Introductory Algebraic Number Theory

• Publisher:   Cambridge University Press
• Number Of Pages:   446
• Publication Date:   2003-11-17
• ISBN-10 / ASIN:   0521832500
• ISBN-13 / EAN:   9780521832502

Suitable for senior undergraduates and beginning graduate students in mathematics, this book is an introduction to algebraic number theory at an elementary level. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested readings and to the biographies of mathematicians who have contributed to the development of algebraic number theory are provided at the end of each chapter. Other features include over 320 exercises, an extensive index, and helpful location guides to theorems in the text.

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.

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