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About this book
Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
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Keywords
Table of contents (20 chapters)
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Front Matter
Reviews
From the reviews of the second edition:
K. Ireland and M. Rosen
A Classical Introduction to Modern Number Theory
"Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution."
— MATHEMATICAL REVIEWS
"This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. … for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvêa, MathDL, January, 2006)
Authors and Affiliations
Bibliographic Information
Book Title: A Classical Introduction to Modern Number Theory
Authors: Kenneth Ireland, Michael Rosen
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4757-2103-4
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1990
Hardcover ISBN: 978-0-387-97329-6Published: 07 September 1990
Softcover ISBN: 978-1-4419-3094-1Published: 01 December 2010
eBook ISBN: 978-1-4757-2103-4Published: 17 April 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XIV, 394
Topics: Number Theory