I'm going to be taking Abstract Algebra this upcoming semester, and am hoping to spend the next few weeks preparing for the class. I was hoping that people who have taken the course could provide some insights on how I might go about preparing for it. I have a bit of a background in proofs, having taken two courses, most recently Discrete Math, where the last few weeks were spent on group theory, modular arithmetic, and some other concepts that I believe are fairly important in abstract algebra (also quite a bit of combinatorics, though I don't believe these are covered.)
My question is: how might I prepare? Should I read an abstract algebra text outright and try to always stay a week or two ahead of the instructor, or would I be better suited reviewing, say, relevant linear algebra and/or studying up on real analysis, via perhaps Ross's textbook (which seems perfect given my current background).
I'd appreciate any helpful comments. Thanks in advance.
You definitely won't need real analysis. A good introductory book for Abs. Alg is the one by Gallian. I always buy several books on a given subject anyways as sometimes where one of them is weak on a point the other one is strong. Algebra by Mark Sepanski I can recommend as well (In fact I edited this book). Really you need to refamilarize yourself with equivalence relations, modular arithmetic, proof methodology, bijections/injections/surjections,divisibility etc. Basically the discrete math stuff.
Note you could be fine without this as the beginning of the course tends to be a review of discrete math anyways. The most important to review would probably be modular arithmetic.
I wouldn't stress over it too much. There's a lot of really fancy jargon but really its not that hard. If you did fine in real analysis then algebra should be well within your intellectual grasp. It's actually a lot of fun!