Not Always Buried Deep: A Second Course in Elementary Number Theory (Monograph Books) - Hardcover

Pollack, Paul

Hardcover

ISBN 10: 0821848801 ISBN 13: 9780821848807

Publisher: American Mathematical Society, 2009

Synopsis

Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. ""Not Always Buried Deep"" is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is 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. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss' theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: the reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.

About this title

Review

“...one of the best mathematics books that I have read recently. It is beautifully written and very well organized, the kind of book that is well within the reach of an undergraduate student, even one with little complex analysis. Indeed, a good knowledge of the analysis of real functions of one variable is probably enough for reading most of the book. ...I know of no better place to learn about Dirichlet’s Theorem on arithmetic progressions or Selberg’s proof of the Prime Number Theorem. And if these are two results of analytic number theory that deserve to be known to every mathematician, these are certainly they.”
-- S. C. Coutinho

Edition details

• Publisher: American Mathematical Society
• Publication date: 2009
• ISBN 10: 0821848801
• ISBN 13: 9780821848807
• Binding: Hardcover
• Language: English
• Number of pages: 303