Introductory Algebraic Number Theory

Rating:
Summary: Grab bag of good and bad
Review: Strengths:
1. Easy reading, detailed proofs
2. Covered required algebra background (modules, ideals, Dedekind domains, etc)
3. Many, many examples

Weaknesses:
1. Too detailed in some cases
2. Does not develop more advanced ideas that actually make the material easier
3. Poor index
4. Examples are often too simple

This book takes the reader through the required algebra background and moves them into the realm of using these abstract algebraic construction to study the theory of numbers. The book is aimed at upper-level undergraduates, so it's easy reading. Sometimes too easy reading, as proofs are often long-winded and contain many trivial details. In some instances, I wanted all those details, often it was simply annoying.

The real strength of this book lies in the many explicit examples. It was worth the price for these examples, as most higher-level books offer few examples.

The index is terrible, but the additional reading section at the end of each chapter is a nice addition.

Overall, I learned a lot from this book, but would have liked to have the authors approached the material at a little bit higher level. For instance, instead of using complex conjugates extensively, I would have preferred introducing a mapping to the complex conjugates (say sigma) for use in most proofs.