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Who Is Fourier?: A Mathematical Adventure Paperback – April 1, 1995
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About the Author
The Transnational College of LEX (TCL) in Tokyo, Japan, is a research institute run by the Hippo Family Club, an organization dedicated to the natural acquisition of multiple languages and to cultural exchange programs. At TCL the students study subjects related to the natural science of language and humanity. They approach mathematics, physics, biology, and other subjects from a viewpoint that transcends disciplines. The students are especially interested in investigating how humans acquire language and ways of developing a natural learning environment. TCL students gather information, research, and discover together. They are aided by Senior Fellows, experts in their fields who advise the students and who are invited to speak about topics of interest in their own research.
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However even the best of professors often assume basic prerequisite knowledge underpinning the courses they instruct. If there are any gaps in knowledge by the learning student, then they will struggle to take more and more on faith, when all they might need is a simple review of some of the basics, i.e. the gaps in their knowledge that makes the more complex principles of Fourier Analysis make sense.
Twenty years after college I ran across this book and found it very refreshing. It presents the knowledge in such a way that you know you're truly learning it because you can imagine yourself teaching someone else the same principles. It's not like college where you understand 80% of the course but 20% is just "monkey see, monkey do and monkey pass tests", perhaps even getting "A"'s but just out of sheer willpower and short term memorization, only to forget much of the course that didn't make any sense after it's all done.
The only parts of this book that I found irrelevent were the number crunching, paper cutting and pasting exercises, but I could see how these could be valuable for the young high-school student who is not as familiar with calculus and trigonometry and needs the manual exercises of crunching the numbers and entering them into tables in order to appreciate their relevance.
- Walks you through the reasoning and mechanics of the math
- Starts slowly with a couple of example problems which are explored in complete detail
- Gets you involved in doing the math hands on. There is no fallback to letting an advanced calculator or Excel spreadsheet do the work for you.
- By the end of the book you are working in the complex number format (i + j for the EE types).
- There are occasions where the lessons take a bit of a leap in understanding and you have to backtrack and figure out what's going on.
- Pages are filled with lots of side notes and doodles that are a bit of a distraction. But it does show that youngsters developed most of this stuff.
Now for some gratuitously picky criticism: This book is entitled "Who is Fourier?". I would like to know a few historical things about the man so I can tell him apart from the Economist of the same name or the Egyptologist. [Hey, wait a minute. . . He was that Egyptologist!]. What about his personal life? Maybe one of his love letters to Sophie Germain would spice up the book.
Seriously, lights turned on when I read this book. The early chapters showed how to use filters. The middle chapters are review that connect e, i, pi, and trigonometric functions together in preparation for the final chapters on the Fast Fourier Transform. The last 2 chapters on the FFT were the hardest, and I shall have to reread them. I am giving this 5 stars because it does teach a difficult subject in a most insightful and entertaining way. Nevertheless, I'd like to see what improvements are made in the Second Edition.
For that it is remarkable and deals with fourier series and transforms in great detail, insisting on instilling the intuitions.
For these I would give it 5 stars.
For those who have a good grounding in calculus it may drive them crazy by being so long winded.
If you havent seen calculus for 30 years then this could be a great, in fact unique book.
I bought it to see how the subject could be taught.
I would recommend it to a PhD student friend who skipped calculus and now is regretting it.
I used this book as a supplement to an engineering math course, and the explanations here were quite helpful to me in understanding the fundamental ideas.
My only complaint is that some of the cutesy stuff was a little distracting for me. When the authors stuck to straight language in explaining the material the book is at its best. Overall I highly recommend this book.
computer programs that carry out the Fourier transform.