{"product_id":"journey-through-genius-isbn-9780140147391","title":"Journey through Genius","description":"\u003cb\u003eLike 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.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eDunham 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, \u003ci\u003eJourney Through Genius\u003c\/i\u003e is a fascinating introduction to a neglected field of human creativity.\u003cbr\u003e\u003cbr\u003e“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 AsimovJourney through Genius - William Dunham       Preface\u003cbr\u003eAcknowledgments\u003cbr\u003e\u003cb\u003eChapter 1. Hippocrates' Quadrature of the Lune (ca. 440 B.C.)\u003c\/b\u003e\u003cbr\u003eThe Appearance of Demonstrative Mathematics\u003cbr\u003eSome Remarks on Quadrature\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 2. Euclid's Proof of the Pythagorean Theorem (ca. 300 B.C.)\u003c\/b\u003e\u003cbr\u003eThe \u003ci\u003eElements\u003c\/i\u003e of Euclid\u003cbr\u003eBook I: Preliminaries\u003cbr\u003eBook I: The Early Propositions\u003cbr\u003eBook I: Parallelism and Related Topics\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 3. Euclid and the Infinitude of Primes (ca. 300 B.C.)\u003c\/b\u003e\u003cbr\u003eThe \u003ci\u003eElements\u003c\/i\u003e, Books II-VI\u003cbr\u003eNumber Theory in Euclid\u003cbr\u003eGreat Theorem\u003cbr\u003eThe Final Books of the \u003ci\u003eElements\u003c\/i\u003e\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 4. Archimedes' Determination of Circular Area (ca. 225 B.C.)\u003c\/b\u003e\u003cbr\u003eThe Life of Archimedes\u003cbr\u003eGreat Theorem\u003cbr\u003eArchimedes' Masterpiece: \u003ci\u003eOn the Sphere and the Cylinder\u003c\/i\u003e\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 5. Heron's Formula for Triangular Area (ca. A.D. 75)\u003c\/b\u003e\u003cbr\u003eClassical Mathematics after Archimedes\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 6. Cardano and the Solution of the Cubic (1545)\u003c\/b\u003e\u003cbr\u003eA Horatio Algebra Story\u003cbr\u003eGreat Theorem\u003cbr\u003eFurther Topics on Solving Equations\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 7. A Gem from Isaac Newton (Late 1660s)\u003c\/b\u003e\u003cbr\u003eMathematics of the Heroic Century\u003cbr\u003eA Mind Unleashed\u003cbr\u003eNewton's Binomial Theorem\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 8. The Bernoullis and the Harmonic Series (1689)\u003c\/b\u003e\u003cbr\u003eThe Contributions of Leibniz\u003cbr\u003eThe Brothers Bernoulli\u003cbr\u003eGreat Theorem\u003cbr\u003eThe Challenge of the Brachistochrone\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 9. The Extraordinary Sums of Leonhard Euler (1734)\u003c\/b\u003e\u003cbr\u003eThe Master of All Mathematical Trades\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 10. A Sampler of Euler's Number Theory (1736)\u003c\/b\u003e\u003cbr\u003eThe Legacy of Fermat\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 11. The Non-Denumerability of the Continuum (1874)\u003c\/b\u003e\u003cbr\u003eMathematics of the Nineteenth Century\u003cbr\u003eCantor and the Challenge of the Infinite\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003e\u003cb\u003eChapter 12. Cantor and the Transfinite Realm (1891)\u003c\/b\u003e\u003cbr\u003eThe Nature of Infinite Cardinals\u003cbr\u003eGreat Theorem\u003cbr\u003eEpilogue\u003cbr\u003eAfterword\u003cbr\u003eChapter Notes\u003cbr\u003eReferences\u003cbr\u003eIndex\"An inspired piece of intellectual history.\"— \u003ci\u003eLos Angeles Times\u003c\/i\u003e\u003cp\u003e“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\u003c\/p\u003e\u003cp\u003e“Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.”—Ivars Peterson, author of \u003ci\u003eThe Mathematical Tourist\u003c\/i\u003e\u003c\/p\u003e\u003cb\u003eWilliam Dunham\u003c\/b\u003e 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.\"","brand":"Penguin Books","offers":[{"title":"Default Title","offer_id":48233285615845,"sku":"NP9780140147391","price":19.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780140147391.jpg?v=1767730478","url":"https:\/\/k12savings.com\/products\/journey-through-genius-isbn-9780140147391","provider":"K12savings","version":"1.0","type":"link"}