Mathematics

by Devlin, Keith J.

• ISBN13: 9780231116398
• ISBN10: 023111639X
• Edition: Revised
• Format: Paperback
• Copyright: 2001-03-01
• Publisher: Columbia Univ Pr

Summary

Mathematics: The New Golden Ageoffers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hilbert's tenth problem and the four-color theorem, Gaussian integers, chaotic dynamics and the Mandelbrot set, infinite numbers, and strange number systems. Why a "new golden age"? According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most significant developments that have taken place in mathematics since 1960, Devlin expertly describes these advances for the interested layperson and adroitly summarizes their significance as he leads the reader into the heart of the most interesting mathematical perplexities -- from the biggest known prime number to the Shimura-Taniyama conjecture for Fermat's Last Theorem. Revised and updated to take into account dramatic developments of the 1980s and 1990s, Mathematics: The New Golden Ageincludes, in addition to Fermat's Last Theorem, major new sections on knots and topology, and the mathematics of the physical universe. Devlin portrays mathematics not as a collection of procedures for solving problems, but as a unified part of human culture, as part of mankind's eternal quest to understand ourselves and the world in which we live. Though a genuine science, mathematics has strong artistic elements as well; this creativity is in evidence here as Devlin shows what mathematicians do -- and reveals that it has little to do with numbers and arithmetic. This book brilliantly captures the fascinating new age of mathematics.

Table of Contents

Preface	vii
Acknowledgments	xi
Prime Numbers, Factoring, and Secret Codes	1	(36)
Sets, Infinity, and the Undecidable	37	(24)
Number Systems and the Class Number Problem	61	(24)
Beauty from Chaos	85	(26)
Simple Groups	111	(32)
Hilbert's Tenth Problem	143	(20)
The Four-Color Problem	163	(30)
Hard Problems About Complex Numbers	193	(30)
Knots, Topology, and the Universe	223	(40)
Fermat's Last Theorem	263	(28)
The Efficiency of Algorithms	291	(20)
Index	311