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3 of 3 people found the following review helpful
5.0 out of 5 stars
A True Adventure,
By "chandp" (Fremont, CA USA)  See all my reviews
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
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.
1 of 1 people found the following review helpful
5.0 out of 5 stars
The Best Math Book I Ever Read,
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 "Nonperiodic 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.
1 of 1 people found the following review helpful
5.0 out of 5 stars
DESRVE MORE THAN 100 STARS,
By Ahmed Morsi (JEDDAH, AZZIZEYA Saudi Arabia)  See all my reviews
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
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.
1 of 1 people found the following review helpful
5.0 out of 5 stars
"It can be shown that...",
By John McConnell (Boston, MA)  See all my reviews
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
My introduction to Fourier mathematics was as a chemistry undergraduate  it was always irritating to keep seeing these equations introduced in FTIR and NMR texts with the apparently obligatory "it can be shown that...". But, of course, it was never shown in a clear manner.
This book is filled with cartoons and rather simplistic explanations, but it also has the nuts and bolts of what the basic underlying assumptions are, and you finish with a set of about 20 revised pages of mathematics which give you a very clear picture, and a comfortable one as well, of just what is involved in the Fourier mathematics. I give this book high marks and much praise. And also am very grateful to the authors for demystifying a rather abstruse 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.
1 of 1 people found the following review helpful
5.0 out of 5 stars
Wonderful Book!,
By
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
I develop time series software and teach classes on time series for a living. I saw this book while looking for material that would help me teach adults some of the concepts of time series. It has been a wonderful resource for me personally because I use FFTs, but it has also been a wonderful resource in terms of how it teaches the material. I highly recommend this book for anyone who teaches math or science.
I help homeschool our three elementaryaged children. We've been working through some of the pages in the book together so they have some idea of what I do while I'm at work. They are really enjoying learning about how to add together sine waves to make different patterns. This book has given me wonderful insight into teaching and into what my kids can learn even in elementary school. It's also changed the way I lecture when training new staff and the way I choose math curriculum for my children.
1 of 1 people found the following review helpful
5.0 out of 5 stars
Very Cool Book,
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
This book is quite fascinating even if you have no particular reason to be interested in the subject. If you have been trying to understand what is Fourier Math with out taking several semesters worth of courses this book will help. However, having a background in calculus will make the book much more understandable than without.
The book was written by students of foreign languages and they approached the subject of math as a foreign language. They have distilled Fourier to its essence as simply as possible. I found their treatment of subjects I already knew (such as trigonometry) enlightening as they approached them with a fresh and unbiased approach aiming to truely understand what is going on. The book is not a text book, but a book to read through slowly, mediate and open new horizons.
1 of 1 people found the following review helpful
5.0 out of 5 stars
Make your student life easy and read this.,
By M.F.J. Josefsson (Germany)  See all my reviews
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
The people who wrote this are involved in learning and teaching foreign languages in the way a small child learns its mother tongue and they decided to apply the same method to Fourier mathematics up to and including the Fourier Transform. This organicevolutionary method works wonderfully and this book is to be very highly recommended to anyone intending to study this subject.
I wish I had something like this when I was labouring through Fourier maths over two decades ago! It really cracks the nut of the concept of the whole thing. It is also useful to people who have been through Fourier maths but want to firm up their fragile knowledge of it or any of the more fundamental maths underlying it. Lecturers should read this too for pedagogic reasons.
1 of 1 people found the following review helpful
5.0 out of 5 stars
Excellent book,
By Zabeda Kalid (Tampere Finland)  See all my reviews
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
I never read a technical book from cover to cover except this book. I am holding M.Sc. in DSP and I never understood what Fourier was talking about, just swallowing his equations without understanding the idea behind them. His equations were puzzels till I read this excellent book. It is very well written, explained in an easy, obvious and excellent way. The only drawback is that the last chapter (FFT) is not very well explained as the rest of the book, but it doesn't harm it.
If all/most of the scientific books written like this book, science become much more interesting and desirable. I hope that transnational College of LEX show more scientific books like this one. The authers and the translator deserve BIG thanks.
1 of 1 people found the following review helpful
5.0 out of 5 stars
Good Intro,
By "merlioncity" (Singapore)  See all my reviews
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
I just got the book and i am halfway done. The book really provides a very clear explanation on the subject(although elementary). The authors really makes sure you understand everything they talk about(like the addition of sine waves and trigonometric functions etc.). I can't wait to finish the book. I browsed through the 2nd half of the book and saw treatments of e, integration, differentiation and projection and orthogonality. Can't wait to go there! The drawback for me was that the book was a little too simple...I would prefer a more mathematically rigorous book(maybe i should get another after finishing this). But overall this is a good book to learn the basics of Fourier. Buy it! and Read it!
1 of 1 people found the following review helpful
5.0 out of 5 stars
Understanding not technique  highest recommendation,
By
This review is from: Who Is Fourier? a Mathematical Adventure (Paperback)
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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Who Is Fourier? a Mathematical Adventure by Transnational College of Lex Tokyo (Paperback  1995)
Used & New from: CDN$ 44.77
 