owlpride wrote:Are you good with combinatorics and modular arithmetic? If not, you should study those before you start thinking about algebra or topology.
As far as abstract algebra is concerned, I would focus on elementary group theory: basic properties, the isomorphism theorems and standard examples (finitely generated abelian groups, permutation groups, the dihedral group). That's not a lot of material but you want to understand it really really well. Artin is a great resource for this, but any other comprehensive algebra book should be fine too. (Why bother studying at all if you are not going to learn it well enough to use it on the GRE?)
You also want to know what rings and fields are, but you don't need to know much about them. I found that the GRE questions involving rings and fields could be answered straight from the definitions. (Though it might help to have a bit of practice proving simple statements about algebraic structures.)
I personally would not study topology for the GRE unless I had everything else down cold. Put your effort where you expect the highest pay-off per study time. Working through an entire topology book for 1-2 questions on the GRE is probably not a good use of your time.
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