A Classical Introduction to Modern Number Theory / Edition 2

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More About This Textbook

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

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: 9780387973296
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 9/7/1990
  • Series: Graduate Texts in Mathematics Series , #84
  • Edition description: 2nd ed. 1990. Corr. 5th printing 1998
  • Edition number: 2
  • Pages: 408
  • Sales rank: 1,300,884
  • Product dimensions: 1.00 (w) x 6.14 (h) x 9.21 (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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