Amazon.com: The Calculus Gallery: Masterpieces from Newton to Lebesgue (9780691095653): William Dunham: Books

Buy Used
Used - Good See details
$20.29 & eligible for FREE Super Saver Shipping on orders over $25. Details

or
Sign in to turn on 1-Click ordering.
 
   
Sell Back Your Copy
For a $2.43 Gift Card
Trade in
Have one to sell? Sell yours here
The Calculus Gallery: Masterpieces from Newton to Lebesgue
 
 
Tell the Publisher!
I'd like to read this book on Kindle

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

The Calculus Gallery: Masterpieces from Newton to Lebesgue [Hardcover]

William Dunham (Author)
4.9 out of 5 stars  See all reviews (18 customer reviews)


Available from these sellers.


Textbook Student FREE Two-Day Shipping for students on millions of items. Learn more

Formats

Amazon Price New from Used from
Hardcover --  
Paperback $17.54  
Unknown Binding --  
Sell Back Your Copy for $2.43
Whether you buy it used on Amazon for $9.99 or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $2.43.
Used Price$9.99
Trade-in Price$2.43
Price after
Trade-in
$7.56

Book Description

December 13, 2004 0691095655 978-0691095653

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.



Editorial Reviews

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

From the Inside Flap

"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

"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 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

"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


Product Details

  • Hardcover: 256 pages
  • Publisher: Princeton University Press (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
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #455,434 in Books (See Top 100 in Books)

More About the Author

William 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.

 

Customer Reviews

18 Reviews
5 star:
 (17)
4 star:
 (1)
3 star:    (0)
2 star:    (0)
1 star:    (0)
 
 
 
 
 
Average Customer Review
4.9 out of 5 stars (18 customer reviews)
 
 
 
 
Share your thoughts with other customers:
Most Helpful Customer Reviews

97 of 97 people found the following review helpful:
5.0 out of 5 stars Full of Interesting Examples and Proofs, May 6, 2005
This review is from: The Calculus Gallery: Masterpieces from Newton to Lebesgue (Hardcover)
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.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


76 of 76 people found the following review helpful:
5.0 out of 5 stars A Great Book For Math Fans, September 29, 2005
By 
This review is from: The Calculus Gallery: Masterpieces from Newton to Lebesgue (Hardcover)
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!
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


45 of 45 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)   
This review is from: The Calculus Gallery: Masterpieces from Newton to Lebesgue (Hardcover)
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.

Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No

Share your thoughts with other customers: Create your own review
 
 
 
Most Recent Customer Reviews











Only search this product's reviews



Inside This Book (learn more)
First Sentence:
Isaac Newton (1642-1727) stands as a seminal figure not just in mathematics but in all of Western intellectual history. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pointwise discontinuity, transmutation theorem, pointwise discontinuous, outer content, ruler function, denumerable collection, denumerable union, intermediate value property, open subinterval, bounded convergence theorem, pathological function, category theorem, vanishing quantities, function oscillates, infinitely small quantity, completeness property, pointwise limit
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jakob Bernoulli, Georg Cantor, Henri Lebesgue, Isaac Newton, Karl Weierstrass, René Baire, Augustin-Louis Cauchy, Johann Bernoulli, Vito Volterra, Eric Temple Bell, Hermann Hankel, James Gregory, Joseph Liouville
New!
Books on Related Topics | Concordance | Text Stats
Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Search Inside This Book:





Tags Customers Associate with This Product

 (What's this?)
Click on a tag to find related items, discussions, and people.
 
(1)

Your tags: Add your first tag
 

Sell a Digital Version of This Book in the Kindle Store

If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store. Learn more

Customer Discussions

This product's forum
Discussion Replies Latest Post
No discussions yet

Ask questions, Share opinions, Gain insight
Start a new discussion
Topic:
First post:
Prompts for sign-in
 


Active discussions in related forums
Search Customer Discussions
Search all Amazon discussions
   
Related forums





Look for Similar Items by Category


Look for Similar Items by Subject