The Calculus Gallery: Masterpieces from Newton to Lebesgue

The Calculus Gallery: Masterpieces from Newton to Lebesgue

by William Dunham
     
 

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ISBN-10: 0691095655

ISBN-13: 9780691095653

Pub. Date: 12/13/2004

Publisher: Princeton University Press

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri

Overview

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. William Dunham lucidly presents the definitions, theorems, and proofs. "Students of literature read Shakespeare; students of music listen to Bach," he writes. But this tradition of studying the major works of the "masters" is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.

Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of [pi] (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original "category theorem" (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching-a story of genius triumphing over some of the toughest, subtlest problems imaginable.

Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

Product Details

ISBN-13:
9780691095653
Publisher:
Princeton University Press
Publication date:
12/13/2004
Pages:
256
Product dimensions:
6.40(w) x 9.62(h) x 0.93(d)

Related Subjects

Table of Contents

Illustrationsix
Acknowledgmentsxiii
Introduction1
Chapter 1Newton5
Chapter 2Leibniz20
Chapter 3The Bernoullis35
Chapter 4Euler52
Chapter 5First Interlude69
Chapter 6Cauchy76
Chapter 7Riemann96
Chapter 8Liouville116
Chapter 9Weierstrass128
Chapter 10Second Interlude149
Chapter 11Cantor158
Chapter 12Volterra170
Chapter 13Baire183
Chapter 14Lebesgue200
Afterword220
Notes223
Index233

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