As for study hints: the way I studied was by "collecting results" -- basically get an overview of the material one thinks one could ideally/realistically hope to be responsible for in all 6 = 5+1 areas. Actually I subdivided my specials into 3 areas so I was collecting results from 8 = 5 + 3 areas. Then I systematically covered those areas, mostly getting theorems and their proofs down. Then I tried to review those results as often as possible. Here's what I would do differently: I would break down the terrain as mentioned, but I would, for all but the most central results, forgo the learning of the proof in favor of trying to come up with the simplest possible example or application of the theorem. My panel didn't ask me to prove anything, but they did ask me to apply many theorems in dimension 2, or with a state space of 3 states, etc. They wanted to observe intuition about what the results *meant*, and to do so they seem to ask very simple questions that one hasn't thought of. Trying to ask oneself simple questions about the results is, I think, the best way to prepare for that.