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Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills Hardcover – April 30, 2006

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Paul J. Nahin (Author)
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Paul J. Nahin (Author)
4.4 out of 5 stars 30 customer reviews
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Product Details

  • Hardcover: 416 pages
  • Publisher: Princeton University Press; First Edition edition (April 30, 2006)
  • Language: English
  • ISBN-10: 0691118221
  • ISBN-13: 978-0691118222
  • Product Dimensions: 9.2 x 6.6 x 1.3 inches
  • Shipping Weight: 12 ounces
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (30 customer reviews)
  • Amazon Best Sellers Rank: #270,513 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

88 of 92 people found the following review helpful
Sequel to An Imaginary Tale
By T. J. Shortridge on April 26, 2006
Format: 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.
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45 of 46 people found the following review helpful
Another fabulous book from Paul Nahin
By David S. Mazel on August 29, 2006
Format: Hardcover Verified Purchase
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.
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74 of 79 people found the following review helpful
Errata please
By John W. Fuqua on February 13, 2007
Format: 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"
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15 of 15 people found the following review helpful
Excellent expository book
By Aristarchus on March 24, 2007
Format: Hardcover
Paul Nahin's book, "Dr. Euler's Fabulous Formula," is an excellent expository treatment of Euler's formula (you say, "which one?") e^i*theta = cos(theta) + i*sin(theta) and its profound, and far-reaching, ramifications. Dr. Nahin also gives an extensive informal discussion of Fourier series, Fourier transforms, the Dirac Delta Function, and what electrical engineers would call "signals and systems theory." Some mathematical purists may criticize the lack of pure rigor. However, this book is an "expository" book, not a rigorous "textbook." Ideally, I recommend that you read Dr. Nahin's book in conjunction with your standard college textbook. That way, you will get the best of both worlds. Your textbook will give you the disciplined rigor. Dr. Nahin's book will give you the "Aha... insight!" I read Dr. Nahin's book before taking a graduate level course in electrical engineering (EE) Signals and Systems. I breezed through the EE course with perfect scores on my exams, and I give a lot of credit to Dr. Nahin. When you study mathematics, you really need BOTH disciplined mathematical rigor AND intuitive insight and understanding. Beware, however, that this book has LOTS of mathematics in it. The book is loaded with serious mathematics. Don't read this book if you want something for the intelligent layperson. Read this book if you love mathematics, if you are an engineering or mathematics student, or if you like industrial-strength mathematics. Paul Nahin may single-handedly save Americans from mathematical illiteracy. He does something that the mathematical community does not do well... "market and sell" mathematics.
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Most Recent Customer Reviews

Five Stars

Fabulous book

Published 4 months ago by G S Tiwari
Prescription for Pleasure (of the mathematical kind!)

This book is awesome! You have to have a reasonable mathematical background to appreciate it, but if you do, it's a gem!!!

Published 11 months ago by Jacques J. Caillault
Five Stars

great product fast delivery

Published 17 months ago by dillon
You better be a mathematician

Still reading through the book, and it is an enjoyable book to read, just don't try to follow too closely and prove what the author is telling and showing you. Read more

Published 18 months ago by Charles Thurman
re: damaged book

The cover of the book had a deep cut mark. Inside was clean and looked good, but damaged cover was very distracting.

Published 20 months ago by Akehiko Takahashi
Excellent history of the application of Euler's formula

While some may be off put by the amount of math, this well thought out and clear treatment of Euler's formula grips you early. Read more

Published on September 10, 2013 by Robert Donato
A nice overview of the uses of Euler's formula

I'm not a mathematician. I had some math classes in college. A fair amount of this was beyond me. But I think the special case of Euler's formula, e^i(pi) + 1 = 0, is just... Read more

Published on August 29, 2013 by rokpyle
Agree: not for the faint-hearted

I understood very little of the math, but the anecdotes throughout the book; and, the abridged biography of Euler at the end, made it a 5-star book. Read more

Published on December 5, 2012 by Bruce Oksol
Poor display of mathematical formulae

I think that the Kindle needs its own version of LaTex in order to display the formulas clearly. The book has a lot of mathematical formulas that are displayed as images and not... Read more

Published on June 18, 2012 by Alberto R.C.
Great study guide for engineering students

I bought this book when my daughter was home from college, she is an electrical engineering major and minoring in physics. Read more

Published on February 5, 2012 by Marc Mest

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