Math books: group theory and topology

[elivil]

Just want to ask for recommendations for good math books on

1) groups, modules, rings - all the basic algebra stuff but for a physicist

2) topological spaces, compactness, ...

I need books for a theoretical physicist to read up on these topics so that I could study, say, algebraic topology next. Now the books needn't be too basic but being a physicist I'm not a big fan of all the finite groups, pure math stuff, so the fewer examples with tiling and such the better.

Can anyone help? Math majors are more than welcome to comment.

 

[Chaostamer]

As a math major, I'd personally recommend the combination of Pinter's "A Book of Abstract Algebra" and Jacobson's "Basic Algebra I" for your algebra needs. Pinter is gentle and builds up motivation nicely (and is an overall pleasant read) while Jacobson develops the subject more rigorously and, in my opinion, more in-depth. In short, read Pinter for an overview and Jacobson for a thorough understanding. As a bonus, both are generally available for under $20.

As for Topology, I've had a decent time with Patty's "Foundations of Topology" alongside Kasriel's "Undergraduate Topology," but I think the standard recommendations are Munkres and Mendelson (which I also like, admittedly). I can't provide much help on the algebraic topology front, unfortunately.

 

[wisvuze]

I've also heard that the Pinter book is a good algebra book for non-pure math people. Dummit and Foote might also be good too.. I think. As for topology, I think "An Introduction to topology and analysis" by Simmons is really good. It's written for math students, but the exposition is very clear and conversational, it should be good for anyone

 

[brocks]

There actually is a book by Schwarz called "Topology for Physicists," but I have no idea how good it is.

 

[xristy]

I like Artin's Algebra very much for thorough coverage of the topics you mention at an upper division undergraduate level. Munkres Topology is at the same level for topology and includes a good introduction to algebraic topology.

 

[aalaniz]

In the post link below, I try to pull out the minimal set of math and physics ideas, backed up by the actual history, that underlie the knowledge needed to navigate from junior level math/physics through graduate school and beyond, including the current methods in theoretical physics.

[Included are texts/references on algebra, topology, geometory and topology for the theoretical physicist in an uploaded Word document].

I list and review a core set of the best, clearest books and literature to this end, often including what you should get from each book/article. I probably would have saved about a decade, and lots of money had I had a "syllabus" like this.

https://www.physicsforums.com/showthread.php?t=553988

Thanks,

A. Alaniz