Any good book to review abstract algebra?

[PieceOfPi]

Hi,

I am a junior and a math major, and I am almost done with my year-long abstract algebra sequence for undergraduates. While I found the materials interesting, I feel like I got lost at some places in this course, and I would like to review (or in some topics, relearn) the materials that I covered in this course over this summer. The textbook we used in this course was Abstract Algebra by Beachy/Blair, and topics we covered in this class include basics of groups, rings, fields, more on groups (including Sylow's theorem, solvable groups, etc.), and Galois Theory. I was wondering if there is another book that I might want to check out from the library to read over the summer to understand the materials better. I would also like to focus on becoming a better "problem solver," as I feel like this is a skill that I need to improve ASAP, so I am looking for a book with good exercises and/or interesting examples as well.

Let me know if you have any suggestion. Thanks.

 

[VeeEight]

Dummit and Foote is a superb reference for Abstract Algebra. Additionally, Ian Stewart's Galois Theory is a great read.

 

[Landau]

Depends on what you mean by review. Dummit and Foote is ok, but is probably a bit longwinded if you already know all the stuff. In your position, I would prefer a book which takes a somewhat different, advanced perspective, to place the things you know in context and look at the bigger picture. Now, Lang's Algebra may be a bit too much (i.e. little review, lots of new stuff), but one of my favorites which fills this purpose perfectly is Knapp's Basic Algebra.

 

[PieceOfPi]

Sounds good. I will be checking out Dummit/Foote from the library soon. Somehow, my library system didn't have Knapp's Basic Algebra at convenient location, but I will try and get that too (Knapp's sounds interesting, as it seems to use a lot of linear algebra in his discussion). I'll take a look at Stewart too.

Thanks! And any other suggestion would be appreciated.

 

[rezeew]

Dear junior math major,

It's great to hear that you are interested in reviewing and improving your understanding of abstract algebra over the summer. I highly recommend "Abstract Algebra" by David S. Dummit and Richard M. Foote. This book covers all the topics you mentioned in your course, and it has a reputation for being a comprehensive and rigorous text on the subject. It also includes challenging exercises and interesting examples to help develop your problem-solving skills.

Another highly recommended book is "A Book of Abstract Algebra" by Charles C. Pinter. This book is known for its clear and concise explanations, making it a great choice for self-study. It also has a wide range of exercises and examples to aid in your understanding of the material.

I also suggest checking out "Algebra: Chapter 0" by Paolo Aluffi. This book takes a more abstract approach to the subject, which may be beneficial for your understanding of the underlying concepts. It also has numerous exercises and examples to help develop problem-solving skills.

I hope these suggestions are helpful in your search for a good book to review abstract algebra. Best of luck in your studies!

Sincerely,