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Textbook in PDF format

This book grew out of various courses given at Queen’s University between 1996 and 2004. In the short span of a semester, it is diffcult to cover enough material to give students the confidence that they have mastered some portion of the subject. Consequently, I have found that a problem-solving format is the best way to deal with this challenge. The salient features of the theory are presented in class along with a few examples, and then the students are expected to teach themselves the finer aspects of the theory through worked examples.
This is a revised and expanded version of “Problems in Algebraic Number Theory” originally published by Springer-Verlag as GTM 190. The new edition has an extra chapter on density theorems. It introduces the reader to the magnificent interplay between algebraic methods and analytic methods that has come to be a dominant theme of number theory