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126 of 129 people found the following review helpful
on July 27, 1999
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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34 of 35 people found the following review helpful
on September 30, 2005
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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20 of 20 people found the following review helpful
on September 4, 1998
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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18 of 19 people found the following review helpful
on March 15, 2001
This is a great book that lets you assimilate the fundamentals of Fourier transform. The way the book accomplishes it is amazing. This book brings out the utter simpilicity behind one of the most beautiful work of all time --- Fourier Transform..
In simple little steps the authors introduce fourier transform, complex numbers and take a peak into vector algebra...
It is a fascinating work. Recommended for all.More so for the students of Digital Signal Processing
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12 of 12 people found the following review helpful
on April 24, 1998
My introduction to Fourier mathematics was as a science undergraduate - it was always disturbing to keep seeing equations introduced in FTIR and NMR texts with the apparently obligatory "it can be shown that" - but, of course, it never was "shown that".

This book is filled with cartoons and simplistic explanations, but it delivers the nuts and bolts of what the basic underlying assumptions of the Fourier equation are, and you finish the book with a set of about twenty revised pages of mathematics that give you a very clear picture and solid grasp of the Fourier equation. Furthermore, you understand it so well you can even pen the mathematical derivation of the equation out in several minutes. Amazing.

I give this book very high marks and more praise. And I am grateful to the authors and their editors for demystifying an arcane mathematical topic. I feel much more comfortable with spectroscopy having read it, and having now some idea of what is actually going on in the black box of the spectrophotometer.

This is a wonderful book. See also The Calculus Tutoring Book.
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10 of 10 people found the following review helpful
on October 27, 2000
This is a superlative book. I wish I had found it when I first learned diff eqs and before I plowed through some heavy stuff on convergence and convolution. it would have given me a clear road map to the subject, and a better 'feel' for it.
If you already have the ideas and just want to learn techniques for solving, this is the wrong book. But if you learned techniques but cannot VISUALIZE or if the subject is new to you then this book is a wonder. It will teach your intuition.
I intend to buy everybook from this group sight unseen on the basis of this one. The dna book comes out in 2001. Can't wait!
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8 of 8 people found the following review helpful
on September 29, 2001
The motivation for this book is rooted in a club in Japan that is dedicated to learning foreign languages. Its members began to wonder about the sounds of languages, and this curiosity led them to the study of Fourier series, which they applied to analyze spoken sounds.
To start with, this book introduces the concepts behind the Fourier series and the calculation of Fourier coefficients. It then discusses Fourier analysis of the five vowels of the Japanese language. The conclusions are enlightening to say the least.
Rather than end here, as it could have, this book continues on to develop in some detail the mathematics behind the Fourier series. This includes forays into trigonometry, limits, differentiaion, integration, vectors, infinite series, the constants e and i, and Euler's formula. At all times it provides concrete motivation for new concepts, and supports them with superb visualization. When previously introduced concepts are needed, they are always reviewed in place, instead of assuming that the reader has mastered them, or will go back to the original material.
One strength of this book that should not be overlooked is that its translation is very good. That is, the reader is not aware that it is a translation.
While most people who are aware of Fourier series probably have the necessary background in mathematics to make this book feel "accessible", I wonder whether someone who has never gone beyond high school algebra and geometry would feel the same way.
One disappointment for me was the final chapter, the one on FFT. Its presentation of the discrete Fourier transform was good, but its development of the algorithm became unnecesarrily complicated. Though I found the explanation in an algorithms book more to my liking, without the background from this book, particularly Euler's formula, I surely would not have understood that one at all.
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9 of 9 people found the following review helpful
on June 12, 1999
Most math teachers can't teach. Whatever they do largely amounts to 'telling' as opposed to teaching. This book written by Japanese students is a gem. It is a rarity to find a book where the reader will share the authors experience and enthusiasm of discovery. Buy this book and learn what mathematics is all about.
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8 of 8 people found the following review helpful
on August 2, 2003
the Transnational Colege of Lex Tokyo has done two beautiful books this one and the other marvelous book "what is quantum mechanics" which also worth its weight gold,I have bought alot of books and i found these two books plus epstein's marvel "thinking physics" are the best sceince books writen in the english language ever.back to this book,,,
in short ..excellent work.its very very pedagogical and step by step one will master the subject.
my only note on fourier's book is on the treatment of the fast fourier transform which is not really as good as the rest of the book.
any one like a crystal clear exposition on this please refer to
"the scientists and engineers guide to digital signal processing".
in future i will buy any book transnational co. will issue.
my only hope is that transnational colege next pne will be on the general relativity and will see subject of tensors and manifolds that kind of clearity and understandability.thanx 4 reading my review.
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7 of 7 people found the following review helpful
on August 15, 2005
The book "Who is Fourier? A Mathematical Adventurer" is a jewel of an innovative book. This book teaches in a unique perspective the math of Fourier analysis, along with some trigonometry and some elementary calculus in a way that adults and kids can understand together. The book is co-authored by kids with Cartoons and several cut and paste activities for reinforcing the concepts.

The unique perspective this book gives is that the key to understanding math is the same as understanding a human language. It shows that a mathematical equation is a precise and concise description of processes and graphs that is a more appropriate way to communicate to someone then using a human language such as English. This is precisely the goal, "to understand math as a language" that one strives to obtain after years of mathematical studies, which this book quickly leads the reader is a most direct path!

This book is published by the Transnational College of LEX (TCL, also konwn as Torakare) founded in Tokyo by the work of Yo Sakakibara a language researcher "as a place to research and learn about the intriguing relationship between human beings and languages".

Anyone who is having trouble learning introductory calculus should not drop the course before they try this book, it may just get you over the rough spots.
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