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There is definitely a big jump between the standard undergraduate curriculum and the standard graduate curriculum.
I don't think there's any way around that, but the interesting thing that I found out over the last couple years was
that you really have a lot of opportunities to explore graduate materials as an undergraduate. And to a lesser extent,
but still significantly, you can also go back and cover undergraduate topics which you may have missed as a graduate student.
So I think this applies equally as well to both research and to pure academic study so long as you're keeping your eyes open for that sort of thing.
Especially as an undergraduate looking forward, if your labs or your classes refer to some advanced topic, even in passing,
and they usually won't test this on an exam or necessarily make it coursework. There are usually a lot of clues you can watch for and again,
you know compare notes with your peers and your instructors and your lab directors and what have you,
but there are usually lots of opportunities both to test the waters before you begin in earnest and to go back to fill in the gaps after the fact,
so long as you're aware of those resources and make some use of them, the transition really seems to take care of itself in a lot of ways.
There are still a lot of challenges but you find yourself with most of the resources you need to meet them.
Once I actually got to the graduate program I actually found that the same courses and meetings and again study materials,
all the references that I had been suspecting might be important in making the transition - it turns out they all paid off for the most part.
While I was a little bit paralyzed as an undergraduate, and quite convinced, because I was already seeing a lot of the graduate materials
that I knew I was going to be studying and I hadn't really made the transition to research quite yet, that takes a little bit longer in a math program.
I was quite worried as an undergraduate, knew what the topics were but by the time I got to the graduate program, even though
there are still a lot of bridges I need to cross, I'm quite comfortable that I have everything I need.