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Notes on Fermat's Last Theorem (Canadian Mathematical Society Series of Monographs and Advanced Texts) Hardcover – February 16, 1996

11 customer reviews
ISBN-13: 978-0471062615 ISBN-10: 0471062618 Edition: 1st

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Editorial Reviews

Review

Have you ever wanted a math book that you could dip into like a favorite, inspired novel? One in which every page has a delicious quote, a provoking viewpoint, or a novel insight? A book that when read for the third time still makes you think or smile? A book that you can't put down, finding yourself reading on, even when you only picked it up to check on one little fact? This is Van der Poorten's polished, eccentric, opinionated, and inspiring Notes on Fermat's Last Theorem. We need more mathematics books like this.

...Finally, let me repeat that Van der Poorten's monograph is a wonderful mathematics book, which dares to breach the stylistic barriers that usually impede understanding. It encompasses a lot of material, from elementary to very deep, but remains accessible. I expect it will turn a lot of people on to number theory and arithmetic geometry, and indeed the beauty of mathematics as a whole. -- American Mathematical Monthly A Publication of the American Mathematical Society

From the Publisher

This is one of the first books to deal with Fermat's theorem and its proof discovered by Andrew Wiles, including a succinct discussion of Wiles' proof and its implications. Each chapter explains a separate area of number theory as it pertains to Fermat's last theorem and combined, presents a concise history of the theorem. The engaging writing style makes the text accessible for non-math students.
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Product Details

  • Hardcover: 240 pages
  • Publisher: Wiley-Interscience; 1st edition (February 16, 1996)
  • Language: English
  • ISBN-10: 0471062618
  • ISBN-13: 978-0471062615
  • Product Dimensions: 6.4 x 0.9 x 9.6 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #2,069,223 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful By Marvin J. Greenberg on February 7, 2010
Format: Hardcover
Look: I am a professor of mathematics (retired) and I did not understand much of the technicalities in this book. So the criticisms by other reviewers that the book was too difficult are correct. It is not an account for the lay person, although if read correctly, a lay person can still get a lot out of browsing through it, because the technical mathematics is peppered with so much history and anecdotes about the living mathematicians involved, plus the marvelous humor of the author, that a lay person could enjoy it greatly with the proper attitude.

There are other books about FLT written specifically for non-mathematicians. They pretend to explain what Wiles did, but that is practically impossible to do in any meaningful way. If you want to go that route, try "Fearless Symmetry" by Ash and Gross. If you think you understand the last chapters in it, maybe you are mathematically talented after all!

I rave about this book because, in addition to some technical information I am trained enough to understand, the author conveyed the incredible drama of Wiles' achievement so well, especially in contrast to the failures over hundreds of years of many expert mathematicians (well, they did have partial successes - Kummer, Vandiver, Faltings et al - but those were not front page news for the New York Times). And what added to that drama was Wiles' initial failure, an irredeemable gap in his first proof; fortunately he found a different method leading to a correct proof with the help of Taylor. Also, having read Wiles' final correct paper in the Annals of Mathematics (and not understanding it), I saw that he generously acknowledged all the preceding results and techniques by so many other fine mathematicians upon which his work was based.
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11 of 12 people found the following review helpful By dwe@groom.com on March 5, 1998
Format: Hardcover
The cover says this book can be understood by anyone with a basic math background and an interest in formulas. Don't believe it! By only the second chapter, the author assumes, without any real explanation, that you know what a euclidean field is and how continued fractions relate to matrices. The presentation strikes me as arrogant; there are far too many gaps to be filled in by the reader. Maybe I'm dumb, but I did somehow manage to stumble through MIT with 16 straight A's in my undergraduate math courses, and spent three years in graduate school studying number theory. The author should have taken more time to explain, and skipped a lot of the sideshows and self-promotion. If I could return this book I would. I give it a 3 only because the appendices are more fun than the main text.
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10 of 12 people found the following review helpful By rjohnp on March 20, 2001
Format: Hardcover
This is grossly inaccurately advertised. In the introduction the author states that high school math plus an acquaintance with a first course in linear algebra is sufficient to understand the general flow. This is silly at best.

The contents are loosely related lectures introducing (and only introducing - this isn't a summary of Wiles' proof) topics in number theory necessary for proving FLT. Each lecture is followed by "Notes and Remarks" often containing more advanced material that is lengthier than the lecture itself. While this separation is good in itself, the lectures still require math far beyond high school and in some cases require graduate work. Lecture 4 starts with a cyclotomic field that is a concept well beyond high school. Lecture 8 starts with the Riemann zeta function that, despite the fact that a high school student can understand it as an infinite series, requires for its appreciation a mathematical sophistication that is not reached until graduate school. Lecture 12 contains the phrase "As regards the zeta function, the trick turns out to be to notice that ... is in fact holomorphic", so one must understand "holomorphic". Note 3 of lecture 13 refers to a residue that, as a topic in complex analysis, is unheard of in high school. Algebraic number fields, the Riemann sphere, poles of complex functions and more all make their appearance, albeit briefly. I truly picked these examples just by opening the book at random multiple times. Woe to the reader who is lacking these topics and more besides.

Pleasure to the reader with the background and, far more importantly, the mathematical sophistication to appreciate this book. As a set of lectures its character is quite different from a number theory textbook. Its audience is small but will no doubt be enthusiastic.
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7 of 8 people found the following review helpful By A Customer on July 11, 1999
Format: Hardcover
The book is a bit confusing until you get into it.
The proof of Fermat's Last Theorem by Andrew Wiles has generated a great interest in number theory and mathematics in general. Alf's book is a huge intellectual meal!
For the reader with a casual interest, read the recent article in Scientific American or watch the NOVA program on PBS. This book gets at the heart of the mathematical issues that made Fermat's Last Theorem such a stimulus for mathematics research for the last 350 years.
Van der Porteen has a nerdish style that is partially explained by his biography. Still, the book was an enjoyable stretch for me, and I am glad he put forth the effort!
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2 of 2 people found the following review helpful By John Nygate on December 31, 2001
Format: Hardcover
Although the author comes over as arrogant, I am, after several years, warming to this book. With concentration and very careful reading I have found that much can be gained from it. It is humorous, witty and iconoclastic. Reading a page here and a paragraph there, I have learned what Mordell's theorem is, almost understood a single paragraph proof of the prime number theorem, and more maths besides.

It is however heavy going and the lectures and notes are in a concentrated form. The cover says the book assumes only one year of university maths. I really doubt this is enough math for this book. So beware.
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Notes on Fermat's Last Theorem (Canadian Mathematical Society Series of Monographs and Advanced Texts)
This item: Notes on Fermat's Last Theorem (Canadian Mathematical Society Series of Monographs and Advanced Texts)
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