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A Classical Introduction to Modern Number Theory : Graduate Texts in Mathematics - Kenneth F. Ireland

A Classical Introduction to Modern Number Theory

Graduate Texts in Mathematics

Hardcover

Published: September 1990
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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.

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)

Unique Factorization
Applications of Unique Factorization
Congruence
The Structure of U
Quadratic Reciprocity
Quadratic Gauss Sums
Finite Fields
Gauss and Jacobi Sums
Cubic and Biquadratic Reciprocity
Equations over Finite Fields
The Zeta Function
Algebraic Number Theory
Quadratic and Cyclotomic Fields
The Stickelberger Relation and the Eisenstein Reciprocity Law
Bernoulli Numbers
Dirichlet L-functions
Diophantine Equations
Elliptic Curves
The Mordell-Weil Theorem
New Progress in Arithmetic Geometry
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387973296
ISBN-10: 038797329X
Series: Graduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 394
Published: September 1990
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 16.4  x 2.8
Weight (kg): 0.77
Edition Number: 2
Edition Type: Revised