A Brief Guide to Algebraic Number Theory
A Brief Guide to Algebraic Number Theory
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.
- By a world class researcher
- Based on a graduate course given at the University of Cambridge
- Much broader coverage than other similar books
Reviews & endorsements
"This little book would be a good place to find out what the subject is all about...this is not an easy book to read, but it is one that will reward the reader's efforts." MAA Online
"I like short concise yet rigorous books such as this one. You can learn a lot of number theory in 140 pages, and then you have a nice concise reference book when you forget what you learned!" The Bulletin of Mathematical Books
Product details
March 2001Paperback
9780521004237
160 pages
229 × 153 × 11 mm
0.24kg
36 exercises
Available
Table of Contents
- Preface
- 1. Numbers and ideals
- 2. Valuations
- 3. Special fields
- 4. Analytic methods
- 5. Class field theory
- Appendix
- Exercises
- Suggested further reading.
