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The Calculus Gallery: Masterpieces from Newton to Lebesgue
 
 

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

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)
4.0 out of 5 stars  See all reviews (1 customer review)
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Product details

  • Paperback: 256 pages
  • Publisher: Princeton University Press (1 Jun 2008)
  • Language English
  • ISBN-10: 0691136262
  • ISBN-13: 978-0691136264
  • Product Dimensions: 23.1 x 15.2 x 1.8 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon.co.uk Sales Rank: 257,492 in Books (See Bestsellers in Books)

    Popular in this category:

    #57 in  Books > Science & Nature > History & Philosophy > History of Mathematics
  • See Complete Table of Contents

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Product Description

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 )

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Isaac Newton (1642-1727) stands as a seminal figure not just in mathematics but in all of Western intellectual history. Read the first page
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The Calculus Gallery: Masterpieces from Newton to Lebesgue
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9 of 9 people found the following review helpful:
4.0 out of 5 stars Nicely Written but Omits Past 100 years, 22 Jan 2006
By JAMES BATTLE (London, UK) - See all my reviews
This nicely written book gives an excellent account of the history of calculus. Most of the material is elementary and should be accessible to a non-specialist audience.

I particularly enjoyed the chapter on Weierstrass and his non-differentiable function. This is the only (elementary) book I know, which includes a proof that this function is continuous but nowhere differentiable.

I'm disappointed that the story ends with Lebesgue and his theory of measure, which now dates back 100-years. The recent revival of “Riemann-style” techniques of integration, pioneered by Perron, Kurzweil, McShane and Henstock would have been interesting. Unlike Lebesgue’s theory, it would have been easy to present the intuition behind the Henstock integral. This would make it more apparent that Mathematics is a “living” subject, which continues to be refined to this day.

It might also have been worth including a brief mention of the Ito-Doeblin “stochastic calculus” and how it led to the Black-Scholes theory of option pricing. This would relate nicely to the chapter on Weirstrass and his “pathological” function.

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