Most Helpful Customer Reviews
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82 of 88 people found the following review helpful:
5.0 out of 5 stars
Required reeding for anybody teaching or studying calculus!, August 13, 2000
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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33 of 34 people found the following review helpful:
5.0 out of 5 stars
More than the story of the second-most famous number, November 8, 2004
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.
Coincidentally, as I was reading Mayor's book my wife was taking a class for teachers, aimed at educators who teach calculus in the middle and high schools. She found the book immensely helpful in both dealing with the actual mathematics in her class as well as providing insight into ways of introducing concepts relating to higher-level mathematics to young students. She introduced Mayor's book to other students in her class, as well as the professor (who had read it already, of course), all of whom enjoyed it immensely.
In terms of the history that he covers, I thought the discussion relating to Newton and Leibniz was the most interesting. My own coursework in Physics used Newton's dot notation, while my courses in mathematics adopted Leibniz's differential notation. Reading Maor's book provided a bit more insight into the historical quirks that led to the notation in common use today.
Especially interesting was his discussion about Newton's approach to the calculus. I think that if students had to use the notation and approach first used by Newton, calculus might still be relegated largely to the college curriculum. I really had no idea, before reading Maor's book, how convoluted Newton's approach was in comparison to that used by Leibniz. Newton is often portrayed (rightfully so) as a genius, and Mayor's description of Newton's calculus left me marveling that Newton managed to work through it as he did, given the (relatively) more difficult approach he took.
The end of Maor's book uses the calculus to illustrate several examples showing how e appears in various mathematical and physical problems. There are examples using aerodynamic drag, music, spirals, hanging chains and the cycloid. No discussion of e would be complete without a nice explanation of the function that is its own derivative, which Maor tells with characteristic clarity.
Frequently while reading Maor's book I found myself wishing I'd had this introduction before taking several of the classes I took during my school years. His treatment of the complex plane, for example, is as clear as his introduction to basic ideas in calculus. Looking back on my first class in complex variables, I recall the fog that surrounded my initial introduction to conformal mapping. Maor, though, makes it easy. With the skill of a master educator, he manages to explain the concept with such ease that you learn the essential ideas almost before you realize where he is taking you. Though most texts of this sort would not tread on a subject as foreboding to the general public as the Cauchy-Riemann equations, Maor explains the basic concepts as clearly and almost as effortlessly as he does conformal mapping. Ordinarily I wouldn't think it's possible to explain Cauchy-Riemann in a book that's intended for the general public with an interest in mathematics, but that's what Maor does, and he does it well.
In short, this nice little book manages to cover a lot of mathematical territory with the skill that only a master educator can muster. It is definitely a whole lot more than just the story of the second-most famous number in mathematics.
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32 of 37 people found the following review helpful:
2.0 out of 5 stars
Where is the story?, December 19, 2005
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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