In most cases it makes sense to pick the supervisor and then go wherever he is, rather than picking the university. I've heard people say that the relationship a student has with his supervisor is the second most important one in his life, after the relationship he has with his spouse; I've also heard people dispute this and argue that the supervisor is more important.
Of course, in order to be in a position to pick a good supervisor, you need to make yourself attractive. Do research; publish papers; go to conferences and present your work there; talk to other people in your field. Faculty are always looking for more good graduate students, and meeting them at conferences will give you a chance to figure out if you get on well with them at a personal level.
That said, I did almost none of the above -- but I was a special case, in that I didn't particularly need any supervision (I'm pretty certain that I literally saw my supervisor less than two dozen times while I was a graduate student, and interacted far fewer times than that).
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Does anyone have any tips for applying to Berkeley or Stanford's mathematics program?
Win the Putnam. :-)
I already have my first bachelor's degree, therefore, I cannot take the exam.
Any other tips?
In most cases it makes sense to pick the supervisor and then go wherever he is, rather than picking the university. I've heard people say that the relationship a student has with his supervisor is the second most important one in his life, after the relationship he has with his spouse; I've also heard people dispute this and argue that the supervisor is more important.
Of course, in order to be in a position to pick a good supervisor, you need to make yourself attractive. Do research; publish papers; go to conferences and present your work there; talk to other people in your field. Faculty are always looking for more good graduate students, and meeting them at conferences will give you a chance to figure out if you get on well with them at a personal level.
That said, I did almost none of the above -- but I was a special case, in that I didn't particularly need any supervision (I'm pretty certain that I literally saw my supervisor less than two dozen times while I was a graduate student, and interacted far fewer times than that).