Elements of Abstract Algebra

I recommend this book for all who are taking undergraduate Abstract Algebra. The book gives clear explanation of most of the concepts taught in class. Another great thing about this book is that it includes definitions and explanations of terms that are usually not discussed in class. This is a must have for math majors!

I'm a math undergrad, and we're using this as our class text. While some of the criticizms in other reviews are true, Clark's treatment of algebra is thourough, rigourous, and full of many details that other books leave out. While it's true that this is a very concise text, I've found that Elements of Abstract Algebra offers deeper, richer insight into the topics it covers when compared to other intro books. As an example - cosets. Many other texts completely leave out the fundamental concept of cosets: they are congruence classes modulo a subgroup. In at least three other intro texts I've looked at, the left coset of a subroup was simply defined as gH = {gh | h an elt of H}. While this is true and easier to cope with at first, Clark offers full discussion and suggests where the reader needs to fill in the gaps with proof. For at least the first two chapters, the reader may want to consider supplementing this book with another, simpler book like Maxfield's "Abstract Algebra and Solutions by Radicals" (another great book). However, any beginner with enough time and discipline will find Clark's book to be a thorough and enlightening introduction.

This is a book whose level is between an undergraduate (e.g. Herstein) and a graduate algebra book (e.g. Hungerford,Jacobson). I am a graduate student and I used it for a quick review and i really liked it. It is a little book of 200 pages. One interesting feature is that it first covers field & Galois theory and then ring theory.Contents (w.o. subsections):1. Set Theory2. Group Theory3. Field Theory4. Galois Theory5. Ring Theory6. Classical Ideal Theory.One thing I also liked is that the exercised are scattered throughout the text rather then collected at the chapter ends. You read something and immediately work on a couple (or more) of questions. You understand at the spot rather than waiting the chapter end.

This book is certainly not for everyone. If you prefer a book where you are held by the hand through the material, where you are fed the interpretation, and where all of the work is done for you then do not buy this book. This book is for people who not only want to memorize facts about algebra, but also want to learn to do algebra. The only way to learn to do algebra (or anything else for that matter) is to do it. For example, the first section is (reasonably enough) on sets and has nine subsections. Within these nine sections you are expected to perform nine tasks. This is done in three and a half pages. The section on symmetric groups has ten sections and eighteen tasks in eight pages. This averages to a fraction more than three tasks per page for a 196 page book. This is a lot of problems to work through! It is not so many that the task is impossible in a reasonable period of time. Will you solve every problem the first time? No. Many of these are quite challenging. If you at least study each problem and spend at least five minutes trying to understand it, by the time you are done with the book you will have a good understanding of abstract algebra, and you will be prepared to grapple with more elegant treatments of the subject.

I used the previous version of this book while I was a mathematics graduate student at Duke University in 1982. I have never seen a better book for LEARNING field and Galois theory; however, this book is not intended as a reference source. The exercises lead one incrementally through the theory, and this is certainly the best way to learn abstract algebra. I lost my copy of the previous version, but have replaced it with the new one - to have a copy to lend to my own graduate students who want to learn this material.