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- Who Is Fourier? a Mathematical Adventure
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3 of 3 people found this helpful

ByAmazon Customeron 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.

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.

0 of 1 people found this helpful

ByAmazon Customeron April 17, 2003

If you ever watched the entertainment TV programs in Japan, you would understand my review: The dialogs in the book are not only useless, but annoying. [...] After a long time reading the dialogs, then who is Fourier, and where is Fourier's discovery?

The book CAN be written in fewer than 50 pages! It's not as good as an "introductory" Fourier Analysis book, or even a story telling about Fourier's life and scientific discovery. ]...] This book is not a useful book in the real world -- far from that. It's "useful" only when you are familiar with the techniques required to apply Fourier Analysis to the real problems. But then why should I own this book? This is why: Look at the pictures and recall some other books' contents, and then throw it away. As science book for the general audience , it's misleading the readers to a boring playground, where we cannot find any entertaining toys, even if you are there just for fun.

I have read many Japanese books about science, and this one is the worst -- not funny enough to kill time, and not good enough to attract people into the world of such an important science -- the Fourier Expansion of Periodic Wave Forms.

Get the Schaum's outline instead. That will solve your problems quick. It's not funny, but interesting and USEFUL.

The book CAN be written in fewer than 50 pages! It's not as good as an "introductory" Fourier Analysis book, or even a story telling about Fourier's life and scientific discovery. ]...] This book is not a useful book in the real world -- far from that. It's "useful" only when you are familiar with the techniques required to apply Fourier Analysis to the real problems. But then why should I own this book? This is why: Look at the pictures and recall some other books' contents, and then throw it away. As science book for the general audience , it's misleading the readers to a boring playground, where we cannot find any entertaining toys, even if you are there just for fun.

I have read many Japanese books about science, and this one is the worst -- not funny enough to kill time, and not good enough to attract people into the world of such an important science -- the Fourier Expansion of Periodic Wave Forms.

Get the Schaum's outline instead. That will solve your problems quick. It's not funny, but interesting and USEFUL.

This book was originally written to convey the experiences of the Transnational College of LEX (TCL), also known as Torakare, to as many members of the Hippo Group as possible. The college was founded in Tokyo in 1984 as a place where people could study the relationships between human beings and languages. People of all ages, from recent high school graduates to grandparents, study there. It is a school with no homework or exams and no taking of attendance, although people do graduate. Senior fellows, scientists and academicians are also there to lecture and help direct the people in their studies. The Hippo Family Club is the name that the group went by before the LEX name was taken, so the members and graduates are often referred to by that legacy title.

The language studies conducted at LEX are amazing, the Hippo members practice speaking eleven different languages at the same time. Their approach is that every form of human endeavor, mathematics included, has its’ own specific language. Therefore, the idea behind this book was to write a description of Fourier series that would be understandable by as many people as possible.

In that capacity, they have succeeded very well, they start with the basic idea that all speech is a set of waveforms that can be described by sine and cosine curves. Moving slowly from this point, the plotting of complex waveforms by combining different curves is demonstrated. The calculus operations of differentiation and integration are included and the final stop is at the Fast Fourier Transforms (FFTs).

Many diagrams are used along this journey, reflecting the incremental nature of the presentation. The slow speed of coverage makes it inappropriate as a textbook, but it would be an excellent book for individual study. However, if you knew some of the math, you would find those sections boring. In many ways, this book has the appearance of a children’s workbook, only there are not very many exercises to work through.

While I often found the pace tedious, I remain impressed by the concept of LEX and this book. It is readily admitted early on that it is the work of amateurs, but the authors clearly had fun in writing it and they do explain the topic in complete detail.

The language studies conducted at LEX are amazing, the Hippo members practice speaking eleven different languages at the same time. Their approach is that every form of human endeavor, mathematics included, has its’ own specific language. Therefore, the idea behind this book was to write a description of Fourier series that would be understandable by as many people as possible.

In that capacity, they have succeeded very well, they start with the basic idea that all speech is a set of waveforms that can be described by sine and cosine curves. Moving slowly from this point, the plotting of complex waveforms by combining different curves is demonstrated. The calculus operations of differentiation and integration are included and the final stop is at the Fast Fourier Transforms (FFTs).

Many diagrams are used along this journey, reflecting the incremental nature of the presentation. The slow speed of coverage makes it inappropriate as a textbook, but it would be an excellent book for individual study. However, if you knew some of the math, you would find those sections boring. In many ways, this book has the appearance of a children’s workbook, only there are not very many exercises to work through.

While I often found the pace tedious, I remain impressed by the concept of LEX and this book. It is readily admitted early on that it is the work of amateurs, but the authors clearly had fun in writing it and they do explain the topic in complete detail.

