As it turns out, not all of my readers are on quora. So because of this and in the spirit of posting non-technical blogs too, I'm reposting an answer I gave to the question there: "What is it like to study mathematics at Saint Petersburg State University?"
I have studied math and other subjects (like physics, computer science and others) during 2002-2005 in Saint Petersburg State University (SPbU) for a Specialist program (comparable to that of Master's degree).
My experience was constantly comparative in the beginning: as I was advancing further into teaching style of SPbU professors and docents I was viewing it side by side with the style of another State University of my home city (10x smaller in population than Saint Petersburg that time).
So perhaps I can approach answering your question from the perspective of comparison.
1. (a) In my home university we were taught to learn long theorem proofs in the fashion that would enable a student to easily reproduce it on an (pre-)exam. I remember only one occasion, when a theorem was so long that learning all the low-level details was impossible (despite how many days I tried), therefore really deriving the proof was the only option. Of course you would learn the fundamental constructs and apparatus for deriving the proof, that is you wouldn't be doing it completely from scratch and finding your ways into it.
(b) In SPbU, in contrast, you wouldn't be expected to learn the entire theorem proof at all, but instead be ready to derive it. Some of the practical tasks given along the theoretical proofs would require the same: derive a solution as you go. This was the first thing that struck me as largely different.
2. (a) In my home university I was expected to learn about 80% of definitions, theorem formulations, their proofs.
(b) It was my first exam on Control Theory in SPbU where its professor told me, a student should learn about 35% (or even less): the _most_ important theorem formulations and their proofs plus the _most_ important definitions. The rest is derivable as explained in (1) (b)
3. (a) The highlight of fun part of studying in my home university that comes to mind was that once a professor of mathematical analysis came to the class and asked: "Do you want theory and tasks today or talk about life?" "Life" was the answer, and the first question from the audience was: "Girls of which country were the most beautiful?".
(b) In SPbU there have been all sorts of surprises that opened student's mind or made studying more fun. One example: during one of the exams on electrodynamics (complex theory with integral calculus, Lie algebra and so on), a professor said 10 minutes past the start: "The ones who would like to get C mark (3 or "satisfactory" in Russia)" can get it right now without answering their questions. Few people rushed towards him and exited the exam room. About 10 mins later he continued: "The ones who would like to get B mark (4 or "good" in Russia)" can get it now, but you have to show me, what you have written. Some more people rushed towards him. 15 min later (and a few drops of sweat on our brave necks) he said: "The rest just get A's, because you have survived and didn't know in advance what to expect. " (5 or "excellent", the best mark). What I have learnt was that it is not always necessary to be an egg head and learn everything to be always ready to stand up. Sometimes it is important to be a good person, brave and keep courage in your heart. That may lead to more adventures and opportunities in the future!
With a few exceptions I would say, that studying math was both fun and rather instructive in that, it developed some fundamental skills of reasoning and attacking a problem at hand without having trained yourself specifically to solve that class of problems before -- what you need in real life, be it further PhD studies or solving other complex problems, including those occurring in life.