I am a first year graduate student in applied math at a relatively good school here in the US. I'm looking to concentrate in something at the intersection of CS and Applied Math (quantum computing perhaps), but I've always been a sucker for pure mathematics, and I'm glad I'll have a chance to learn more if it here. I want to run by my approach on how I think of getting through the first few years:
I am someone who has somewhat broad interests and likes to study mathematics based of its physical applications. Therefore, I am keen during my time here in taking in as diverse areas as algebraic topology, computational geometry etc. I also think I'm sufficiently self-motivated to open up math books on my own and study from them. The problem I feel with me is that I think I'm all over the place, and as someone who isn't naturally talented in mathematics, I find it very hard to commit to memory a lot of things I learn. One thing I don't get at all about graduate school is why still have timed exams under stressful conditions. It seems the whole purpose of teaching math at school, college and university is to weed out the those who can't perform under pressure. No wonder we end up losing a lot of students along the way who don't wish to continue studying mathematics. And here I am someone who's also not naturally talented in math, but I am still trying to go through these stupid motions. Therefore, I've seen myself not being able to perform well in the timed exams here. I've done well on take home exams, and I wish there were more of these in graduate school, because the whole point of doing mathematics is not to be able to do it under a time pressure (sorry for this rant here; I feel very strongly about this issue). So my approach going forward is to try not to worry about my performance on timed exams. Rather focus on the learning outcomes and hope I am able to check off the relevant boxes (pass a written qual etc.) in a timely manner.
Does this approach sound all right going forward? Or do I need to change my way of thinking going forward and perhaps be a bit more focused etc?