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More copies of this ISBNThe Calculus Gallery: Masterpieces from Newton to Lebesgueby William Dunham
Synopses & ReviewsPublisher 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. Furthermoreand this is an astounding achievementthe 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 bookan amazing mathematical pageturner. 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. Furthermoreand this is an astounding achievementthe 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 bookan amazing mathematical pageturner. 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 twentiethmathematicians 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 mindboggling 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 unflinchinga 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 AuthorWilliam 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 ContentsIllustrations 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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