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More copies of this ISBNThis title in other editionsJourney Through Genius: The Great Theorems of Mathematicsby William Dunham
Synopses & ReviewsPublisher Comments: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. Synopsis:A rare combination of the historical, biographical, and mathematicalgenius, this book is a fascinating introduction to a neglected field of human creativity. Dunham places mathematical theorem, along with masterpieces of art, music, and literature and gives them the attention they deserve.
Description:Includes bibliographical references (p. 291-293) and index. About the AuthorWilliam Dunham is a Phi Beta Kappa graduate of the University of Pittsburgh. After receiving his Ph.D. from the Ohio State University in 1974, he joined the mathematics faculty at Hanover College in Indiana. He has directed a summer seminar funded by the National Endowment for the Humanities on the topic of "The Great Theorems of Mathematics in Historical Context." Table of Contents 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
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