*Bits, ink, particles, and words.*

When you’re trying to solve a simple algebraic expression like $ab = 5b$ for the variable $a$, it quickly becomes second-nature to divide both sides of the equation by $b$, yielding $a = 5$. This makes complete sense, and it’s what most people would do right off, without even thinking. I mean, look at both sides of that equation! If there’s a $b$ on both sides, then the other value on each side of the equation should be equal to each other, giving us $a = 5$.

As a student in both mathematics and physics, I often see the differences in mindset between the two fields, and how these mindsets change the way classes are taught. The former is usually about structure and patters, while the latter is about modeling the world using mathematics. The problem is that belonging only in the camp of physics seems to be a dangerous thing to do, in terms of building one’s foundational understanding.

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.