Math, MOOCs, and Miles(Re)discovering the magic of mathematical reasoning
Among undergraduates, mathematics is perhaps one of the University’s most polarizing subjects. For the quantitatively inclined, the rigors of mathematical reasoning provide both a fascinating challenge and an indispensable tool. To these students, numbers bring clarity — and a reward. Though the mechanics of calculation can prove difficult, the sense of accomplishment is well worth the struggle; few things are more satisfying than the feeling of achievement upon completing an arduous problem set.
To others, though, the specter of mathematics is far more frightening than it is inspiring, and many a humanities major has been known to avoid quantitative courses at all costs. For these students, high school math was more than enough. Here at Princeton, they’d rather spend their hours deciphering Adorno than proving theorems.
Yet even for the English major, the value of mathematics is hard to deny. After graduation, the quantitatively adept are in high demand. In our increasingly digital world, the ability to reason mathematically is useful in a seemingly endless range of contexts.
Personally, I’ve always been stuck between these positions. Though I fared well in math prior to Princeton, I’ve never enjoyed it enough to even vaguely entertain the notion of studying college-level mathematics.
Thankfully, Keith Devlin, a professor visiting from Stanford, is offering just the course for people like me. Welcome to Math 195: a class designed to teach the tools of mathematical reasoning without the attendant intricacies of advanced theoretical math. In our first class, Devlin tells us that the world is full of people who can do advanced mathematics competently and accurately. Far rarer, though, are those in the humanities and other non-STEM disciplines who can reason with the precision of mathematicians. It is at these kinds of intersections, where the rigor of mathematics is brought to bear on the challenges of other areas, where things get interesting.
Half a semester in, it’s been a whirlwind of discovery. Devlin is as engaging as they come: a former consultant for the CIA, a wildly popular guest on NPR, and a prolific author, he breaks from the stereotypical mold of the bookish academic. Classes are punctuated with anecdotes drawn from his decades of pedagogical experience. Over the course of his career, Devlin seems to have done mathematics in every context imaginable: government consulting, the private sector — even a popular television program. For us, a group of math students consisting almost entirely of non-quantitative majors, these creative applications of mathematical methods are a revelation. In one particularly striking lecture, Devlin tells us about a formula that’s been used to catch murderers. Hardly the dreadful stuff of 12th grade calculus.
Even more interesting, perhaps, is the way that the course has been delivered. Alongside our group of about 20 Princeton undergraduates, 30,000 others are simultaneously taking the course online. Introduction to Mathematical Thinking is offered as a MOOC, a massively open online course. Around the world, many, many others are learning about the issues that we grapple with in class. In fact, we watch the very same online lectures as every other student, and are graded on identical problem sets. What is different, though, is that we get the ‘VIP version’ of the course, so to speak. Alongside the online lectures, our class also benefits from three hours of in-person class time a week to ask Devlin questions and work together on the more challenging problems. Witnessing this against the backdrop of thousands of other students who would relish such an opportunity, every class feels like a luxury. It’s a sense of gratitude worth cultivating.
As we near the end of the semester, we are meant to be thinking about a final project. Fascinatingly, we’ve practically been given carte blanche — pick a subject we’re personally interested in, Devlin tells us, and he’ll help us find a mathematical angle to approach it from. As soon as I heard that, I knew exactly what I’d be writing. One of my more idiosyncratic passions is collecting credit card and airline miles, and figuring out how to best optimize my spending, booking my flights strategically, and signing up for new credit cards where lucrative bonuses beckon. Until now, my approach to all of this has largely been ramshackle. I usually meander around the Internet until I find a few opinions on which award schemes are superior to others. Confronted with dissenting opinions, I tend to go with what seems superficially most plausible. With this class, though, I’m excited to add a bit more rigor to what is admittedly a rather strange hobby.
Thankfully, Devlin is no point-neophyte himself, having flown more than 2 million miles on United, a landmark he hit during one of the first weeks of class. Having him advise my project then, seems particularly fitting.
Ultimately, this class has motivated a desire to dig deeper and go farther in the pursuit of mathematical knowledge. It’s a result I hardly ever thought would be possible in college, but an outcome, I think, worth being excited about.