How to prepare for the Quals in Math early on?

Question

I'll be starting graduate school in mathematics this fall. Obviously what worries me are the qualifying exams. What is the best way for me to prepare myself in these subjects from now on? I'm kind of undecided whether to do all the solutions of past qualifiers from my institution (and other institutions) so early on, or whether to save them for later and practice them as a mock. Do you think that rehearsing with past exams in mock form (i.e., as in exam conditions) is better than just going for a long time to solve all the problems from all the exams? I understand that this should be accompanied by solving other book exercises or understanding the important theorems well. I am mainly talking about algebra, topology, and real analysis.

So in my situation would you start doing those exams while starting classes or do something else?

I just want different perspectives.

Thanks in advance.

Answer 1

My experience is old, but it is that there are specific advanced courses intended to prepare you for them. Take those courses, or, in any case, an advanced course in the subject of each exam shortly prior to the exam if possible. Ask a lot of questions. Do a lot of exercises.

Many places will provide old exams for you to study from. Do that if possible and create (not read) adequate answers for the questions. If you can't then get some help in improving your insight.

It isn't rare to have much better insight in some fields than in others. Deal with that.

An, for 24 hours before any exam, do something different and get a lot of sleep that night. Aerobics is good the day before. Cramming is terrible.

Answer 2

Everyone studies differently, but for whatever it's worth:

1. Save your practice problems until after you've finished the corresponding courses. You probably won't have the background to answer the questions before then anyway.
2. If you only have old exams, I'd choose some percentage between 50-80% of them. Use that percentage for "slow practice", simply working through the problems until you're extremely certain that you've written up good responses. Then use the remaining exams as mocks.
3. You may also include a list of major theorems and definitions in your study rotation and make sure you can write those down pretty much from memory.