A Guide to Elementary Number TheoryUnderwood Dudley
151 pp., hardcover, 2009. Series: MAA Guides #5; Dolciani Mathematical Expositions #41
ISBN: 978-0-88385-347-4
December 4, 2009
A Guide to Elementary Number Theory
Underwood Dudley
151 pp., hardcover, 2009. Series: MAA Guides #5; Dolciani Mathematical Expositions #41
ISBN: 978-0-88385-347-4
This Guide is intended for two kinds of readers, according to author-mathematician Woody Dudley. The first are those who once knew but have forgotten, for instance, which integers are the sums of two squares and why they have that property, and who want their memories refreshed. The second are those who were never told about sums of squares and want to find out about them, quickly and without nonsense.
In 150 pages, Dudley masterfully contends with 40 topics in number theory, including greatest number divisors, unique factorization, congruences, amicable numbers, perfect numbers, Gauss's Lemma, Pythagorean triples, sums of four squares, Sophie Germain primes, and the Riemann Hypothesis.
No nonsense and concision are the hallmarks of this delightful book by a true expositor of mathematics. "The Guide does not contain some things I will mention here lest readers think they were omitted through carelessness," Dudley states. "There is no mention of cryptography because this is an application of number theory. Elliptical curves are intermediate, not elementary, number theory. Only a few diophantine equations appear. Quadratic forms are missing. . . . Algebraic number theory is a whole other subject." And because of vast resources on the Web, there is no need for references or suggestions for further reading.
Excerpt (p. 91): Pell's Equation
About the Author:
Underwood Dudley taught at DePauw University for 37 years. He earned his B.S. and M.S. degrees from the Carnegie Institute of Technology and his doctorate in number theory from the University of Michigan. A longtime member of the MAA, Dudley was the J. Sutherland Frame Lecturer in 1992, the Pólya Lecturer in 1995-96, and editor of the College Mathematics Journal from 1999-2003. He received the MAA's Meritorious Service Award in 2004, the year he officially "retired."
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