On Math

tl;dr: Maybe we should teach math as math.

I sent out an email earlier this semester looking for students to join the graph theory research group. Joseph and I are both graduating in May, so we want to have some non-graduating students in the group next semester.

I got thirteen replies. From Olin students, I got thirteen replies. I've had two people later talk to me expressing interest.

We have both math and coding projects next semester, and a few people are definitely more interested in the programming side. While many others are interested in both and some of them might lean coding, part of what would make the project cool for them is that they think the math is exciting, as well. So essentially, I sent out an email asking if anyone wanted to do math research without many direct applications, and more than four percent of Olin said yes. (And we excluded the 25-30% of the school graduating in December or May as well as the tenth or so that will be abroad/on leave next semester!)

I know that's not a huge percentage of Olin, but that's fifteen non-seniors who would like to make room in their schedule to do mathematics, mathematics that might not get anywhere, mathematics for which we don't yet have answers, new mathematics. And that's enough to make me think, even more than I already did, that we do Oliners a disservice when we hide math away.

I'm not saying we shouldn't show math in its applications. We must do that. But we shouldn't eliminate mathematics as an art or science in favor of mathematics as a tool. There's a balance, and I see some classes -- even math classes -- at Olin moving more and more towards math as a tool only or as something to hide.

No.
Stop.

Look, I'm taking Nonlinear Dynamics and Chaos right now, and it's been a joy to see other people get to bend their minds around concepts like infinity and fractals, to see them think it's cool and exciting and weird, because it is. And it all has applications, which we're talking about, but even before we do, the math can stand on its own.

I took the Putnam math competition this weekend along with seven other Olin students. Eight of us devoted six hours to doing math for fun on Saturday. As we talked about solutions, though, over and over again I heard people say they didn't know linear algebra. That stings a little because Linearity I is the class meant to teach linear algebra, and it's been my class in many ways while I've been a student here. I'm going to NINJA it for the fourth time this spring. It has improved a lot over the past three years, but it's still not where it needs to be for people to actually feel like they know linear algebra.

Part of what I'm reacting to is an experimental course being offered for the next three years. It will be two semesters long, eight credits each semester, and is intended to cover the material of Linearity I & II (lin alg, ODEs, vector calc), Mechanics, and Dynamics or Signals and Systems. (Dynamics and SigSys are both linear systems courses, just for different majors.)  I know I shouldn't be as cynical about it as I am before the class has even begun, but I worry that in response to people not knowing theory or math, we're reacting by hiding the theory and math.

I shouldn't worry this soon. I should wait and see what The Experiment is like this year, and they're running it three times at least because they know they won't get it right the first time. (Note: I've been really happy with how upfront the teaching team has been about this class being an experiment.) But it seems like part of a trend of classes that just act as continuations of Modeling & Simulation, which very much hides away mathematical content. It's a modeling class, not a math class. I love modeling, and exposing people to more modeling is good, but you have to increase people's mathematical toolboxes in order for them to model more complicated systems in more accurate ways, and students need to understand those new tools.