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Journey Through Genius: The Great Theorems of Mathematics

by

Journey Through Genius: The Great Theorems of Mathematics Cover

 

Synopses & Reviews

Publisher 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 Author

William 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

Product Details

ISBN:
9780140147391
performance:
Dunham, William
Publisher:
Penguin Books
Author:
Dunham, William
Location:
New York, N.Y., U.S.A. :
Subject:
General
Subject:
Biography
Subject:
History
Subject:
Mathematics
Subject:
Mathematical Analysis
Subject:
Mathematicians
Subject:
Mathematicians -- Biography.
Subject:
Mathematics -- History.
Subject:
Mathematics - General
Copyright:
Edition Description:
Paperback / softback
Series Volume:
no. 13
Publication Date:
19910831
Binding:
TRADE PAPER
Grade Level:
from 12
Language:
English
Illustrations:
Yes
Pages:
320
Dimensions:
7.76x5.09x.60 in. .49 lbs.
Age Level:
from 18

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Related Subjects


Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History

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Product details 320 pages Penguin Books - English 9780140147391 Reviews:
"Synopsis" by , 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.

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