Recently I’ve been doing a lot of relatively advanced mathematics. Since most kids are off from school, I don’t have much work. In many ways this is a blessing; while I love tutoring, it has become exhausting in recent weeks. I’ve needed a break for a while now, and those last few days were becoming rather desperate. I had one session today, which was actually pretty nice and felt highly productive. I think that’s another thing; I need to take breaks every once in a while to do my job well. If I don’t, I end up burning out, and tutoring feels like a chore and I just want to get through the hour. But today felt useful, and it was kind of just nice to talk about math to someone for a little while.
Math is usually this kind of solitary thing, where you don’t really communicate with too many people. I mean, I spend a lot of time online searching forums and watching YouTube videos for information, but I never talk to anyone about more advanced topics. I think this is a temporary state, and will change as I move forward. It’s also a matter of confidence to a certain degree. I know that I’m learning a lot, but I still feel like a baby in this world. Some things that I really struggled with a few months or weeks ago are now starting to make a lot of sense, which is a great achievement for me. I’m also spending so much time each day working on these ideas that I think I’m going to progress very quickly. So perhaps in the near future I’ll summon the confidence to reach out to those as passionate as I am.
I’ve been spending a lot of time working through Maxwell Rosenlichts Introduction to Analysis and Theodore Gamelin’s Introduction to Topology books recently. While I did take a real analysis course back in college, I don’t really remember any of it. All this information feels to me either brand new or vaguely familiar. Even worse, I never took a topology class, so all of that subject is pretty much new to me. That being said, since analysis and topology are extremely similar topics, there is a lot of the same information in both, just phrased differently. Having received the topology book for Christmas, I’m only in the early pages of it, but the entire first chapter is on metric spaces, which is my current chapter 3 subject in Introduction to Analysis.
I’m enjoying both books a lot. Math is such a fun, freeing, joyful subject. There is so much to understand and explore, and the feeling you get from really understanding a topic, or even just pushing the boundaries of your own comprehension is really wonderful in my view. I do wish I had more people to share that with.
I haven’t uploaded here in a while because in all honesty I’m a bit lazy when it comes to journaling. I would rather just be working. On that front, I was overzealous as always, and felt I could get a lot more done than I reasonably could. I’m currently working on problem 19 of my analysis textbook in chapter 3, so I’m getting there. I did a few today, but a lot of my time was spent scratching my head and being acutely uncertain. My LaTeX document is getting excessively long now, nearing 45 pages, and I figure it’ll likely make 100 before I’m done. More realistically, 150. As far as a timeline goes, I anticipate the rest of the problems will take me through to the summer, especially with my time being split between analysis, topology, and tutoring.
Anyways, I’m going to return to work now for a while. See you later.
Tommy Benjamin 