Overview
- Includes up-to-date material on recent developments and topics of significant interest, such as the new primality test
- Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight
Part of the book series: Graduate Texts in Mathematics (GTM, volume 232)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject.
A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.
Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to learn some of the big ideas in number theory.
Reviews
From the reviews:
"This number theory text is somewhat different than traditional number theory texts. The authors’ guiding principle is unique factorization and its consequences. … This is not a traditional number theory text, but one that tries to guide the reader through the beginnings of the subject towards the modern frontiers. This is helped along by a good sized bibliography plus many problems … . it might provide an interesting experience when used at the graduate level." (Don Redmond, Mathematical Reviews, Issue 2006 j)
"The book under review contains several topics which are usually not brought together in an introductory text. The book is meant to give a broad introduction to advanced undergraduate students … of number theory. … Each chapter contains many exercises and historical notes. … In my opinion, because so many topics are treated in an accessible way, the book is very well suited for an introductory course in number theory." (Jan-Hendrik Evertse, Zentralblatt MATH, Vol. 1089 (15), 2006)
"In An Introduction to Number Theory, the authors strive to have the best of all worlds: they cover a broad range of topics … . This book could be used for a number of different courses. … The full book would be appropriate for a first-year graduate course. It’s also a nice introduction to the subject for established mathematicians form other fields. … its extensive bibliography, tasteful collection of topics, and clear presentation make it a pleasant reference even for working number theorists." (Rob Benedetto, MathDL, January 2006)
Authors and Affiliations
Bibliographic Information
Book Title: An Introduction to Number Theory
Authors: Graham Everest, Thomas Ward
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/b137432
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2005
Hardcover ISBN: 978-1-85233-917-3Published: 15 June 2005
Softcover ISBN: 978-1-84996-959-8Published: 19 October 2010
eBook ISBN: 978-1-84628-044-3Published: 24 November 2005
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: IX, 297
Topics: Number Theory