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ByJeanon August 25, 2014

I wish I had this book when I entered engineering school. In school the concept of Fourier and Laplace transforms were thrown at the student by a math teacher who really did not belong in an engineering school. No effort in providing any insight, just the formula and a few problems. And on the excuse it was already covered by a prerequisite course, subsequent courses in circuit analysis, feedback systems and communications would graciously include the same worthless 5-minute refresher on barely understood material.

I find myself issuing a 5-star rating for a mathematics book from ... a language school for children ?! Yes! Slow-paced and methodical.

35 years ago when I needed such a book, I chanced early upon Lathi's book (ISBN 0 471 51832 8). This turned the formidable, mysterious Fourier transform into an accessible tool. Instead of obscuring the actual problem, the tool became very handy and allowed me to concentrate on solving the problem.

The Lex book requires no prerequisite and its slower pace makes the material more accessible. It might be too slow and starting from too low for engineers but I do encourage such efforts to make difficult topics accessible. In fact, the language school ?! has also produced similar books on DNA and no less than Quantum Mechanics. Based on the Fourier book, I have procured the two other books and will also review these when I am done reading them.

I find myself issuing a 5-star rating for a mathematics book from ... a language school for children ?! Yes! Slow-paced and methodical.

35 years ago when I needed such a book, I chanced early upon Lathi's book (ISBN 0 471 51832 8). This turned the formidable, mysterious Fourier transform into an accessible tool. Instead of obscuring the actual problem, the tool became very handy and allowed me to concentrate on solving the problem.

The Lex book requires no prerequisite and its slower pace makes the material more accessible. It might be too slow and starting from too low for engineers but I do encourage such efforts to make difficult topics accessible. In fact, the language school ?! has also produced similar books on DNA and no less than Quantum Mechanics. Based on the Fourier book, I have procured the two other books and will also review these when I am done reading them.

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ByTing Lon January 11, 2004

This book has done an excellent job on explaining fourier transformation. Although I believe I have clear understanding on fourier transform, this book takes me to a new journey and let me look at this transform from another perspective. Well done!

However, the reason I can not give this book five star is that the book contains many redundant and irrelavant dialogues which distract your attention from time to time. To speed up your reading, you have to filter it out.

In addition, this book is over size and make it difficult for bed-time reading.

However, the reason I can not give this book five star is that the book contains many redundant and irrelavant dialogues which distract your attention from time to time. To speed up your reading, you have to filter it out.

In addition, this book is over size and make it difficult for bed-time reading.

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ByAhmed Morsion August 2, 2003

THE TRANSNATIONAL COLLEGE 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 HUNDERDS OF BOOKS IN MY LIFE AND I FOUND THESE TWO BOOKS

PLUS THE EPISTEIN'S MARVEL "THINKING PHYSICS" ARE THE BEST BOOKS

WRITTEN IN THE ENGLISH LANGAUGE SCIENCE BOOKS EVER.

SORRY BACK TO THIS BOOK ...IN SHORT ...EXCELLENT WORK .

AND VERY VERY PEDAGOGICAL AND STEP BY STEP YOU WILL MASTER THE SUBJECT.

ANY ONE LIKE THIS KIND OF EDUCATIONAL STYLE WILL BE SPELLED BY THE OTHER

GEM I JUST MENTIONED BEFORE FROM THE SAME COMPANY. REALLY WELL DONE,

I ONLY HAVE A LITTLE NOTE ON THE FAST FOURIER TRANSFORM FFT AT THE END OF

THIS BOOK WHICH IS NOT REALLY AT THE SAME LEVEL OF CLEARITY AS THE REST

OF THE BOOK,,SO FOR ELECTRICAL ENGINEERS ...GET EITHER OF THESE BOOKS,

1-UNDERSTANDING DIGITAL SIGNAL PROCESSING

2-THE SCIENTISTS AND ENGINEERS GUIDE TO DIGITAL SIGNAL PROCESSING

THE SECOND BOOK HAS A REALLY CRYSTAL CLEAR EXPLANATION TO FFT I EVER READ.

THANX ALOT TRANSNATIONAL COLLEGE FOR THESE TWO WONDERFUL BOOKS,

IN FUTURE I WILL BUY ANY BOOK THIS COMPANY WILL ISSUE BLINDLY.

AND I HOPE THEY WILL CONSIDER TO WRITE ANOTHER BOOK ABOUT GENERAL RELATIVITY TO MAKE THE SUBJECT OF TENSORS AND MANIFOLDS AS CLEAR.

THANX 4 READING MY REVIEW.

ENJOY.

THIS ONE AND THE OTHER MARVELOUS BOOK "WHAT IS QUANTUM MECHANICS"

WHICH ALSO WORTH ITS WEIGHT GOLD.

