Overview

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.

Full Product Details

Author:   Kenneth Ireland ,  Michael Rosen
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 2nd ed. 1990
Volume:   84
Dimensions:   Width: 15.50cm , Height: 2.10cm , Length: 23.50cm
Weight:   1.260kg
ISBN:  

9781441930941

ISBN 10:   1441930949
Pages:   394
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Unique Factorization.- 2 Applications of Unique Factorization.- 3 Congruence.- 4 The Structure of U(?/n?).- 5 Quadratic Reciprocity.- 6 Quadratic Gauss Sums.- 7 Finite Fields.- 8 Gauss and Jacobi Sums.- 9 Cubic and Biquadratic Reciprocity.- 10 Equations over Finite Fields.- 11 The Zeta Function.- 12 Algebraic Number Theory.- 13 Quadratic and Cyclotomic Fields.- 14 The Stickelberger Relation and the Eisenstein Reciprocity Law.- 15 Bernoulli Numbers.- 16 Dirichlet L-functions.- 17 Diophantine Equations.- 18 Elliptic Curves.- 19 The Mordell-Weil Theorem.- 20 New Progress in Arithmetic Geometry.- Selected Hints for the Exercises.

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. Gouvea, MathDL, January, 2006)

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. Gouvea, MathDL, January, 2006)

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. Gouvea, MathDL, January, 2006)

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