I’ve been quite motivated to study harder lately, owing somewhat to a realization of just how little I know. I was recommended a rant video from a Korean online mathematics tutor on Youtube and he asked his senior high school students, “do you know why the sum of geometric series is one over r minus one?” It’s a simple equation, widely used in various applications, and one that has become ingrained in my memory at this point. Embarrassingly enough, I didn’t know how to derive it. I knew, and the tutor knew, that that means I didn’t really understand the equation. Of course, there are quite a few equations that are crammed out of my head, like all the variations of trigonometric identities and integration and differential formulas. The difference is that I could derive the latter by myself in a pinch, but not the geometric sum equation.
That stunned me and forced me to reflect upon my recent study habits. I’ve often come to default to Googling any facts or formulas that I forgot. Of these, how many could I have figured out on my own if I sat down and thought about it? How many homework questions were Googled in a hurry to turn them in on time, that would’ve been a valuable exercise to improve my skills? When was the last time, after I quit competitive mathematics, that I sat on a difficult problem for more than a day?
Here are, in no particular order, some topics that I am interested in learning in the future - let’s say, during my undergraduate years.
- Analysis of algorithms
- Computational theory (automata theory)
- Functional programming
- C programming
- Graphical application programming
- Computer networking
- Circuit analysis & network theory
- HSK6 level Chinese - the highest level of Chinese test for foreigners
- ToKL (Test of Korean Language) level Korean reading comprehension - ToKL is a Korean aptitude test aimed at adult native speakers
I’d wager that a simple mantra of “don’t look it up” (well, obviously until you’ve thought about it) could accelerate the deep understanding of quite a few of these subjects.