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Title: The Mathematical Experience by Philip J. Davis, Reuben Hersh, Gian-Carlo Rota ISBN: 0-395-32131-X Publisher: Houghton Mifflin Company Pub. Date: May, 1982 Format: Paperback Volumes: 1 List Price(USD): $15.95 |
Average Customer Rating: 4.92 (12 reviews)
Rating: 5
Summary: Excellent dialog on the development of mathematics..
Comment: This book was a sheer joy to read and digest. The authors skilfully comingle history, mathematics, philosophy, and biography. The result is a truly fantastic voyage into the meaning and gist of discovery and conjecture. In chapter after chapter important ideas like Fourier analysis, Non-Cantorian Set Theory, and Objects and Structures are scrutinized in a very interesting manner.
The deeper you go into the book the more will you revel in the sheer majesty and scope of the topics. I had to read the chapter on Inner Issues twice to really get everything out of the text. Topics such as Teaching and Learning are very insightful and full of little hidden gems.
If you are prepared to expend some effort and if you wish to know what mathematics "really is like", grab this book. I am sure this will become a permanent treasure in your library and you will peruse it often long into the night.
Rating: 5
Summary: rare.
Comment: It was about five years ago. Physics suddenly seemed fascinating but I was struggling with math. My tutor suggested two books for me. One of them was this book. I cannot say this book was particularly helpful but it gave me a good sense of what mathematics is: its people, culture, history, and philosophy. Quite unlike E.T. Bell's Men of Mathematics, this book does not contain romantically presented stories of some math heros. And unlike some popular math books by Ian Stewart, it does not attempt to explain (rather unsuccessfully) some esoteric theories. It is just as the title suggest--what a mathematical experience can be. A book of this kind is rare.
P.S. Now, some five years later, I am not sure if mathematical knowledge maintains a separte existence as Plato had thought, and as the authors believe. (Ref. Plato, Phaedo)
Rating: 5
Summary: Philosophy, History and Myths of Mathematics
Comment: The Mathematical Experience by Philip J. Davis and Reuben Hersh
1981 Houghton Mifflin Company, Boston
Is all of pure mathematics a meaningless game? What are the contradictions that upset the very foundations of mathematics? If a can of tuna cost $1.05 how much does two cans of tuna cost (Pg. 71)? If you think you know the answer, don't be so sure. How old are the oldest mathematical tables? What is mathematics anyway, and why does it work? Can anyone prove that 1 + 1 = 2?
This is a book about the history and philosophy of mathematics. I'm certainly not a mathematician, and there are parts of the book I will never understand, yet the balance of it made the experience well worth while. The authors presented the material so that it is interesting and (mostly) easily understood. They have a creative way of making a difficult subject exciting. They do this by giving us insights into how mathematicians work and create. They live up to the title making mathematics a human experience by adding fascinating history. Frankly I was shocked when they pointing out how even mathematicians have made questionable assumptions and taken some basic "truths" on faith. They show the beauty of math in the "Aesthetic Component" chapter. Ultimately the question that comes up again and again is the question of whether or not we can really know anything about time and space independent of our own experience to make an adequate foundation for a complete system in mathematics. If you have ever wondered about the world of mathematics and the personalities involved you might consider this book. If you are a mathematics teacher you should read this book. If you are a mathematician you could find it quite unsettling.
It contains eight chapters, each one broken up into many subtitles so if you do get bogged down in the mathematics it isn't for long. There are 440 pages. I'd like to see a much more complete glossary for people like me who need it.
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Title: Foundations and Fundamental Concepts of Mathematics by Howard Eves ISBN: 048669609X Publisher: Dover Pubns Pub. Date: 20 May, 1997 List Price(USD): $16.95 |
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Title: What Is Mathematics?: An Elementary Approach to Ideas and Methods by Richard Courant, Herbert Robbins, Ian Stewart ISBN: 0195105192 Publisher: Oxford University Press Pub. Date: May, 1996 List Price(USD): $21.50 |
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Title: What Is Mathematics, Really? by Reuben Hersh ISBN: 0195130871 Publisher: Oxford University Press Pub. Date: July, 1999 List Price(USD): $19.95 |
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Title: Concepts of Modern Mathematics by Ian Stewart ISBN: 0486284247 Publisher: Dover Pubns Pub. Date: 01 February, 1995 List Price(USD): $12.95 |
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Title: Mathematics and the Physical World by Morris Kline ISBN: 0486241041 Publisher: Dover Pubns Pub. Date: 01 March, 1981 List Price(USD): $16.95 |
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