For background, I'm a first year PhD student in a mathematics program. Basically, I can't tell if I'm "where I should be".
As an undergrad, I read before class and lecture felt like a nice review. As a grad student, I can read before class, spend an hour or two pouring over a few pages, understanding every sentence, and the professor will breeze over it in 10 minutes. If I don't prepare, I'll be left in the dust, totally lost. Or, he will cover material with so few details it's hard to tell if I understand anything at all. Talking to classmates, I'm not unusual, but I find this very stressful because it's consistent and I'm not used to it. If it's typical to get lost and not understand the lecture, how can I tell if I understand anything at all? Is this just standard?
Reading papers or attending talks is worse. I feel like I get things only at 'handwavey' level, without details or subtlety. I know this is normal so I don't stress much, but some day I will have to be giving talks, writing papers. How can I get there if without a firm basis?
I think my fear is that I could be learning the absolute minimum and barely skating by -- which will bite me when it comes time to take prelims/do my own research -- or I could be doing perfectly fine and just stressing myself out. My question is, how can I tell? How can I gauge if I'm making typical or appropriate progress?
My grades and homework are good, but this seems meaningless. I always receive full marks, even when I find errors in my own work later, and work comes back with no comments. Talking with peers helps a lot, but is hard with distance learning. Asking a professor directly seems like it would be awkward and unprofessional, and also how could they know? They don't grade the homework and we speak for maybe 20 minutes in office hours occasionally. What else could I consider?
I've also read this post, which is relevant, but the answers are directed at the research stage of the PhD. I'm still taking courses, etc. I've also read posts on imposter syndrome and I feel like my issue is distinct. It's not that I feel like an imposter, but more that I feel like I'm untethered and in la la land as Dan writes. I'm interested in ways to feel more tethered, and in understanding how common/typical this untethered feeling is so it doesn't stress me out as much.