Journey through Genius: Great Theorems of Mathematics / Edition 1

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Overview

There is a remarkable permanence about mathematical ideas. Whereas other scientific disciplines regularly discard the old and outmoded, in mathematics new results build upon their predecessors without rendering them obsolete. The astronomical theories and medical practices of the Alexandrian Greeks, works of undisputed genius in their day, have long since become archaic curios. Yet Euclid’s proof of the Pythagorean theorem, set forth in 300 B.C., has lost none of its beauty or validity with the passage of time. A theorem, correctly proved within the rigors of logic, is a theorem forever. Journey Through Genius explores some of the most significant and enduring ideas in mathematics: the great theorems, discoveries of beauty and insight that stand today as monuments to the human intellect. Writing with extraordinary clarity, wit, and enthusiasm, Professor William Dunham takes us on a fascinating journey through the intricate reasoning of these masterworks and the often turbulent lives and times of their creators. Along with the essential mathematics, Professor Dunham uniquely captures the humanity of these great mathematicians. You’ll meet Archimedes of Syracuse, who pushed mathematics to frontiers that would stand some 1,500 years. Unchallenged as the greatest mathematician of antiquity, Archimedes was the stereotypically "absent minded" mathematician, capable of forgetting to eat or bathe while at work on a problem. From the sixteenth century you’ll encounter Gerolamo Cardano, whose mathematical accomplishments provide a fascinating counterpoint to his extraordinary misadventures. In the next century, there appeared the competitive, bickering Bernoulli brothers, who explored the arcane world of infinite series when not engaged in contentious wrangling with one another. And from more modern times you’ll read of the paranoid genius of Georg Cantor, who had the ability and courage to make a frontal assault on that most challenging of mathematical ideas—the infinite. Journey Through Genius is a rare combination of the historical, biographical, and mathematical. Readers will find the history engaging and fast-paced, the mathematics presented in careful steps. Indeed, those who keep paper, pencil, and straightedge nearby will find themselves rewarded by a deeper understanding and appreciation of these powerful discoveries. Regardless of one’s mathematical facility, all readers will come away from this exhilarating book with a keen sense of the majesty and power, the creativity and genius of these mathematical masterpieces.

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Editorial Reviews

Booknews
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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Product Details

  • ISBN-13: 9780471500308
  • Publisher: Wiley
  • Publication date: 3/30/1990
  • Series: Science Editions Series
  • Edition number: 1
  • Pages: 320
  • Sales rank: 907,338
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.88 (d)

Meet 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."

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Table of Contents

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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  • Anonymous

    Posted April 21, 2000

    Wonderful

    Research was remarkable. The author gives considerable information about the lives of great mathematicians, which add a tremendous element of human interest to the book. The great theorems are explained clearly so that most people with a mathematical background can understand. You don't have to be math major to understand this book, but you do need to know algebra, geometry, and a little calculus is a plus.

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