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.
Thanks for the response.
That (in bold) is exactly the reason I want to read beyond what it is presented in Princeton book.
I was pretty good with calculus, and decent with combinatorics & modular arithmetic (JEE level (assuming you are Indian), and whatever is taught in first year Maths courses in Engineering). But I have been out of touch of maths for very long time, and studying specifically for GRE-Maths.
I understood the definitions of Groups (Abelian etc.), fields, rings and other stuff mentioned in Princeton book. However, I have this habit of going a bit deep into the topic - so that I can understand the how this knowledge is used in real life ( and/or analysis, problems).
E.g. Even if I am out of touch with Calculus, it took me only single reading to recall how it is used, in real world or theoretical problems. However, when it comes to Abstract Algebra, I am still struggling to use it to solve problems.
So, I picked this Artin book, but it seems too big, and as you said perhaps not an intelligent investment of time with goal of solving GRE problems. So, I am looking for some material that can be done within 10-15 days.
Also, your point is well taken on Topology. I was under the impression that there might be 4-5 question on that topic, so thought perhaps I can tackle the easy ones.