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Title: Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills
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Manufacturer: Princeton University Press
List Price: $29.95
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| Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Princeton University Press Dr Euler's Fabulous Formula | | 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. | | Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Princeton University Press Catchy title and cover graphic but reads like a textbook | 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. | | Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Princeton University Press An excellence introductory book on advanced mathematics such as Euler's Identity, Irrationalioty, Fourier Series | 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.
| | Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Princeton University Press Good clear explanation of Fourier series | | 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. | | Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Princeton University Press excellent for fourrier series and fourrier transform exposition | | 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. | | Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Princeton University Press Product Description | I used to think math was no fun
'Cause I couldn't see how it was done
Now Euler's my hero
For I now see why zero
Equals e[pi] i+1
--Paul Nahin, electrical engineer
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems. The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, "Euler's formula will still be beautiful and stunning and untarnished by time." |
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