Teaching probability

This semester I am teaching an undergraduate introductory class on probability. I don’t typically announce my courses here, but teaching probability is a special enough task to deserve mention -- for me at least.

As a high school student, I used to dread questions about blue, black and red balls drawn at random from an opaque box. The typical question went like this: if the first three balls are blue, what is the chance a black one will be next? The initial questions were innocuous enough, but they quickly got complicated. They also tested your ability to count – to figure the number of permutations or combinations, without which you couldn't answer. At the incredibly difficult mathematics examination for admission to the prestigious Indian Institutes of Technology (IITs), there were quite a few of these counting questions. Let’s just say that I did not even attempt them.

College contributed nothing to my knowledge about probability (college, to be frank, was a four year vacation and I have no regrets). It was only during graduate school, where I took a number of statistics courses, that I was introduced to the mathematics of randomness. And over the last few years, much of my research has involved probability models – some very sophisticated ones at that, thanks to my colleagues who have majors in math and physics. Even now, my early lack of aptitude for the field and poor undergraduate training comes back to haunt me.

But there’s no better way to drive insecurities away than by teaching. The cliché that the best way to learn is to teach is very, very true. Which is why I am excited about my class this semester. The material itself is not difficult, since it’s an undergraduate class. But even the simplest topics in probability can cause confusion; and what better way to tackle them than at the foundational level.

Last week, I went to check my classroom. It was late in the afternoon and the campus was empty. The classroom was in the Chemistry building, and had tiered, auditorium style seating; the seats were bright red. It was a grand setting, and I could imagine it bustling with sophomore year students -- there are ninety students enrolled at this time. And for the first time I’ll be using what is called the PRS clicker system: I will ask students multiple choice questions during each lecture. Students will choose what they think is the right answer on their personal clickers (they’ll press a button, in other words). A slide will immediately display how many clicked each option, as in a game show. Wouldn’t it be fascinating to have this type of instant interaction – and, importantly, feedback on how well the class is understanding the material – especially in a class about probability, as slippery a topic as any in the whole of mathematics?

Fancy embellishments aside, the real grandness of probability lies in its elusive, mysterious quality. Everything we do in life is governed by chance. Our instinct toward religion partly stems from the uncertainty that always seems to stalk our futures. The theory of probability lends mathematical formalism to uncertainty. But it also makes us think of some very vexing questions: What does it mean when we say things are truly random? Why do things turn out the way they do?

That’s the charm of it: it’s more philosophy than mathematics.