I HAVE BOUGHT HUNDERDS OF BOOKS IN MY LIFE AND I FOUND THESE TWO BOOKS

PLUS THE EPISTEIN'S MARVEL "THINKING PHYSICS" ARE THE BEST BOOKS

WRITTEN IN THE ENGLISH LANGAUGE SCIENCE BOOKS EVER.

SORRY BACK TO THIS BOOK ...IN SHORT ...EXCELLENT WORK .

AND VERY VERY PEDAGOGICAL AND STEP BY STEP YOU WILL MASTER THE SUBJECT.

ANY ONE LIKE THIS KIND OF EDUCATIONAL STYLE WILL BE SPELLED BY THE OTHER

GEM I JUST MENTIONED BEFORE FROM THE SAME COMPANY. REALLY WELL DONE,

I ONLY HAVE A LITTLE NOTE ON THE FAST FOURIER TRANSFORM FFT AT THE END OF

THIS BOOK WHICH IS NOT REALLY AT THE SAME LEVEL OF CLEARITY AS THE REST

OF THE BOOK,,SO FOR ELECTRICAL ENGINEERS ...GET EITHER OF THESE BOOKS,

1-UNDERSTANDING DIGITAL SIGNAL PROCESSING

2-THE SCIENTISTS AND ENGINEERS GUIDE TO DIGITAL SIGNAL PROCESSING

THE SECOND BOOK HAS A REALLY CRYSTAL CLEAR EXPLANATION TO FFT I EVER READ.

THANX ALOT TRANSNATIONAL COLLEGE FOR THESE TWO WONDERFUL BOOKS,

IN FUTURE I WILL BUY ANY BOOK THIS COMPANY WILL ISSUE BLINDLY.

AND I HOPE THEY WILL CONSIDER TO WRITE ANOTHER BOOK ABOUT GENERAL RELATIVITY TO MAKE THE SUBJECT OF TENSORS AND MANIFOLDS AS CLEAR.

THANX 4 READING MY REVIEW.

ENJOY.

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ByAhmed Morsion 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.

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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ByAmazon Customeron April 17, 2003

If you ever watched the entertainment TV programs in Japan, you would understand my review: The dialogs in the book are not only useless, but annoying. [...] After a long time reading the dialogs, then who is Fourier, and where is Fourier's discovery?

The book CAN be written in fewer than 50 pages! It's not as good as an "introductory" Fourier Analysis book, or even a story telling about Fourier's life and scientific discovery. ]...] This book is not a useful book in the real world -- far from that. It's "useful" only when you are familiar with the techniques required to apply Fourier Analysis to the real problems. But then why should I own this book? This is why: Look at the pictures and recall some other books' contents, and then throw it away. As science book for the general audience , it's misleading the readers to a boring playground, where we cannot find any entertaining toys, even if you are there just for fun.

I have read many Japanese books about science, and this one is the worst -- not funny enough to kill time, and not good enough to attract people into the world of such an important science -- the Fourier Expansion of Periodic Wave Forms.

Get the Schaum's outline instead. That will solve your problems quick. It's not funny, but interesting and USEFUL.

The book CAN be written in fewer than 50 pages! It's not as good as an "introductory" Fourier Analysis book, or even a story telling about Fourier's life and scientific discovery. ]...] This book is not a useful book in the real world -- far from that. It's "useful" only when you are familiar with the techniques required to apply Fourier Analysis to the real problems. But then why should I own this book? This is why: Look at the pictures and recall some other books' contents, and then throw it away. As science book for the general audience , it's misleading the readers to a boring playground, where we cannot find any entertaining toys, even if you are there just for fun.

I have read many Japanese books about science, and this one is the worst -- not funny enough to kill time, and not good enough to attract people into the world of such an important science -- the Fourier Expansion of Periodic Wave Forms.

Get the Schaum's outline instead. That will solve your problems quick. It's not funny, but interesting and USEFUL.

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ByCatherine Hoodon March 28, 2003

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 elementary-aged 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.

I help homeschool our three elementary-aged 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.

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ByAmazon Customeron February 23, 2003

Some boring guys get together, pretending cute, and wrote up a big comic book. Fooling around is good for something, but this one is too much. Though they don't care about precious time, you are fooled all the way. I never laughed while I read it -- not interesting at all.

Boring for college students, and meaningless for pedestrians.

I suggest Tolstov, if you want SOME fun and MUCH knowledge, but DO NOT have much time.

Don't waste your time and money if you would study science.

Boring for college students, and meaningless for pedestrians.

I suggest Tolstov, if you want SOME fun and MUCH knowledge, but DO NOT have much time.

Don't waste your time and money if you would study science.

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ByZabeda Kalidon October 22, 2002

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.

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.

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ByZabeda Kalidon October 22, 2002

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.

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.

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