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e: The Story of a Number (Princeton Science Library) Princeton Science Library Edition

4.2 out of 5 stars 120 customer reviews
ISBN-13: 978-0691141343
ISBN-10: 0691141347
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Until about 1975, logarithms were every scientist's best friend. They were the basis of the slide rule that was the totemic wand of the trade, listed in huge books consulted in every library. Then hand-held calculators arrived, and within a few years slide rules were museum pieces.

But e remains, the center of the natural logarithmic function and of calculus. Eli Maor's book is the only more or less popular account of the history of this universal constant. Maor gives human faces to fundamental mathematics, as in his fantasia of a meeting between Johann Bernoulli and J.S. Bach. e: The Story of a Number would be an excellent choice for a high school or college student of trigonometry or calculus. --Mary Ellen Curtin --This text refers to an out of print or unavailable edition of this title.

From Library Journal

Everyone whose mathematical education has gone beyond elementary school is familiar with the number known as pi. Far fewer have been introduced to e, a number that is of equal importance in theoretical mathematics. Maor (mathematics, Northeastern Illinois Univ.) tries to fill this gap with this excellent book. He traces the history of mathematics from the 16th century to the present through the intriguing properties of this number. Maor says that his book is aimed at the reader with a "modest" mathematical background. Be warned that his definition of modest may not be yours. The text introduces and discusses logarithms, limits, calculus, differential equations, and even the theory of functions of complex variables. Not easy stuff! Nevertheless, the writing is clear and the material fascinating. Highly recommended.
- Harold D. Shane, Baruch Coll., CUNY
Copyright 1994 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

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Product Details

  • Series: Princeton Science Library
  • Paperback: 248 pages
  • Publisher: Princeton University Press; Princeton Science Library edition (February 8, 2009)
  • Language: English
  • ISBN-10: 0691141347
  • ISBN-13: 978-0691141343
  • Product Dimensions: 9.1 x 6.1 x 0.6 inches
  • Shipping Weight: 9.6 ounces
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (120 customer reviews)
  • Amazon Best Sellers Rank: #563,654 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Duwayne Anderson on November 8, 2004
Format: Paperback
This is the second book by Eli Maor that I have read and reviewed in as many months (the previous book was "To Infinity and beyond"). As I was reading this latest book I thought several times that the title was wrong. I think a more appropriate title might be "A popular introduction to calculus" or "The road to calculus." Then, again, he does more than just calculus, too. So I'm not sure what to call it. It's more than just about e, and it's more than just about calculus. It's all that, with a lot of other interesting tidbits tied in as well. While Eli does spend quite a bit of time discussing e, this book goes well beyond a simple linear history of a number that's fundamental to modern mathematics.

Eli begins his story with John Napier and the invention/use of logarithms as tools for calculation. I found this introduction interesting because it reminded me how valuable calculation tools were, in the days before electronic calculators. I even found myself rummaging through my desk for that long-forgotten slide rule and remembering with a degree of nostalgia the many hours spent working through problems in mathematics and physics during my high school years, and how I'd pride myself on being able to carry the a full three significant digits through a complex sting of calculations.

It seems as though the initial chapters of Maor's book deal more with the history of e than does the middle of the book. Somewhere around page 40 Maor moves away from mathematical history aimed squarely at natural logarithms and focuses more on what is (I suspect) his true love: calculus. This is one of the best introductions to calculus I've seen, primarily because Maor did such a nice job of bring together all the historical footnotes.
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Format: Paperback
To those of you who are not familiar with Maor, let me point out that he is a mathematician (as opposed to a lot of the other people who write popular math books) with an immense knowledge of math history and also an excellent writer. Some reviewers have compared this book to books like "An Imaginary Tale" by Paul J. Nahin and "History of Pi" by Petr Beckmann. This is totally missing the point. Both of those books are written by non-mathematicians, and contain error that will annoy mathematicians. Maor on the other hand is a superb scholar. I've read all his four books quite carefull, and I've not found any errors.
This book will give you a great understanding of what calculus is all about.
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Format: Paperback
I am a bit bothered by all those 5-star reviews and feel obligated to tell any potential readers of this book the other side of the story. (Please also check out another review of this book by guttes on January 21, 2001.)

First of all, this book lacks a focus. It jumps back and forth with things related or even unrelated to the number e (it spends more than a chapter on the discovery of calculus, and on and off on the topic of pi). While it is more than verbose on something not (totally) relevant, it simply does not have some topics that you wanna know more about -- for instance, who/why there is such a notation 'e' for the number, or what are the latest hot topics about the number. It has no consistency in presenting its mathematical formulation either, in the first half of the book it assumes readers with minimal calculus background, but then in the second half of the book it assumes readers with background on complex and multi-variable analysis. In the very last chapter, it touches on the topic of transcendence, but again, fails to deliver anything substantial and signifies an hollow story for such an interesting and promising topic.

In a nutshell, the problems of the whole book are the choice of materials presented and the organization of the materials for the topic. It may be one of the very few books out there with a title related to the number 'e', but it surely is not a book telling you a story of this number.

For those who also finds this book disappointing, there are indeed way better "popular" math books out there. I would recommend books written by William Dunham, such as "Journey Through Genius" (for some easy reading) or "The Calculus Gallery" (for those with more calculus backgroud).
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The beginning and the end of Maor's story are compelling. He spells out exactly what John Napier put in his original "logarithmic" tables--it turns out that these were logs to the base 1/e, shifted by a factor of 10,000,000, even though their creator wouldn't have put it that way. I was, however, disappointed that no actual *example* is given of a calculation that was made possible by these unusual original tables. Maor tells us how excited Kepler and others were by the possibilities, and hints that computations involving sines were especially aided, but there's not a single example of how the pre-Briggs (log to base 10) logarithm was ever used. (And let me point out that this is not an obvious matter; after extensive googling I have only been able to locate very artificial examples of what Napier's very incomplete tables were good for.)

Still, the opening chapters on the "pre-history" of e (before the invention of calculus) are one of the strongest parts of this book. Where Maor gets bogged down is in the long digression telling of the invention of calculus and the bitter priority dispute. In my opinion, there's a solid block of dead weight beginning from the first page of Chapter 8, and Maor doesn't get his steam back until the latter part of Chapter 11 (when we meet the truly "mirabilis" logarithmic spiral).

Some of the sidebars are excellent--e.g. the math behind terminal velocity, which makes parachuting possible ("The Parachutist") and the Weber-Fechner law, which claims to give a mathematical model of human response to affective stimuli ("Can Perceptions Be Quantified?").

As in his "Trigonometric Delights," Maor excels in presenting the world of complex analysis that was opened up by Leonhard Euler in the 18th century.
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