A Classical Introduction to Modern Number Theory / Edition 2

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Overview

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-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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Editorial Reviews

From the Publisher
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)

Booknews
To the edition of 1980 have been added two new chapters, intended to convey the essence of recent developments in this ancient but ever- lively field. The text--addressed to graduate students and to advanced undergraduates--treats all the issues standard to its subject matter, but concentrates when possible on those aspects of the field which are at present "research active", and generally avoids complicated analytical machinery. Respectful attention is given to the history of the subject, and there are exercises (with hints) at the ends of the twenty chapters. Superbly produced. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781441930941
  • Publisher: Springer New York
  • Publication date: 12/1/2010
  • Series: Graduate Texts in Mathematics Series , #84
  • Edition description: Softcover reprint of hardcover 2nd ed. 1990
  • Edition number: 2
  • Pages: 394
  • Product dimensions: 0.84 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

1: Unique Factorization. 2: Applications of Unique Factorization. 3: Congruence. 4: The Structure of U. 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.

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