Customer Reviews

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

5 star:		(11)
4 star:		(4)
3 star:		(4)
2 star:		(1)
1 star:		(0)

 

 

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.

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.

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"

A very readable book. Many concepts developed around Euler's magic formula are clearly explained. Including a lucid exposition on the calculus of the sum of classical series such as the value of zeta function for several positive integer values of its argument. Paul Nahin excels in describing the origin and the development of fourrier series and fourrier integrals from Bernoulli to Fourrier and more. Anyone interested in this field will find something interesting in this book to learn. The reason I didn't rank it five stars is that I found explanations often too lengthy while the addition of a chapter on distribution theory could fill the gaps in mathematical rigor and make the transition from fourrier series to fourrier integrals more logical. I should add that the lack of rigor in transition from fourrier series to fourrier integrals, as described by P. Nahin, is inherent to the more fundamental problem of transition from discrete to continuous. Indeed, in mathematics, this is a very slippery terrain. In functional analysis, mathematicians go round this problem by introducing distribution theory. P. Nahin mentions only the name of distribution theory without any decription. I think a chapter on this theory would make the book a must have.

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.

Dr Eulers fabulous formula fits a niche between books for non mathematicians (too simple) and books only understood by mathematicians. It provides the best explanation of Fourier series and integrals that I have read. Its explanation of imaginary numbers is excellent, but not as good as Feynman in his lectures on physics. I reccomend it for those who want to understand how Fourier series work.

After the first few pages I got the feeling that this book was based on notes from a class that Nahin had taught. And sure enough, the acknowledgement section confirmed my suspicion (p. 375). Now, on its face, this isn't necessarily good or necessarily bad. But it can give you a hint of what the book might be like: the course notes were from two, third-year electrical engineering classes on systems engineering. And that's what the book reads like.

It's not what I expected with a title like Dr. Euler's Fabulous Formula. I doubt that's what Nahin's classes were called. The title is probably the doing of the publisher's marketing department, not Nahin. In addition, I think the title is actually misleading. I didn't do a page count but it seems like more pages are devoted to Fourier analysis, as opposed to anything else.

I have only a layperson's interest in math books, perhaps caused by having the worse calculus teacher in the universe. Even so, I should have looked for detailed reviews, rather than being seduced by the title. If I had, I might have known what to expect. But I didn't. I bought the book from Amazon but on the basis of an ad in Science News, I think it was. So I now have a very clean, once-read copy of this book for sale!

On a topic I don't believe is covered by other reviewers is Nahin's rant about Jackson Pollock's drip paintings as he attempts to discuss the beauty of theories and equations (p. xix of the Preface). That's why I bought the book in the first place: I was pursuing my interest in the clear and intriguing beauty of Euler's Fabulous Formula. However, I nearly stopped reading only a few pages in after Nahin's incredibly clichéd statement: ..."but anybody who can observe the result of throwing paint on canvas--what two-year olds routinely do in ten thousand day-care centers every day (my gosh, what I do every time I pain my ceiling)--and call the outcome art, much less beautiful art, is delusional or a least deeply confused (in my humble opinion)". Nahin says he places Norman Rockwell far above Pollock as an artist.

He doesn't leave it at that. In a footnote (p. 348), when discussing Pollock's use of a can with a hole in the bottom, he says: "a gravity-driven mechanical system did all of the `creative' work". That's somewhat like me saying that a friction device (Nahin's pencil?) was responsible for whatever "creative" work might be discovered in his book. (As an aside, the footnotes are enjoyable. I liked them as much as the text itself.)

Perhaps Nahin thought it was OK to put this screed in the Preface because it was, as he says, just his "opinion". The fact is, both Pollock and Rockwell are fabulous in their own right and this kind of reasoning made me distrust ANY judgment Nahin might make about beauty, mathematical or otherwise. Having done a little of both professional level science and art, and even a smattering of math (if you can count probability and statistics), I would agree with Nahin's wife, he is indeed a "cultural Neanderthal" (Preface, p. xix). Perhaps even a mathematical one. And to that list I would add, the stereotype of a grumpy, old fashioned.... On second though, I'm not going to say it. I have acquaintances that fortunately do not fit that stereotype.

Least I seem totally negative, Nahin does explain why Euler deserves an enormous amount or respect and admiration and I liked his explanation of Heisenberg's Uncertainty Principle (p. 255) and why Pi shows up in such strange places (p. 359-60).

So I give Nahin a 3 and his publisher a 1 (for misleading marketing). I think that's an arithmetic mean of 2, if my friction device serves me correctly.

This is a great book covering Fourier Series and Fourier Integrals. The author makes the material very accessible and I'd recommend this book to anyone currently studying or having studied the subject of Fourier Series/Integrals. I found the chapters covering pure math to be pure joy since the author's way of presenting the material is so pedagogical. If you enjoy books on the history of math and are keen on following along intersting derivations on the way to beautiful results, then this book is for you.

A very interesting book. I am a retired Electrical Engineer and hence find this book particularly interesting. Not for the faint hearted as it contains a very large amount of complex mathematics. Overall, very good.

The primary topic of Nahin's "Dr. Euler's Fabulous Formula" is the complex number or more appropriately the Euler's identity: e power to (it) = cos(t) + isin(t). Nahin called this book the second half of his complex number series. The first book in the series is named "An Imaginary Tale: The Story of square root of minus one." The second book is called "Dr. Euler's Fabulous Formula." The primary topics of the second book are: Fourier series, which is covered on Chapter 4; Fourier Integrals on Chapter 5; the application of complex numbers on electronics Chapter 6.

The book has six chapters, which contains both pure and applied mathematics materials. Other than the three chapters mentioned above, the other three chapters are (i) Complex Numbers, (ii) Vector Trips, and (iii) The Irrationality of pi square. Chapter one is about the assortment of non elementary complex numbers such as applying complex number on obtaining the sum of a real series. Chapter three provides a detail proof of the irrationality of the number pi square using Euler's Identity. On the applied side: Chapter two demonstrates the application of complex number on mathematical modeling. Since Nahin is an eminent electrical engineering professor, his book also provides plenty of material on (a) partial differential equations (PDE) such as wave equation on chapter four, and (b) electrical engineering material such as baseband, carrying frequencies, antennas, radio receivers and speech scrambler on chapter six.

This is an excellence introductory book not only on pure complex numbers usage in mathematics such as summing a series but also on the usage of PDE, Fourier series, and Fourier Integral in physics and engineering.