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**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's 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.

**Review:**
. . . excellent introductory book to analytic number theory. It is ideal for a first course in analytic number theory for undergraduate level. - Zentralblatt MATH

One gets the sense that Pollack took great care to make the material as accessible as possible. [...] a good text for a second undergraduate course in number theory [...] would provide a smooth transition to advanced study [...] - MAA reviews

. . . one of the best mathematics books that I have read recently. . . beautifully written and very well organised . . well within the reach of an undergraduate. . . - SIGACT book reviews

Title: **Not Always Buried Deep: A Second Course in ...**

Publisher: **Amer Mathematical Society**

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Published by
American Mathematical Society
(2009)

ISBN 10: 0821848801
ISBN 13: 9780821848807

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**Book Description **American Mathematical Society, 2009. Hardcover. 4to. Near fine. Seller Inventory # 039835

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**Book Description **American Mathematical Society. Hardcover. Condition: Very Good. 0821848801 Item in very good condition! Textbooks may not include supplemental items i.e. CDs, access codes etc. Seller Inventory # Z0821848801Z2

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**Book Description **American Mathematical Society, 2009. Hardcover. Condition: Good. Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes supplemental or companion materials if applicable. Access codes may or may not work. Connecting readers since 1972. Customer service is our top priority. Seller Inventory # mon0000709711

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**Book Description **American Mathematical Society, United States, 2009. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAN9780821848807

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**Book Description **Condition: New. Depending on your location, this item may ship from the US or UK. Seller Inventory # 97808218488070000000

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**Book Description **American Mathematical Society, United States, 2009. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAN9780821848807

Published by
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**Book Description **American Mathematical Society, 2009. Hardcover. Condition: Used: Good. Seller Inventory # SONG0821848801

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**Book Description **EUROSPAN, 2009. Hardback. Condition: NEW. 9780821848807 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE01476519

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**Book Description **American Mathematical Society, 2009. Hardcover. Condition: New. Seller Inventory # DADAX0821848801