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The Calculus Gallery By William Dunham

The Calculus Gallery

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Charts calculus' 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.

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The Calculus Gallery Summary


The Calculus Gallery: Masterpieces from Newton to Lebesgue by William Dunham

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 - mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. 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, most subtle 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.

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The Calculus Gallery Reviews


The Calculus Gallery is a wonderful book. The style is inviting; the explanations are clear and accessible... Mathematicians, scientists, and historians alike can learn much that is interesting, much that is mathematically significant, and a good deal that is both. -- Judith V. Grabiner, Science [A] brilliant book... I predict that Dunham's book will itself come to be considered a masterpiece in its field. -- Victor J. Katz, American Scientist What distinguishes this selection is it truly provides a history of mathematics, not just a history of mathematicians... If a better historical treatment of the development of the calculus is available, this reviewer has yet to see it... Essential. -- Choice A joy to read, The Calculus Gallery showcases one of the great intellectual pursuits of all time and, in the words of John von Neumann, 'the first achievement of modern mathematics.' Thirteen scholars, beginning with Newton and Leibniz, who gave birth to calculus in the seventeenth century, are featured in this sequential development of the important ideas that shaped calculus as we know it and gave rise to modern analysis... [I]t is a lovely and engaging gallery of the 'masters' that belongs in the library of everyone who seriously teaches or studies the subject. -- Diane M. Spresser, Mathematics Teacher A fascinating, competent visit too the calculus gallery. -- Eberhard Knobloch, Zentralblatt MATH

About William Dunham


William Dunham, Koehler Professor of Mathematics at Muhlenberg College, is the author of "Journey Through Genius: The Great Theorems of Mathematics"; "The Mathematical Universe"; and "Euler: The Master of Us All". He has received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.

Table of Contents


Illustrations ix Acknowledgments xiii INTRODUCTION 1 CHAPTER 1: Newton 5 CHAPTER 2: Leibniz 20 CHAPTER 3: The Bernoullis 35 CHAPTER 4: Euler 52 CHAPTER 5: First Interlude 69 CHAPTER 6: Cauchy 76 CHAPTER 7: Riemann 96 CHAPTER 8: Liouville 116 CHAPTER 9: Weierstrass 128 CHAPTER 10: Second Interlude 149 CHAPTER 11: Cantor 158 CHAPTER 12: Volterra 170 CHAPTER 13: Baire 183 CHAPTER 14: Lebesgue 200 Afterword 220 Notes 223 Index 233

Additional information

GOR006161295
The Calculus Gallery: Masterpieces from Newton to Lebesgue by William Dunham
William Dunham
Used - Very Good
Hardback
Princeton University Press
2004-12-13
256
0691095655
9780691095653
Runner-up for Choice Magazine Outstanding Reference/Academic Book Award 2005
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us.