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Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Texts in Mathematics)by P. Hilton
Synopses & ReviewsPublisher Comments: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.
Synopsis:In a relaxed, informal style, this book conveys the joy of mathematical discovery and insight, helping readers to see mathematics as an accessible world of thought. Explores spirals, fractals, Fibonacci numbers, Pascal's Triangle and paper folding, and more.
Synopsis: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.
Table of Contents1. Going Down the Drain 2. A Far Nicer Arithmetic 3. Fibonacci and Lucas Numbers 4. Paper Folding and Number Theory 5. Quilts and Other Decorative Geometries 6. Pascal, Euler, Triangles, and Windmills 7. Hair and Beyond 8. An Introduction to the Mathematics of Fractal Geometry 9. Some of Our Reflections
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