The Calculus Gallery: Masterpieces from Newton to Lebesgue (Hardcover)

by William Dunham (Author) "Isaac Newton (1642-1727) stands as a seminal figure not just in mathematics but in all of Western intellectual history..." (more)
Key Phrases: pointwise discontinuity, transmutation theorem, pointwise discontinuous, Jakob Bernoulli, Georg Cantor, Henri Lebesgue (more...)

Editorial Reviews

Review
"Dunham succeeds in making the explanation understandable to those with the patience to go through each step. -- Victor J. Katz, American Scientist

"If a better historical treatment of the development of the calculus is available, this reviewer has yet to see it". -- D.S. Larson, Choice

"The Calculus Gallery is a wonderful book. The style is inviting; the explanations are clear and accessible". -- Judith V. Grabiner, Science

Review
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 )

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Product Details

• Hardcover: 256 pages
• Publisher: Princeton University Press; illustrated edition edition (December 13, 2004)
• Language: English
• ISBN-10: 0691095655
• ISBN-13: 978-0691095653
• Product Dimensions: 9.2 x 6.4 x 1 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars See all reviews (12 customer reviews)
• Amazon.com Sales Rank: #455,413 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

75 of 75 people found the following review helpful:

5.0 out of 5 stars Full of Interesting Examples and Proofs, May 6, 2005

By	Peter Kwok - See all my reviews (REAL NAME)

First of all, this is not a graduate textbook or reference book. I would not compare it with Counterexamples in Analysis even though both books have something in common. This is rather a "popular math" book with lots of proofs. And for a popular book with this much details, I am impressed . Those proofs are not just some nice-to-have's sweeped aside in the appendix. They are actually the main events and are showcased after each exihibit of the chapter. The table of content does not do justice to the richness and excitement of the examples in the book. Interesting topics include a function that is everywhere continuous but nowhere differentiable, a function that is nowhere continuous yet integrable, and other noteworthy discoveries throughout the history of calculus (or, rather, analysis). The book's title says "gallery". But, in my opinion, it aims more towards becoming a "museum". This book should be a good read for most people interested in the subject.

62 of 62 people found the following review helpful:

5.0 out of 5 stars A Great Book For Math Fans, September 29, 2005

By	Michael Gunther (Maryland, USA) - See all my reviews (TOP 1000 REVIEWER)    (REAL NAME)

If you like math, I guarantee you'll like this book! The author starts out with some very nice infinite sums from 17th and 18th century mathematics (Newton, Leibniz, the Bernoullis, and Euler's Gamma function). He continues into the 19th century with Riemann and Lebesque integrals, Weierstrass' pathological functions, Cantor's set theory, and winds up with Baire's category theorem.

Reading this book is like taking a guided tour through Real Analysis (= calculus of one real variable) with the math prof you always wished you had. Its only prerequisite is a working knowledge of calculus; the main points are explained very clearly, so the reader can skip through the book or fill in the details, and will learn a lot, either way. The book is very well written, and a great pleasure to read; I highly recommend it, for students, fans, and teachers!

30 of 30 people found the following review helpful:

4.0 out of 5 stars For the right audience, a good book, May 30, 2005

By	Peter Flom (New York City) - See all my reviews (REAL NAME)

There are many good things about this book - the theorems are beuatiful and they are part of 'real' mathematics. The writing is reasonably good. The only qualm I have is that the audience is quite specialized, more so than for most 'popular math' books. I think that anyone who has not had at least 3 semesters of calculus will find this mostly meaningless. However, for those who are familiar with calculus, this is an excellent book.