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Journey through Genius

Great Theorems of Mathematics

William Dunham

$65.95

Hardback

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English
JOHN WILEY & SONS
16 March 1990
"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"

By:  
Imprint:   JOHN WILEY & SONS
Country of Publication:   United States
Dimensions:   Height: 236mm,  Width: 160mm,  Spine: 28mm
Weight:   624g
ISBN:   9780471500308
ISBN 10:   0471500305
Pages:   320
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Further / Higher Education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Preface v Acknowledgements ix Chapter 1 Hippocrates' Quadrature of the Lune (ca 440 BC) 1 Chapter 2 Euclid's Proof of the Pythagorean Theorem (ca 300 BC) 27 Chapter 3 Euclid and the Infinitude of Primes (ca 300 BC) 61 Chapter 4 Archimedes' Determination of Circular Area (ca 225 BC) 84 Chapter 5 Heron's Formula for Triangular Area (ca AD 75) 113 Chapter 6 Cardano and the Solution of the Cubic (1545) 133 Chapter 7 A Gem from Isaac Newton (Late 1660s) 155 Chapter 8 The Bernoullis and the Harmonic Series (1689) 184 Chapter 9 The Extraordinary Sums of Leonhard Euler (1734) 207 Chapter 10 A Sampler of Euler's Number Theory (1736) 223 Chapter 11 The Non-Denumerability of the Continuum (1874) 245 Chapter 12 Cantor and the Transfinite Realm (1891) 267 Afterword 285 Chapter Notes 287 References 291 Index 295

About the author WILLIAM DUNHAM is a Phi Beta Kappa graduate of the University of Pittsburgh. After receiving his PhD 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.

Reviews for Journey through Genius: Great Theorems of Mathematics

An eloquent exposition of what Dunham (Mathematics/Hanover) calls the Mona Lisas or Hamlets of mathematics - 12 classic theorems ranging from Hippocrates' quadrature of the lunes (c. 440 B.C.) and Euclid's proof of the Pythagorean theorem (c. 300 B.C.) to Georg Cantor's theorem of the non-denumerability of the continuum (1874) and his crowning achievement, Cantor's Theorem (1891), which, as Dunham puts it, pushed mathematics into unexplored territory where it began to merge into the realms of philosophy and metaphysics. Dunham brackets his explanation of each theorem with an accessible discussion of the state of mathematics - and of the world - prior to the theorem, and relevant biographical information about the mathematicians. The theorem explanations themselves, for all their elegance, require a current familiarity with high-school-level math; while not for many of us, then, Dunham's fine tour through the best of mathematics will prove a treat for those who know the difference between a finite cardinal and an infinite one. (Kirkus Reviews)


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