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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.

Mr. Tea
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    Maybe you should review: https://math.stackexchange.com/questions/198373/choosing-an-abstract-algebra-text?rq=1 – Moo May 25 '17 at 12:58
  • @Moo, Thank you for your comment. I have already seen it. This is why I am leaning toward Herstein's book, because of it's great problem set. However, as I mentioned, some people mentioned it as not an insightful book. – Mr. Tea May 25 '17 at 13:23
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    So, why rely on any single book? Why not get that one, but also others that have simple problems (you mention two) and also another equivalent one with hard problems? Find used copies - which exist for many of these. – Moo May 25 '17 at 14:22
  • @Moo. I know that the ideal is to learn from a few books, and it is clear to me. But here, when it concerns purchasing a book, some people are quite limited with the number of books they can buy. – Mr. Tea May 25 '17 at 16:13
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    Personally I wouldn't recommend you any of those books. Instead I suggest you to take a look at Rotman's book and Dummit and Foote's book. – Xam May 25 '17 at 19:18
  • @Xam. Do you mean "Advanced Modern Algebra" or "A First Course..."? – Mr. Tea May 25 '17 at 20:58
  • @Mr.Tea I was referring to "Advanced Modern Algebra", more specifically the second edition. – Xam May 25 '17 at 21:25

3 Answers3

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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.

PeterJL
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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.

Hikaru
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  • Thanks for the answer. What do you think about Herstein's exposition? Unfortunately, I am allergic to monstrous textbooks with 900+ pages... – Mr. Tea May 25 '17 at 13:24
  • I really like Herstein's exposition. It could be a bit dry, but the proofs are very clear.If you have access to the book from a library, I would suggest you work through a few sections and see if you like it. – Hikaru May 25 '17 at 13:31
  • as I wrote in the beginning, I did visit the library and skimmed through, and I liked it, but unfortunately I also liked Pinter's book, which makes the decision harder. – Mr. Tea May 25 '17 at 16:17
  • I have only read through Pinter's book briefly, so i cannot comment on the book as a whole. But the exposition is much friendlier compared to Hersterin's from what i read. If you prefer the exposition of Pinter, you can maybe get Herstein's book from the library later and work through the problems. – Hikaru May 25 '17 at 17:14
  • Books over 900+ pages aren't bad perse. Actually these kind of books like D&F contain a lot of theory, examples and exercises. I mean you can study with these books not only basic abstract algebra, but also have the opportunity to study an introduction to homological/commutative algebra/representation theory, etc. – Xam May 25 '17 at 19:23
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    @Xam Thank you, I'll take a loot at Rotman's book. I thought that when concerning some specific topic, it would be better to use a book that is dedicated only to this subject, rather than going for a all-around book, isn't it the case? – Mr. Tea May 25 '17 at 23:43
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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.

Dragonite
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