Abstract Algebra (3rd Edition)
Quick Informations
Where to buy it: Wiley
Authors: David S. Dummit and Richard M. Foote
Release date: July 14, 2003
Language: English
Personal Progress: I currently read the first three chapters.
Description
This textbook contains all the abstract algebra you will need for your undergraduate studies, and even morethan that. It covers all the key concepts, such as Groups, Rings, Fields, Modules, Vector Spaces, and all the properties linking these objects together. The book is divided into general parts (Group Theory, Ring Theory, ...), which are divided into chapters, which are divided into sections. The structure of the book introduces very naturally these numerous new concepts. This book can be read by people discovering the subject, as well as advanced students searching for a precise topic. It is very readable in both cases.
Review
[I didn't finish the book yet.] I would say that this is an excellent textbook. A large amount of it is dedicated to motivate the concepts in the best way possible. The explanations are clear. There are various examples trying to link the content with as much other topics as possible. Its size may seem intimidating, but it is, in my opinion, a really good thing. You know that after reading this book, you will never need to read an other abstract algebra textbook ever again. I highly recommend it.
Exercises
There are many many exercises in this book, more than any other book I've read. In the first chapters, most of them are either computational, or very easy (in my opinion) which makes the feeling of solving the exercises different from the other books. I don't know if the level of difficulty will be higher in the following chapters, but for the moment this is the feeling that I have. Even though the exercises are simple, they really helped me getting familiar with the usual examples such as the Dihedral groups, the Symmetric groups or simply the integers modulo n. In (classical) Analysis, we are already familiar with the main concepts of derivatives, integrals and functions through calculus. However, in Abstract Algebra, most of the main structures that serve as examples and motivations are new which makes these kind of exercises really helpful. I posted in the Textbook Solutions section of this website my current solutions to the exercises in the first chapters of the book.
Prerequisites
A clear prerequisite would be some familiarity with proofs techniques and some mathematical maturity. These can be aquired by reading the book A Transition to Advanced Mathematics. Even if the book introduces all the Number Theory you will ever need in its Preliminaries, I would highly recommend reading a textbook on Elementary Number Theory first. It would help motivate many concepts. The textbook Elementary Number Theory by David M. Burton is a very good book on that subject. Similarly, it can be useful to read a textbook focused on Linear Algebra first because the chapter on vector spaces only covers the bare minimum. The book Linear Algebra Done Right by Sheldon Axler is an excellent elementary textbook on the subject. Again, this is not essential but it would help.
Further Readings
I didn't finish the book yet so for the moment, I don't have any recommendations for further readings.