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Not always buried deep; a second course in elementary number theory.


Not always buried deep; a second course in elementary number theory.

Pollack, Paul.

American Mathematical Society


303 pages




Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with a minimal mathematical background. With this in mind, Pollack (Mathematics, University of Illinois at Urbana-Champaign) presents a book for readers who want to explore elementary methods in modern number theory. (Readers do, however, need some familiarity with number theory at an undergraduate level and should have taken a first course in modern algebra.) The author begins with a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. He then turns to topics that are particularly attractive and accessible, including Gauss' theory of cyclotomy and its applications to rational reciprocity laws; Hilbert's solution to Waring's problem; and modern work on perfect numbers.

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Publication:SciTech Book News
Article Type:Book review
Date:Dec 1, 2009
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