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

9780821848807

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

Pollack, Paul.

American Mathematical Society

2009

303 pages

$62.00

Hardcover

QA241

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 |
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Article Type: | Book review |

Date: | Dec 1, 2009 |

Words: | 172 |

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