The Nature and Power of Mathematics

By Donald M. Davis

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0691025622
• ISBN13: 9780691025629
• Release Date: November 1993
• Publisher: Princeton University Press
• Length: 408 Pages
• Weight: 1.35 lbs.
• Dimensions: 9.3" x 1.0" x 6.3"

Customer Reviews

An existence proof that popular mathematics can be written to include equations and still be effecti

Popular mathematics can be done at a level that is also suitable for "advanced" survey courses in mathematics. This book is an existence proof of that. Davis does a superb job of tracing the development of five major areas of mathematics, some of which are more historical than others. The areas are: *) Greek mathematics of irrational numbers, Euclidean geometry, conic sections and Kepler's discovery of the motion of the planets. *) The development of non-Euclidean geometry, and examples of non-Euclidean geometries such as hyperbolic and spherical geometries. This includes a brief discussion of Einstein's theories of relativity. *) Number theory, factorization, prime numbers, the Euclidean algorithm, congruence arithmetic, and the work of Pierre de Fermat. *) Cryptography, in particular that number theory is the theoretical foundation of modern cryptographic methods. *) Fractal geometry and how iteration is used to construct the Mandelbrot and Julia sets. Davis does an excellent job in explaining how the math was developed and is used and makes no attempt to "spoil the reader by sparing the equation", although equations are not multiplied beyond their necessity. A large number of exercises are included at the end of each section, which makes it possible to use it as a textbook.