circa 1300 | p. 197 |
The Medieval Period in Europe | p. 200 |
The Beginnings of a European Civilization | p. 200 |
The Materials Available for Learning | p. 201 |
The Role of Mathematics in Early Medieval Europe | p. 202 |
The Stagnation in Mathematics | p. 203 |
The First Revival of the Greek Works | p. 205 |
The Revival of Rationalism and Interest in Nature | p. 206 |
Progress in Mathematics Proper | p. 209 |
Progress in Physical Science | p. 211 |
Summary | p. 213 |
The Renaissance | p. 216 |
Revolutionary Influences in Europe | p. 216 |
The New Intellectual Outlook | p. 218 |
The Spread of Learning | p. 220 |
Humanistic Activity in Mathematics | p. 221 |
The Clamor for the Reform of Science | p. 223 |
The Rise of Empiricism | p. 227 |
Mathematical Contributions in the Renaissance | p. 231 |
Perspective | p. 231 |
Geometry Proper | p. 234 |
Algebra | p. 236 |
Trigonometry | p. 237 |
The Major Scientific Progress in the Renaissance | p. 240 |
Remarks on the Renaissance | p. 247 |
Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries | p. 250 |
Introduction | p. 250 |
The Status of the Number System and Arithmetic | p. 251 |
Symbolism | p. 259 |
The Solution of Third and Fourth Degree Equations | p. 263 |
The Theory of Equations | p. 270 |
The Binomial Theorem and Allied Topics | p. 272 |
The Theory of Numbers | p. 274 |
The Relationship of Algebra to Geometry | p. 278 |
The Beginnings of Projective Geometry | p. 285 |
The Rebirth of Geometry | p. 285 |
The Problems Raised by the Work on Perspective | p. 286 |
The Work of Desargues | p. 288 |
The Work of Pascal and La Hire | p. 295 |
The Emergence of New Principles | p. 299 |
Coordinate Geometry | p. 302 |
The Motivation for Coordinate Geometry | p. 302 |
The Coordinate Geometry of Fermat | p. 303 |
Rene Descartes | p. 304 |
Descartes's Work in Coordinate Geometry | p. 308 |
Seventeenth-Century Extensions of Coordinate Geometry | p. 317 |
The Importance of Coordinate Geometry | p. 321 |
The Mathematization of Science | p. 325 |
Introduction | p. 325 |
Descartes's Concept of Science | p. 325 |
Galileo's Approach to Science | p. 327 |
The Function Concept | p. 335 |
The Creation of the Calculus | p. 342 |
The Motivation for the Calculus | p. 342 |
Early Seventeenth-Century Work on the Calculus | p. 344 |
The Work of Newton | p. 356 |
The Work of Leibniz | p. 370 |
A Comparison of the Work of Newton and Leibniz | p. 378 |
The Controversy over Priority | p. 380 |
Some Immediate Additions to the Calculus | p. 381 |
The Soundness of the Calculus | p. 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): 0.5