Product Description

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.

Product Details

• Amazon Sales Rank: #114205 in Books
• Published on: 2008-07-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 256 pages

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 )

Review
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 )

Customer Reviews

Full of Interesting Examples and Proofs
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.

A Great Book For Math Fans
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!

For the right audience, a good book
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.