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The Calculus Gallery: Masterpieces from Newton to Lebesgue

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The Calculus Gallery: Masterpieces from Newton to Lebesgue Cover

 

Synopses & Reviews

Publisher Comments:

"The Calculus Gallery is one of the best efforts at mathematical exposition I have ever read! Dunham presents in detail and in his own words the sequence of ideas of classical giants of mathematics, but each new idea is described in modern terms and notation, so I had absolutely no trouble following along. Furthermore--and this is an astounding achievement--the entire work has a tightly woven development. If it were a detective story I would say it had a plot with no loose ends. An amazing feat. I wish I could plan a single lecture, never mind a course or a book, that well!"--Henry Pollak, Teachers College, Columbia University

"What a fine resource! All of the famous functions that have shaped calculus and analysis parade before the reader in the original words of their creators. Bill Dunham has produced an excellent volume that teachers and students will enjoy and appreciate."--Thomas Banchoff, Brown University

"Bill Dunham has done it again. The Calculus Gallery is a masterly journey through the works of thirteen mathematicians who formulated, formalised, and reformed the calculus into the modern analysis we learn today. Readers of his earlier books have learned to expect a clarity of exposition that few others can attain: they will not be disappointed."--Robin Wilson, author of Four Colors Suffice

"This is an excellent book--an amazing mathematical page-turner. William Dunham has done the seemingly impossible: he has taken some difficult, advanced mathematics and, without sacrificing the technical details, written a lively, readable book about it."--Barry Cipra, author of Misteaks . . . and How to Find Them Before the Teacher Does

"Pedagogically excellent and extremely well written, The Calculus Gallery bridges the gap between general histories and detailed studies of individual mathematicians. Dunham has described mathematical developments in an engaging style rarely found in literature of this kind."--Annette Imhausen, Trinity Hall, Cambridge

"A welcome addition to the literature. The idea of presenting a 'museum of mathematics' is new. It allows the author to present a nonstandard selection of theorems, so that even mathematicians with a strong historical background will learn a few things."--Franz Lemmermeyer, Bilkent University, author of Reciprocity Laws: From Euler to Eisenstein

Synopsis:

"The Calculus Gallery is one of the best efforts at mathematical exposition I have ever read! Dunham presents in detail and in his own words the sequence of ideas of classical giants of mathematics, but each new idea is described in modern terms and notation, so I had absolutely no trouble following along. Furthermore--and this is an astounding achievement--the entire work has a tightly woven development. If it were a detective story I would say it had a plot with no loose ends. An amazing feat. I wish I could plan a single lecture, never mind a course or a book, that well!"--Henry Pollak, Teachers College, Columbia University

"What a fine resource! All of the famous functions that have shaped calculus and analysis parade before the reader in the original words of their creators. Bill Dunham has produced an excellent volume that teachers and students will enjoy and appreciate."--Thomas Banchoff, Brown University

"Bill Dunham has done it again. The Calculus Gallery is a masterly journey through the works of thirteen mathematicians who formulated, formalised, and reformed the calculus into the modern analysis we learn today. Readers of his earlier books have learned to expect a clarity of exposition that few others can attain: they will not be disappointed."--Robin Wilson, author of Four Colors Suffice

"This is an excellent book--an amazing mathematical page-turner. William Dunham has done the seemingly impossible: he has taken some difficult, advanced mathematics and, without sacrificing the technical details, written a lively, readable book about it."--Barry Cipra, author of Misteaks . . . and How to Find Them Before the Teacher Does

"Pedagogically excellent and extremely well written, The Calculus Gallery bridges the gap between general histories and detailed studies of individual mathematicians. Dunham has described mathematical developments in an engaging style rarely found in literature of this kind."--Annette Imhausen, Trinity Hall, Cambridge

"A welcome addition to the literature. The idea of presenting a 'museum of mathematics' is new. It allows the author to present a nonstandard selection of theorems, so that even mathematicians with a strong historical background will learn a few things."--Franz Lemmermeyer, Bilkent University, author of Reciprocity Laws: From Euler to Eisenstein

Synopsis:

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.

About the Author

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

Product Details

ISBN:
9780691136264
Author:
Dunham, William
Publisher:
Princeton University Press
Location:
Princeton
Subject:
History -- Philosophy.
Subject:
Calculus
Subject:
History
Subject:
Mathematics
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Mathematics -- History.
Edition Description:
Trade paper
Publication Date:
20080631
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
19 halftones. 44 line illus.
Pages:
256
Dimensions:
9 x 6 in

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The Calculus Gallery: Masterpieces from Newton to Lebesgue New Trade Paper
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Product details 256 pages Princeton University Press - English 9780691136264 Reviews:
"Synopsis" by , "The Calculus Gallery is one of the best efforts at mathematical exposition I have ever read! Dunham presents in detail and in his own words the sequence of ideas of classical giants of mathematics, but each new idea is described in modern terms and notation, so I had absolutely no trouble following along. Furthermore--and this is an astounding achievement--the entire work has a tightly woven development. If it were a detective story I would say it had a plot with no loose ends. An amazing feat. I wish I could plan a single lecture, never mind a course or a book, that well!"--Henry Pollak, Teachers College, Columbia University

"What a fine resource! All of the famous functions that have shaped calculus and analysis parade before the reader in the original words of their creators. Bill Dunham has produced an excellent volume that teachers and students will enjoy and appreciate."--Thomas Banchoff, Brown University

"Bill Dunham has done it again. The Calculus Gallery is a masterly journey through the works of thirteen mathematicians who formulated, formalised, and reformed the calculus into the modern analysis we learn today. Readers of his earlier books have learned to expect a clarity of exposition that few others can attain: they will not be disappointed."--Robin Wilson, author of Four Colors Suffice

"This is an excellent book--an amazing mathematical page-turner. William Dunham has done the seemingly impossible: he has taken some difficult, advanced mathematics and, without sacrificing the technical details, written a lively, readable book about it."--Barry Cipra, author of Misteaks . . . and How to Find Them Before the Teacher Does

"Pedagogically excellent and extremely well written, The Calculus Gallery bridges the gap between general histories and detailed studies of individual mathematicians. Dunham has described mathematical developments in an engaging style rarely found in literature of this kind."--Annette Imhausen, Trinity Hall, Cambridge

"A welcome addition to the literature. The idea of presenting a 'museum of mathematics' is new. It allows the author to present a nonstandard selection of theorems, so that even mathematicians with a strong historical background will learn a few things."--Franz Lemmermeyer, Bilkent University, author of Reciprocity Laws: From Euler to Eisenstein

"Synopsis" by , 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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