Question Regarding Purchasing an Algebra Book

Question

I am a math undergraduate major and just finished my first abstract algebra course. Unfortunately, we used the lecturer's notes which are quite dry, without motivation, and it really felt bad. I am really interested in abstract algebra, and thus has decided to re-learn it over the summer. After a long research over the internet, I have seen that both Herstein's topics and Pinter's book are well regarded and highly recommended.

But now I have some difficulties to decide which one I should purchase.

My concerns about Herstein's: I have read that it (a) does not give insights on the subjects(which sounds weird - how can it become a classic if it is not that good?) and (b) as he writes in the preface that some of the problem are not meant to be solved but rather just to tackle, which sounds a bit odd.

My concerns about Pinter's: in the MAA review, they say that the problems are not challenging, and I am not sure if it is at the same level as Herstein's.

My purpose is to continue with abstract algebra. So this course will not be my last one, and therefore I want to really understand what is going on.

I checked them both at the library, and both are wonderful books(and also D&F). I also checked Artin's, Jacobson's, Van Der Waerden but didn't like them very much.

I will be grateful for any advice and/or recommendations.

(Sorry about my English, I am not a native speaker).

Thank you.

Answer 1

Herstein's book has a few exercises which can be pretty hard. Also, every now and then you encounter some exercises which require concepts and ideas from a later section. From what i remember, in the preface he means that the reader may not be able to solve these exercises easily because they are meant to serve as a motivation for those topics which are yet to come. In my opinion, Herstein's book may not be comprehensive but is worth the look for its exercises. D&F is also a good book and maybe you can use it in conjunction with Herstein's book.

Answer 2

Pinter is a great introduction, I read it before taking my first course in abstract algebra and constantly referred to it while in the course for a better understanding of material. Dummit and Foote is great for problem sets and the standard for undergraduate abstract algebra. I would probably do a healthy balance between these two.

Answer 3

In terms of developing intuition, I'd think that either Fraleigh's or Gallian's book would be nice. Herstein is a classic, but definitely feels dated (and a bit dry) to me. Dummit and Foote is a favorite of mine, but its sheer size can be overwhelming. Are you looking for a book that will provide intuition and extend your knowledge beyond the typical undergraduate level? Or are you mostly interested in building an intuition for the basics? If the former, I'd go with Dummit and Foote. If the latter, I'd use Fraleigh or Gallian.