Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills [Hardcover]

Paul J. Nahin (Author)

Editorial Reviews

Review

"...a peek into areas of mathematics replete with beauty and crucial to many applications. Who could ask for more?" -- Arieh Iserles, Nature

"But be warned: it contains thousands of equations, and is a challenging read". -- Matthew Killeya, New Scientist, May 27, 2006

"Takes Euler's formula as his starting point and demonstrates the wide range of uses to which it has been put." -- Timothy Gower, Nature

Review

If you ever wondered about the beauties and powers of mathematics, this book is a treasure trove. Paul Nahin uses Euler's formula as the magic key to unlock a wealth of surprising consequences, ranging from number theory to electronics, presented clearly, carefully, and with verve.
(Peter Pesic, St. John's College )

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Product Details

• Hardcover: 404 pages
• Publisher: Princeton University Press (April 10, 2006)
• Language: English
• ISBN-10: 0691118221
• ISBN-13: 978-0691118222
• Product Dimensions: 9.3 x 6.3 x 1.4 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (17 customer reviews)
• Amazon Bestsellers Rank: #44,416 in Books (See Top 100 in Books)

  #24 in	Books > Science > Mathematics > Mathematical Analysis
  #10 in	Books > Science > Mathematics > Pure Mathematics > Number Theory

Customer Reviews

Most Helpful Customer Reviews

79 of 82 people found the following review helpful:

5.0 out of 5 stars Sequel to An Imaginary Tale, April 26, 2006

By	T. J. Shortridge "T.J. Shortridge" - See all my reviews (REAL NAME)

This review is from: Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (Hardcover)

The reviews of An Imaginary Tale capture much of what will be said of Dr. Euler's Fabulous Formula. I happen to like Paul Nahin's books very much ever since reading The Science of Radio, one of my favorite books of all time. If you didn't like Imaginary, you won't like Dr. Euler's . If you like the earlier book, this one is a must.

Chapter One starts with an introduction to complex numbers. This would make nice supplemental material for an introduction to complex numbers. The chapter is not the standard treatment. It gives a very clear introduction to Gauss' proof of the construction of the regular heptadecagon . The chapter goes on to factoring complex numbers in the context of Fermat's last theorem, with a very clear discussion of Lame's proof for n=7 . Earlier in the chapter Nahin uses the Cayley-Hamilton theorem to get De Moivre's theorem in matrix form without any mention of physical rotations.

Fourier series and integrals comprise most of the book which ends with applications to single side band radio. This last topic is a nice inclusion for folks like me who liked Nahin's early book The Science of Radio. There is a story about G.H. Hardy and Arthur Schuster, that I had never seen elsewhere.

I would recommend this book to anyone who likes undergraduate calculus and has some exposure to linear algebra, maybe a second or third year undergraduate. The material is idiosyncratic enough to be entertaining for anyone who has had courses in complex analysis and number theory. It is a good introduction and supplemental reading for such courses, but not as a primary text.

39 of 40 people found the following review helpful:

5.0 out of 5 stars Another fabulous book from Paul Nahin, August 29, 2006

By	David S. Mazel "www.bytesofscience.com" (Washington, DC) - See all my reviews (REAL NAME)

Amazon Verified Purchase

This review is from: Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (Hardcover)

Here is a book that is a delight to read. It is well-written and the text flows marvelously between each page and around the many formulas that are so carefully presented and worked out. I rate this book as 5-stars for presenting ever more mathematics relating to complex numbers in a clear and detailed manner.

The book is, as the author notes, a continuation of his book, An Imaginary Tale, where Nahin discusses the square root of -1. (If you haven't read that book, read it first because many of the footnotes refer to it.) In this book, we see more of complex numbers and, in particular, we see many applications of Euler's Identity that "e^{i theta} = cos(theta)+ i sin(theta)." This simple looking indentity is rich in applications and explorations. Nahin takes you on a journey to these topics and does so in an easy to follow way.

There are interesting stories as you go such as the one where we find the Gibbs did not, contrary to almost all textbooks, discover what is call Gibbs Phenomena. There are other stories and anecdotes but I'll let you enjoy them on your own.

That said, I must also say that the book assumes you have a good understanding of complex numbers and are comfortable manipulating them. A solid undergraduate understanding is all that's needed and if you have done graduate work, all the better. If you're considering the book at all, and have the math background, read it.

If you don't know anything about complex numbers, well, this book may not be as good as it could be for you.

48 of 51 people found the following review helpful:

5.0 out of 5 stars Errata please, February 13, 2007

By	John W. Fuqua - See all my reviews (REAL NAME)

This review is from: Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (Hardcover)

Like all of Paul Nahin's books, I really like this one.
However, as with so many books an Errata would help. Mathematical and mathematical finance books are getting so expensive, that unless authors or publishers have a URL for Errata, readers esp. of mathematical books will wait for [sometimes years] for a second corrected edition of books.

I could be wrong about these but it seems these are typos:
p. 30 lines 5 & 6 curly bracket should only be around the 2 * cos(x/2) term
p. 121 second equation should be t=(v+u)/(2*c)
p. 121 '* (1/(2*c)' missing at end of the line
p. 123 line 17, first word should be 'bother' not 'other'
p. 127 line 3 and 4, it seems that the 'icnPI/l' [not the ones in the cos() or sin() terms] term after the 'B' and before the '2*cos' respectively, should not be there. Or am I missing something ?
p. 128 4th line from bottom should be 1753 not 1733
p. 143 2nd line before last equation should be '... (x- i * y)...'
p. 144 equation under 'In summary, then...' cases are reversed
p. 216 seems 1/(2*PI) is missing from right side of first equation, i.e. from "...G(u)G(omega-u)...du"