Nature and Power of Mathematics

ISBN-10: 0486438961

ISBN-13: 9780486438962

Edition: 2004

Authors: Donald M. Davis
List price: $19.95
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Description: In this engaging book, Donald Davis explains some of the most fascinating ideas in mathematics to the nonspecialist, highlighting their philosophical and historical interest, their often surprising applicability, and their beauty. The three main topics discussed are non- Euclidean geometry, with its application to the theory of relativity; number theory, with its application to cryptography; and fractals, which are an application in art, among other areas, of early mathematical work on iteration. Other topics include the influence of Greek mathematics on Kepler's laws of planetary motion, and the theoretical work that led to the development of computers. Assuming the reader has some background in basic algebra and geometry, Davis relies on exercises to develop some of the important concepts. These exercises are designed to improve the reader's ability in logic, and enable him or her actually to experience mathematics at increasingly advanced levels.

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Book details

List price: $19.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 12/23/2004
Binding: Paperback
Pages: 400
Size: 5.50" wide x 8.25" long x 1.00" tall
Weight: 0.946
Language: English

Preface
Some Greek Mathematics
[phi] and Irrational Numbers: An Introduction to Greek Mathematics
Euclidean Geometry
Greek Mathematics and Kepler
Non-Euclidean Geometry
Formal Axiom Systems
Precursors to Non-Euclidean Geometry
Hyperbolic Geometry
Spherical Geometry
Models of Hyperbolic Geometry
The Geometry of the Universe
Number Theory
Prime Numbers
The Euclidean Algorithm
Congruence Arithmetic
The Little Fermat Theorem
Cryptography
Some Basic Methods of Cryptography
Public Key Cryptography
Fractals
Fractal Dimension
Iteration and Computers
Mandelbrot and Julia sets
Epilogue
Bibliography
Credits
Index
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