Abstract Algebra Preparation 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.
 A: 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!
A: I would agree with the user that said to get several books. However, I’m not sure if I can say exactly about “how” to study for the class. I have asked several professors for advice, so I will say a few of what they said. One said to memorize as many proofs as you can. Another said to memorize proofs to the theorems and lemmas presented in the book, and another said to learn the “main idea” of each proof without worrying too much about the details. If anyone would like to give their way of studying courses such as these, that would be great, too. I feel as though you should be fine with your current background.
