A Brief Guide to Algebraic Number Theory

London Mathematical Society Student Texts

by H.P.F. Swinnerton-Dyer

This account of Algebraic Number Theory is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermat's Last Theorem, as well as a comprehensive account of class field theory. Many exercises and an annotated reading list are also included.

160 pages, Paperback

First published January 1, 2001

About the author

Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet (also known as Peter Swinnerton-Dyer), is a British mathematician.