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A Brief Guide to Algebraic Number Theory 1st Edition by H P F Swinnerton Dyer ISBN 0521004233 9780521004237

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A Brief Guide to Algebraic Number Theory London Mathematical Society Student Texts Swinnerton-Dyer Digital Instant Download

Author(s): Swinnerton-Dyer, H.P. F.
ISBN(s): 9780521004237, 0521004233
Edition: Annotated
File Details: PDF, 9.02 MB
Year: 2001
Language: english
SKU: EB-32948652 Category: Tags: ,

A Brief Guide to Algebraic Number Theory 1st Edition by H P F Swinnerton Dyer – Ebook PDF Instant Download/Delivery: 0521004233, 9780521004237
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Product details:

ISBN 10: 0521004233 
ISBN 13: 9780521004237
Author: H P F Swinnerton Dyer

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.

A Brief Guide to Algebraic Number Theory 1st Table of contents:

1 Numbers and Ideals
1 The ring of integers
2 Ideals and factorization
3 Embedding in the complex numbers
4 Change of fields
5 Normal extensions

2 Valuations
6 Valuations and completions
7 Field extensions and ramification
8 The Different
9 Idèles and Adèles

3 Special Fields
10 Quadratic fields
11 Pure cubic fields
12 Biquadratic fields
13 Cyclotomic fields
 13.1 Class numbers of cyclotomic fields
 13.2 Fermat’s Last Theorem

4 Analytic Methods
14 Zeta functions and L-series
15 Analytic continuation and the functional equation
16 Density theorems

5 Class Field Theory
17 The classical theory
18 Chevalley’s reformulation
19 Reciprocity theorems
20 The Kronecker-Weber Theorem

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Tags: H P F Swinnerton Dyer, Brief, Algebraic Number