A Brief Guide to Algebraic Number Theory

A Brief Guide to Algebraic Number Theory

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Description

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.show more

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Review quote

'... masterfully written. It has to be recommended to number theorists and more general to working algebraists.' J. Schoissengeier, Monatshefte fur Mathematik '... ideally suited for non-specialists who would like to know quickly what algebraic number theory is about but who do not wish to study thick volumes dealing with that subject.' Wladyslaw Narkiewicz, Zentralblatt fur Mathematik '... very readable. It is suitable for graduate students or non-specialists who wish to learn algebraic number theory.' Gabor Megyesi, Acta Sci. Math. 'It is written in a nice (but necessarily concise) style, containing exercises to broaden the reader's knowledge and skills. The result is a very solid introduction to the subject.' EMS '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 Wiskundeshow more

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.show more

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