Princeton University Press
The Calculus Gallery
Author / Editor information
Reviews
"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
A fascinating, competent visit too the calculus gallery.---Eberhard Knobloch, Zentralblatt MATH
One of Choice's Outstanding Academic Titles for 2005
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
"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
"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
"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
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.
[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
"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
"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
William Dunham, Winner of the 2006 Lester R. Ford Award for his expository article on "Touring the Calculus Gallery" in The American Mathematical Monthly
Topics
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Frontmatter
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Contents
vii -
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Illustrations
ix -
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Acknowledgments
xiii -
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Introduction
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Chapter 1. Newton
5 -
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Chapter 2. Leibniz
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Chapter 3. Bernoullis
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Chapter 4. Euler
52 -
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Chapter 5. First Interlude
69 -
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Chapter 6. Cauchy
76 -
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Chapter 7. Riemann
96 -
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Chapter 8. Liouville
116 -
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Chapter 9. Weierstrass
128 -
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Chapter 10. Second Interlude
149 -
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Chapter 11. Cantor
158 -
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Chapter 12. Volterra
170 -
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Chapter 13. Baire
183 -
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Chapter 14. Lebesgue
200 -
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Afterword
220 -
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Notes
223 -
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Index
233