Help me focus my study for the GRE math subject exam?

Question

I'm preparing for the GRE Math Subject test, but I'm at a bit of a disadvantage, having never taken an algebra class or a probability class. Obviously I'm not going to learn a semester of abstract algebra in 3 weeks, but I'm hoping I can at least learn the basic definitions and memorize some of the most important basic results from these two fields so I'm not batting zero on these questions. My question is: what results and definitions from a first semester of abstract algebra or probability theory would you say are indispensable? I wouldn't object to a similar list for basic real analysis, but I actually have a background here; I just don't have a sufficiently strong background that I can necessarily pick out which parts were essential and which were just curiosities along the way. Thanks!

Answer 1

The amount of knowledge needed from Abstract Algebra is extremely small for the GRE. I'd recommend learning the definitions of Groups, Rings, Fields, and permutations along with a few examples of each and you would probably be good with that. I cannot comment on the probability part.

Best of luck!