A Brief Guide to Algebraic Number Theory

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

H. P. F. Swinnerton-Dyer (Author)

9780521802925, Cambridge University Press

Hardback, published 22 February 2001

160 pages, 36 exercises
22.9 x 15.2 x 1.3 cm, 0.41 kg

'The carefully chosen material is further accompanied by a large number of illustrative examples and exercises. Those features make the book an excellent guide for the reader who wants to find out what algebraic number theory is all about.' Nieuw Archief voor Wiskunde

This is a 2001 account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. It 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.

Preface
1. Numbers and ideals
2. Valuations
3. Special fields
4. Analytic methods
5. Class field theory
Appendix
Exercises
Suggested further reading.

Subject Areas: Number theory [PBH], Algebra [PBF]