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  • Print publication year: 2003
  • Online publication date: September 2012

Introduction

Summary

This book is intended as an introductory text for senior undergraduate and beginning graduate students wishing to learn the fundamentals of algebraic number theory. It is based upon a course in algebraic number theory given by the second author at Carleton University for more than thirty years. Keeping in mind that this is an introductory text, the authors have strived to present the material in as straightforward, clear, and elementary fashion as possible. Throughout the text many numerical examples are given to illustrate the theory. Each chapter closes with a set of exercises on the material covered in the chapter, as well as some suggested further reading. References cited in each chapter are listed under suggested reading. Biographical references for some of the mathematicians mentioned in the text are also given at the end of each chapter. For the convenience of the reader, the book concludes with page references for the definitions, theorems, and lemmas in the text. In addition an extensive bibliography of books on algebraic number theory is provided.

The main aim of the book is to present to the reader a detailed self-contained development of the classical theory of algebraic numbers. This theory is one of the crowning achievements of nineteenth-century mathematics. It came into being through the attempts of mathematicians of that century to prove Fermat's last theorem, namely, that the equation xn + yn = zn has no solutions in nonzero integers x, y, z, where n is an integer ≥ 3.