An Introduction to Algebraic Number Theory

Abstract

This book is based on notes I created for a one-semester undergraduate course on Algebraic Number Theory, which I taught at Harvard during Spring 2004. The primary sources for the course were chapter 1 of Swinnerton-Dyer's book A Brief Guide to Algebraic Number Theory SD01 and chapter 2 of Cassels's article Global Fields Cas67. I wrote these notes by following closely the above two chapters; in some cases I added substantial text and examples. For example, chapter 1 of SD01 is 30 pages, whereas my rewrite of it occupies over 100 pages. In contrast, I follow Cas67 more closely. I have no intent whatever to plagiarize. I acknowledge as such those chapters in this book which are simply a close rewrite of Cas67. My goal is to take the useful classical article (Cas67) and make it more accessible to students by modernizing the notation, and adding additional explanations and examples. I have no intent to publish this book with a traditional publisher, so it will remain freely available indefinitely. If you have comments, corrections, suggestions for additions, etc., please send them to me!