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125 of 128 people found the following review helpful:
5.0 out of 5 stars
The Best Math Book I Ever Read, July 27, 1999
By A Customer
This review is from: Who Is Fourier?: A Mathematical Adventure (Paperback)
This is the best math book I ever read. Before reading it I had a vague knowledge of Fourier series (that you could decompose a curve into a sum of simple sine and cosine waves) but I had no idea of the power of this method or its applications. After reading it (several times) I'm pretty well versed (or at least I talk like I am) in Fourier series, Fourier coefficients, discrete Fourier expansions, Fourier transforms and FFTs (fast Fourier transforms), certainly enough to read and understand (in a brief search of the web) applications such as finding buried landmines, identifying aircraft as friend or foe, recovering latent fingerprints, or compressing data to a fraction of the original size. What impressed me more, however, was that I understood why there are only five vowels in the English language, why an infinite vector space is equivalent to a Fourier expansion, and why Heinsenberg's uncertainty principle makes perfect intuitive sense. This book is nothing if not eclectic, and the range of topics discussed is immense. If I hadn't already studied calculus and linear algebra in college I would also, for the first time, understand differentiation, integration, vector spaces, Euler's formula, Maclaurin series and the number e, all of which are presented with unusual clarity. This book is a tour de force, a summary of almost everything that is interersting (at least to me) in mathematics. You have to get beyond certain things when you read this book. Understand that it was written by a bunch of kids and is replete with cartoon characters saying things like "Good grief!" and subbplots in which, for example, the "Non-periodic kid" sends taunting messages to the Magistrate and his constables. I found this obnoxious at first, but later I found it inspirational. If those kids could do it, I could do it. Thus inspired, I read the book three times, until I finally understood it. The Transnational College of Lex has its own theories of leaning, and it looks like they're right. I cannot recommend this book too highly, or to too many readers. Even (or perhaps especially) if you don't like mathematics, you should check it out. You'll learn something.
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28 of 29 people found the following review helpful:
5.0 out of 5 stars
Unique and Quite Amazing, September 30, 2005
This review is from: Who Is Fourier?: A Mathematical Adventure (Paperback)
This is a great book, but probably different from anything you might expect. On flipping through the pages it looks like one of those comic book guides, but don't let that decieve you; there is a lot of serious material in this book. "Who is Fourier" is certainly not equivalent to a college level textbook on Fourier Analysis, but neither is it simply a descriptive overview. The book is filled with equations, and some of them are quite complex. What is unique in this book is that the equations are explained from the ground up, starting from an extremely basic level, yet building to a fair level of complexity. If you have taken any math beyond high school algebra, this can sometimes be annoying because the book really assumes essentially no knowledge of anything beyond basic math. On the other hand, if you have not had much math, this is really good because it makes the text accessible to virtually everyone, and if you have taken some more advanced classes in math, you may still find some interesting surprises in the basics. I know I did.
In spite of the very basic building blocks that this book begins with, the book does take you through some pretty serious stuff. The Fourier series itself is covered in roughly the first third of the book. From there, the basics of differentiation, integration, vectors, complex numbers, Maclaurin series, and the Euler formula are described, leading one steadily from the Fourier series to the Fourier transform.
The only thing I can see that might turn some people off is the somewhat comic book style in which the book is written. To understand the reason behind the style, one must understand who wrote the book and why. The book really was not originally written for the general public, but for members of a club whose members learn up to 11 differnet languages simultaneously. The club is related to the Transnational College of LEX which does research into the way we learn languages. The study of waveforms was a natural extension of their interest in languages, and this led, of course, to Fourier analysis. The book essentially chronicles the students' own learning of Fourier analysis, and it was written as a means of sharing what they learned with other students and members of their club, so it was written in a very casual style, including little stick figure illustrations of characters representing the students and various historical figures. It even has simulated dialogue between the students and fictional characters. I debated about giving the book four stars instead of five because I personally do not care for this style very much, but in the end, I'm not sure the book would be quite as effective if it were written in a more formal style, so I left it at five stars. The book is truly unique and quite amazing.
As a side note, I just glanced at the preview pages on Amazon. These really don't do justice to the book. Although they give a good idea of the general layout of the book, and the sort of comic book style in which it is written, they don't show any of the meat in the book. There is much more to the book than suggested by the preview pages.
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19 of 19 people found the following review helpful:
5.0 out of 5 stars
BSEE,MSEE,MSCS This book explains what those degrees didn't, September 3, 1998
By A Customer
This review is from: Who Is Fourier?: A Mathematical Adventure (Paperback)
This book is entertaining, enlightning and engaging. How many times have I encountered this subject during my studies only to go away feeling like I hadn't fully grasped it! This book will take you step by step through the math. NO steps left "for the reader". The book is clear, concise and humorous. It has made me want to get out my old math books and tackle the problems again now that I am armed with a richer understanding. Besides Fourier analysis you get bonus points with excursions into what's behind "e", "i" and Euler's formula!
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