I’ve been thinking a lot about where one finds joy in a subject, and how the goal of educators should be to create situations in which this is most likely to happen. In particular, I’ve been reflecting on the way this is achieved in specific subjects during the likes of one’s elementary and secondary education, before choosing a career path to embark on. My question is simple. Are we doing all we can to deliver delight to students? Like always, I want to focus on my particular interests, which encompasses science and mathematics.

As I take my first quantum mechanics class, I’ve come to find that integrating probability density functions are a pain. From only a few problems I’ve worked on, the integrals are long and tedious to do. If there’s a single theme present in these integrals, it’s the strategy of integrating by parts. However, I wanted to show a specific integration today, because it’s quite ingenious and allows one to integrate a function that would otherwise be very difficult.

Despite what many schools actually do, I think most of us can agree that learning is highly personal. What works for you might not work for me, and there’s nothing wrong with that. Thankfully, there’s more than one way to learn a subject.

One aspect of probability I’ve always found to be a little tricky is the part where you need to count things. In theory, this sounds easy enough. After all, it’s just looking at the complete list of things you’re studying, and enumerating them, right?