by Benjamin Fine (Author), Gerhard Rosenberger (Author), Gerhard Rosenberger (Author), Benjamin Fine (Author)
Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.
Key topics and features include:
Format: Hardcover
Pages: 426
Edition: 2nd ed. 2016
Publisher: Birkhäuser
Published: 27 Sep 2016
ISBN 10: 3319438735
ISBN 13: 9783319438733
In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. ... Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students. (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)
The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. ... a good text for an introductory course ... . (Allen Stenger, MAA Reviews, maa.org, November, 2016)Benjamin Fine, PhD, is Professor of Mathematics at Fairfield University, CT, USA.
Gerhard Rosenberger, PhD, is Professor (retired) at Dortmund University of Technology, Germany.