I’ve taught for several semesters in Berkeley now, and I think it’s high time I wrote some thoughts down before my knowledge on teaching fades away.¹ So here’s a collection of thoughts: we begin with a light theory of how people acquire knowledge through inquiry, followed by a quick meta-analysis of learning to learn, ending with teaching.

My initial motivation to learn Computer Science came from doing side projects. It was through doing these projects that I realized how little I knew and how much there was left to learn (and how much there would always be to learn!). Sometime in the past year, I’ve come to realize that the bulk of my time has shifted from doing these side projects to laboring away on problem sets. This is not intrinsically a bad thing! However, as the classes become more and more advanced, the theory I’m learning has become more and more disconnected from the practical usefulness I wanted to get out of college. As a result, I’ve been losing motivation to learn concepts.

“If I may ask, where are you planning to work at full-time? Is it for evil or for good?”

The more classes I take in probability, the more I realize how often my intuition breaks for these problems, especially when the Exponential distribution is involved. Today I’ll be explaining a homework problem for Stat150 (Stochastic Processes) showcasing unintuitive behavior regarding exponential distributions. Furthermore, I’ll also show a simulation that backs up these results, along with the code used to generate the simulation.

Many things in life don’t have a clear estimate at a first glance – many times, 10% will seem like an underestimate, and 100% will seem like an overestimate. In these situations, I’ve learned that it’s actually pretty good to take the geometric mean of the two as a ballpark estimate: ~30%, or roughly something like 1/4 ~ 1/3.