Journey through genius : the great theorems of mathematics
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書誌事項
Journey through genius : the great theorems of mathematics
Penguin Books, 1991, c1990
- pbk.
- hc.
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注記
Includes bibliographical references (p. 291-293)
内容説明・目次
- 巻冊次
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pbk. ISBN 9780140147391
内容説明
Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.
Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator - from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.
"It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash." -Isaac Asimov
目次
Journey through Genius - William Dunham Preface
Acknowledgments
Chapter 1. Hippocrates' Quadrature of the Lune (ca. 440 B.C.)
The Appearance of Demonstrative Mathematics
Some Remarks on Quadrature
Great Theorem
Epilogue
Chapter 2. Euclid's Proof of the Pythagorean Theorem (ca. 300 B.C.)
The Elements of Euclid
Book I: Preliminaries
Book I: The Early Propositions
Book I: Parallelism and Related Topics
Great Theorem
Epilogue
Chapter 3. Euclid and the Infinitude of Primes (ca. 300 B.C.)
The Elements, Books II-VI
Number Theory in Euclid
Great Theorem
The Final Books of the Elements
Epilogue
Chapter 4. Archimedes' Determination of Circular Area (ca. 225 B.C.)
The Life of Archimedes
Great Theorem
Archimedes' Masterpiece: On the Sphere and the Cylinder
Epilogue
Chapter 5. Heron's Formula for Triangular Area (ca. A.D. 75)
Classical Mathematics after Archimedes
Great Theorem
Epilogue
Chapter 6. Cardano and the Solution of the Cubic (1545)
A Horatio Algebra Story
Great Theorem
Further Topics on Solving Equations
Epilogue
Chapter 7. A Gem from Isaac Newton (Late 1660s)
Mathematics of the Heroic Century
A Mind Unleashed
Newton's Binomial Theorem
Great Theorem
Epilogue
Chapter 8. The Bernoullis and the Harmonic Series (1689)
The Contributions of Leibniz
The Brothers Bernoulli
Great Theorem
The Challenge of the Brachistochrone
Epilogue
Chapter 9. The Extraordinary Sums of Leonhard Euler (1734)
The Master of All Mathematical Trades
Great Theorem
Epilogue
Chapter 10. A Sampler of Euler's Number Theory (1736)
The Legacy of Fermat
Great Theorem
Epilogue
Chapter 11. The Non-Denumerability of the Continuum (1874)
Mathematics of the Nineteenth Century
Cantor and the Challenge of the Infinite
Great Theorem
Epilogue
Chapter 12. Cantor and the Transfinite Realm (1891)
The Nature of Infinite Cardinals
Great Theorem
Epilogue
Afterword
Chapter Notes
References
Index
- 巻冊次
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hc. ISBN 9780471500308
内容説明
Praise for William Dunham s Journey Through Genius The GreatTheorems of Mathematics "Dunham deftly guides the reader throughthe verbal and logical intricacies of major mathematical questionsand proofs, conveying a splendid sense of how the greatestmathematicians from ancient to modern times presented theirarguments." Ivars Peterson Author, The Mathematical TouristMathematics and Physics Editor, Science News
"It is mathematics presented as a series of works of art; afascinating lingering over individual examples of ingenuity andinsight. It is mathematics by lightning flash." Isaac Asimov
"It is a captivating collection of essays of major mathematicalachievements brought to life by the personal and historicalanecdotes which the author has skillfully woven into the text. Thisis a book which should find its place on the bookshelf of anyoneinterested in science and the scientists who create it." R. L.Graham, AT&T Bell Laboratories
"Come on a time-machine tour through 2,300 years in which Dunhamdrops in on some of the greatest mathematicians in history. Almostas if we chat over tea and crumpets, we get to know them and theirideas ideas that ring with eternity and that offer glimpses intothe often veiled beauty of mathematics and logic. And all the whilewe marvel, hoping that the tour will not stop." Jearl Walker,Physics Department, Cleveland State University Author of The FlyingCircus of Physics
目次
Hippocrates' Quadrature of the Lune (ca. 440 B.C.).
Euclid's Proof of the Pythagorean Theorem (ca. 300 B.C.).
Euclid and the Infinitude of Primes (ca. 300 B.C.).
Archimedes' Determination of Circular Area (ca. 225 B.C.).
Heron's Formula for Triangular Area (ca. A.D. 75).
Cardano and the Solution of the Cubic (1545).
A Gem from Isaac Newton (Late 1660s).
The Bernoullis and the Harmonic Series (1689).
The Extraordinary Sums of Leonhard Euler (1734).
A Sampler of Euler's Number Theory (1736).
The Non-Denumerability of the Continuum (1874).
Cantor and the Transfinite Realm (1891).
Afterword.
Chapter Notes.
References.
Index.
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