Journey through Genius: Great Theorems of Mathematics / Edition 1

by William Dunham

Overview

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

Product Details

ISBN-13:	9780471500308
Publisher:	Wiley
Publication date:	01/16/1991
Series:	Science Editions Series
Pages:	320
Sales rank:	1,131,342
Product dimensions:	6.30(w) x 9.29(h) x 1.10(d)

About the Author

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."

Table of Contents

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

Editorial Reviews

Dunham (math, Hanover College, Indiana) explores the "masterpieces" of mathematics, seventeen landmarks spanning 2,300 years and representing ten mathematicians. He not only elucidates the theorems, but places each in the context of math at the time, and includes a biographical sketch of the mathematician. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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