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.
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)