First Day

It’s the perfect day.  Pleasantly warm, comfortably dry. The students are back, scurrying about campus looking for their classrooms; rested, happy, excited, expectant. Lots of skimpy shorts and tight-fitting t-shirts (they clearly had a fun summer), so the professors are in a good mood, too. Sure, it is mildly annoying to get to the campus at 9 and have to look for a spot on the staff lot (must be the graduate students), or to deal with long waits at the coffee shop. But it’s good to see them back, they’re our raison d’etre, after all. Not to mention that some of that sexual energy can’t help but radiate to the environment.

I love the first day of classes. I’ve written my syllabi, posted them on the web site. I checked that my textbooks are already at the bookstore (not always the case). I’ve written down notes for my first few lectures. Not too detailed—you have to leave room for spontaneity in the delivery; just enough to give the impression of flowing naturally, without embarrassing moments of hesitation. I rarely have to look at my notes, and students are strangely impressed by that. I’ve secured a set of brand new markers (hate the damn glass boards). About ten minutes before class starts, I close the laptop to collect my thoughts. This will be the term when I’ll be less professorial and more ``approachable”; when I’ll just talk to them, and they’ll respond as curious students of the Academy.  Shouldn’t be hard, it’s a small class.  Fortified by optimistic thoughts, I walk into the classroom two minutes early…

And sitting there are six students; another walks in a moment later. I wonder if my face betrays my feelings, and just in case, I casually move to the business at hand. I introduce myself, and using the online roster (they look like their pictures) try to learn their names.  I knew the enrollment was nine, so seven on the first day is not unreasonable. Still, it is hard not to be taken aback by the reality of it. Mind you, this is not a graduate seminar. It is “Introduction to Advanced Mathematics”, meant for sophomores and juniors who want to learn any math beyond Calculus; our “proofs course”.  I taught it last fall to a class of twenty-four, and it went well. There are two other sections of the course this fall, and both are full, with enrollments of thirty.

I can only conjecture as to the reason, and it goes like this. The science-motivated math majors take the honors section. The other sections are populated by teaching-oriented majors, computer science majors, and engineers for whom this class is a requirement. In practice, most are seniors, trying to clear this last, pesky obstacle to graduation. For somebody like that, the guy with a reputation like “you learn a lot, and he’s friendly; but he expects you to work really hard” would hardly be a first choice. Better take the section where you can reliably expect a B for going through the motions. Math isn’t their interest, after all; so one can’t blame them for optimizing their use of time. Now, the natural question is: why do these majors require students to take the “proofs course” designed for mathematicians? It makes no sense, but that will be for a future post. Today I’m teaching.

And it goes well. I’m not doing anything hard: logical connectives, truth tables, equivalent propositional forms, tautologies.  I tell them about Godel’s Incompleteness Theorem, twin primes, and the conjectures of Goldbach, Catalan, and Collatz. (All this to illustrate the difference between “truth” and “provability”).  To another audience this might seem mysterious, intriguing, or fascinating. Maybe to some of these students, too. But surely some of the engineers are thinking “and this is good for…?”  And they don’t ask, unfortunately.  But I did point out that the text includes discussions of Turing machines, P vs. NP and RSA cryptography. (Some of them have heard about those, so maybe I have a `hook’ there to draw them in.)  They all seem engaged (it’s a small room), sometimes nodding or smiling. I ask them to work on a problem on the spot, and they do it. I ask questions, and get intelligent answers. It’s a good start.

I always get a `high’ from teaching, and it can take half an hour or more to `come down’ enough to be able to think about anything else. Knowing this, I walk out of the building, into the beautiful sunny day and the scurrying half-dressed students, headed for the coffee line.