Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Texts in Mathematics) Corrected Edition

by Peter Hilton (Author), Derek Holton (Author), Jean Pedersen (Author)

2 ratings

ISBN-13: 978-0387947709

ISBN-10: 0387947701

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A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.

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From the Back Cover

The purpose of this book is to show what mathematics is about, how it is done, and what it is good for. The relaxed and informal presentation conveys the joy of mathematical discovery and insight and makes it clear that mathematics can be an exciting and engrossing activity. Frequent questions lead the reader to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics (for mathematics students or for prospective or in-service mathematics teachers) or as enrichment for other courses. It can also be read with pleasure on its own by anyone interested in the intellectually intriguing aspects of mathematics.

Product details

Publisher : Springer; Corrected edition (December 13, 1996)
Language: : English
Hardcover : 368 pages
ISBN-10 : 0387947701
ISBN-13 : 978-0387947709
Item Weight : 4.5 pounds
Dimensions : 7 x 0.88 x 10 inches

Best Sellers Rank: #1,861,569 in Books (See Top 100 in Books)
- #546 in Number Theory (Books)
- #765 in Geometry (Books)
- #1,791 in Geometry & Topology (Books)

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Visual Thinkers Paradise

Reviewed in the United States on August 16, 2000

If you have trouble understanding and particularly visualizing what mathematical formulae mean. If you have a belief that all mathematical concepts CAN be visualized if only mathematicians tried hard enough. If you like math books but wish there were more pictures. If you wish there were instructions on things to do in Math books other than write out formulae and solutions. If you want hope that there's new and exciting stuff out there that you can find by doing things with paper other than writing on it. THIS IS THE BOOK FOR YOU. A particularly interesting section on how to generate the Cantor Set by Geometric iteration using the tent map and a good explanation of sets related to the Cantor set and the general relationship of things like the Cantor Set to more complicated fractals. One of the most interesting books I have eever read vastly increased my understanding and provided me with valuable ideas to furthur my own creative efforts. Well done HHandP I look forward to the new book.

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Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Texts in Mathematics) Corrected Edition

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