The Nature and Power of Mathematics
This captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty. Author Donald M. Davis focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. He also discusses related topics, such as the relevance of Greek mathematics to Kepler's laws of planetary motion, and the theoretical work that led to the development of computers.Only a background in basic algebra and geometry is necessary to appreciate this volume, which features exercises that further develop some of its important concepts. Graded according to difficulty, these exercises are designed to improve readers' skills in logic, and to enable them to experience mathematics at increasingly advanced levels.Supplementary materials at the end of each chapter include intriguing examples of the subjects' applications, as well as biographical sketches of Archimedes, Einstein, Newton, and other luminaries of mathematics.
1000083330
The Nature and Power of Mathematics
This captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty. Author Donald M. Davis focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. He also discusses related topics, such as the relevance of Greek mathematics to Kepler's laws of planetary motion, and the theoretical work that led to the development of computers.Only a background in basic algebra and geometry is necessary to appreciate this volume, which features exercises that further develop some of its important concepts. Graded according to difficulty, these exercises are designed to improve readers' skills in logic, and to enable them to experience mathematics at increasingly advanced levels.Supplementary materials at the end of each chapter include intriguing examples of the subjects' applications, as well as biographical sketches of Archimedes, Einstein, Newton, and other luminaries of mathematics.
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The Nature and Power of Mathematics

The Nature and Power of Mathematics

by Donald M. Davis
The Nature and Power of Mathematics

The Nature and Power of Mathematics

by Donald M. Davis

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$15.99 

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Overview

This captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty. Author Donald M. Davis focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. He also discusses related topics, such as the relevance of Greek mathematics to Kepler's laws of planetary motion, and the theoretical work that led to the development of computers.Only a background in basic algebra and geometry is necessary to appreciate this volume, which features exercises that further develop some of its important concepts. Graded according to difficulty, these exercises are designed to improve readers' skills in logic, and to enable them to experience mathematics at increasingly advanced levels.Supplementary materials at the end of each chapter include intriguing examples of the subjects' applications, as well as biographical sketches of Archimedes, Einstein, Newton, and other luminaries of mathematics.

Product Details

ISBN-13: 9780486152158
Publisher: Dover Publications
Publication date: 02/19/2013
Series: Dover Books on Mathematics
Sold by: Barnes & Noble
Format: eBook
Pages: 400
File size: 28 MB
Note: This product may take a few minutes to download.

About the Author

Donald M. Davis

Table of Contents

Preface

1 Some Greek Mathematics

1.1 [phi] and Irrational Numbers: An Introduction to Greek Mathematics

1.2 Euclidean Geometry

1.3 Greek Mathematics and Kepler

2 Non-Euclidean Geometry

2.1 Formal Axiom Systems

2.2 Precursors to Non-Euclidean Geometry

2.3 Hyperbolic Geometry

2.4 Spherical Geometry

2.5 Models of Hyperbolic Geometry

2.6 The Geometry of the Universe

3 Number Theory

3.1 Prime Numbers

3.2 The Euclidean Algorithm

3.3 Congruence Arithmetic

3.4 The Little Fermat Theorem

4 Cryptography

4.1 Some Basic Methods of Cryptography

4.2 Public Key Cryptography

5 Fractals

5.1 Fractal Dimension

5.2 Iteration and Computers

5.3 Mandelbrot and Julia sets

Epilogue

Bibliography

Credits

Index

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