Last week, I started my second year of graduate school. It feels so very different from my first year - really almost astonishingly so.
I spent the entire summer studying for my qualifying exam in real analysis. I wrote over 300 pages of notes, by hand, working through proofs and ideas, some over and over again. I worked about 2-4 hours pretty much every single weekday, and many weekend days, for all but about 2 weeks of the summer. (I also tutored students in the math lab.)
Even though that may not seem like a huge amount of time to spend (because it wasn't), it was huge for me. I've historically been terrible at making myself work to a far-off deadline, and this work was both hard and sort of ambiguous. How much would be enough? Was it even possible for me to pass (like, ever)? Had others passed these exams in the past only because they were smarter than I am, or had better memories? I struggled with these thoughts a lot, but I kept working.
The qual was an 8-hour exam. It took me 6 hours and 40 minutes, which is somewhere in the typical range. And I passed. I passed it. Amazing.
Now that I've passed it, the material doesn't actually seem like it was that big of a deal. Now that I know the proofs, they don't seem to have all that much to them. Ha.
I also, of course, made it through my first year of classes last year. I struggled with the material a lot at times, but I did well in terms of grades. I didn't seriously screw anything up. I was never one of the worst students. Occasionally I was mildly praised.
Last year, when I started grad school, I was extremely enthusiastic, and then when it got hard, I was really scared a lot. Especially that first semester I had really dramatic mood swings. I sometimes fantasized about leaving, going back to my old job, resuming a better life with more money and things and free time and less failure and stress.
This year, honestly, I wasn't that enthusiastic at the start of school. When I went to the mandatory all-TA/TF meeting, I remembered how exciting it had been the previous year, but I was pretty meh about it. I was mildly interested in meeting the new first-years, but that was about it. I was still recovering from the qual.
But...I'm not scared anymore, either. I still don't know if I can actually do research, but I now know I can pass classes and quals. (I need to pass one more qual, and I have four tries.) I now know I am not borderline for the program, barely clinging to life.
Last year, I remember the first homework that I got with a problem I couldn't easily figure out. It really freaked me out. I'm pretty sure I cried. I calculated what percentage of my grade this one problem would be and thought about the fact that I was already losing that much so early in the term. I wondered whether I belonged here. I did eventually solve the problem, but man, the stress.
Last week, my topology homework had a problem I couldn't figure out. I worked on it on a few different days, but never with any real feeling of stress. I figured out all of the other problems. This one remaining one wasn't a big deal. Turning it in unfinished would not harm my grade or standing or anything like that. I wanted to get it but there was no fear there. It certainly did not drive me to tears.
And that, my friends, is the difference that a year makes.