I'm still in school and am just starting to get into more difficult math; right now I'm learning introductory odes, vector calculus, and introductory analysis. All three are really enjoyable, but in some ways vector calculus and differential equations feel like a review, in that the hardest part of each is just the calculus I've forgotten since Calculus I-III. I find analysis to be the most interesting course because of how novel it is. I remember at the start of the semester, it was so confusing; the concepts weren't difficult to grasp, but I just didn't understand why we were learning what we were learning, or what it had to do with calculus, for which we were supposedly trying to develop some theoretical foundation. But as the weeks went on, I began to appreciate the beauty of the subject, in small increments. I began to understand why the real numbers were constructed just so, and why we needed to understand ideas like compactness before we could talk about ideas like convergence.

One quote about analysis that I read online somewhere is that you should study it until it starts to feel "natural." At the time, I guess it sounded true, but I didn't appreciate what it actually meant. Now, I'm starting to.

It takes a lot of effort to digest each new lecture, but I'm excited to see what the rest of the course holds, and to graduate to "real analysis" afterwards.