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Journey Through Genius

Autor William Dunham
en Limba Engleză Hardback – 16 ian 1991
Praise for William Dunham's Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments." ?Ivars Peterson Author, The Mathematical Tourist Mathematics and Physics Editor, Science News "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
"It is a captivating collection of essays of major mathematical achievements brought to life by the personal and historical anecdotes which the author has skillfully woven into the text. This is a book which should find its place on the bookshelf of anyone interested 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 Dunham drops in on some of the greatest mathematicians in history. Almost as if we chat over tea and crumpets, we get to know them and their ideas?ideas that ring with eternity and that offer glimpses into the often veiled beauty of mathematics and logic. And all the while we marvel, hoping that the tour will not stop." ?Jearl Walker, Physics Department, Cleveland State University Author of The Flying Circus of Physics
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Specificații

ISBN-13: 9780471500308
ISBN-10: 0471500305
Pagini: 320
Ilustrații: illustrations; portraits
Dimensiuni: 157 x 235 x 23 mm
Greutate: 0.61 kg
Editura: Wiley
Locul publicării:Hoboken, United States

Descriere

Praise for William Dunham s Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.

Cuprins

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

Recenzii

"An inspired piece of intellectual history."
Los Angeles Times

“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

“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 The Mathematical Tourist

Notă biografică

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."

Textul de pe ultima copertă

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.