Aaron Hoffman’s office is sparse but lived-in, with a few chalk and crayons drawings on the wall, courtesy of his young daughter. The bookshelf is full of mathematics texts in various colors, and the table is laid with a draft of a problem set.
Originally from a New York suburb, Aaron comes to Olin via Swarthmore, Brown, and Boston University. This is his first teaching post, and he’s spent the last year and a half fostering mathematical enthusiasm wherever it presents itself,and his passion is obvious. Though he answered many of my questions with seeming reluctance, Aaron spoke with exclamation marks when I asked him about math.
FRANKLY: Tell me about the new Linearity course.
HOFFMAN: The idea is to deliver a four-credit, full-semester course that overlaps significantly with the content that you would see in a normal linear algebra plus differential equations course, but which really takes a perspective on what’s happening.
The perspective is from dynamical systems, which really builds on ModSim. We’re revisiting and analyzing models for population ecology, for mechanics, for circuits, for different domains in engineering and applied sciences, trying to understand the mathematical mechanisms that make those models have the behavior that they do.
FRANKLY: Were you involved in the whole creation process of the course?
HOFFMAN: They in fact made it a point when they were hiring me.They waited to start the ideation process until I was on board.
I’ve had a great opportunity. Sarah Spence Adams and John Geddes have more experience than I do, they’ve been thinking about pedagogy in math education for a long time, so I’ve had an opportunity to develop this Linearity course with them.
I’ve observed a change in myself, in my perspectives on teaching. Last year at this time, I would not have been ready to embrace a course like Linearity, which is so heavily studio based. And I’m so excited about it.
FRANKLY: You’re used to lecturing, then?
HOFFMAN: Yes. Interactive lectures where you’re really trying to engage the students, where you’re cold-calling, interacting. But lectures! Lectures where I get to be there talking about math, which I love! And somehow, through the force of my enthusiasm, you’re learning!
But the studio-based approach is really fascinating to me, and I can see how it can work. I’m excited to see what the results of this semester turn up.
I try to bring passion and intensity to my classes. I think if I pump energy into the classes then the students pump energy into the classes, and if I don’t, they won’t, typically. I also want them to be doing math. If the students are not doing math, they are not learning math. But whether that’s accomplished through problem sets that they do at home, or quizzes and tests, or studio problems, or problems embedded in the reading is a matter of personal taste.
FRANKLY: What is your field of research?
HOFFMAN: I’m interested in differential equations, those that support pulses or fronts, like a dislocation moving through a crystal, a spinodal decomposition in an alloy, a wave of advance of an invasive species taking over the habitat of the native species.
Very different kinds of models when you look at their instantiations, but the underlying mathematics is very similar. You have pulses or fronts moving through a spatially extended system. And I’m interested in how those fronts and pulses arise, what their stability properties are, and what their interaction properties are. I try to prove really the underlying mathematical mechanism.
FRANKLY: Are students working with you on your research?
HOFFMAN: I’m new faculty, so I haven’t really ramped up my undergraduate program yet, but this summer I’m going to have a couple students working with me, and we’ll see what goes from there. I’m really looking forward to it.
I think in the classroom, I need to reach 85 percent of the students at least. Hopefully 100, but I’m realistic. To recruit for my research program, I only need to reach five percent of the students. So if there are only a handful of students who are really, really excited about mathematics, I can provide something for them.
FRANKLY: You minored in biology as an undergrad. Do you still have an interest in that field?
HOFFMAN: At Olin, more than other places, faculty really do maintain solid footing in multiple disciplines. It is very hard to do that. Some of the equations that I study are, for example, propagation of electrical signals in nerves, so I’m familiar with those equations, and some of the theorems I prove are related to that. But to really immerse yourself in the world of biology- it’s not something I’ve undertaken at this point as a professional researcher.
FRANKLY: If you could change one thing about Olin, what would it be?
HOFFMAN: It’s hard to figure out what the downstream effects of a change would be. It’s natural to miss having math majors, students who want to learn math for its beauty rather than as a tool. But most people don’t want to learn math for its beauty. Most people want to learn math because it’s a tool that works. And being forced to wrestle with that, figuring out how to deliver that content to engineers in a way that helps them grow as scholars and that gives them the tools they need is a fascinating challenge.
FRANKLY: What do you do when you’re not doing math?
HOFFMAN: My kids are aged 2 ¼ and 4 1/3 and they’re great fun. I spend a lot of time hanging out with them and taking care of them.
I do not have the sort of wholistic, well-balanced life that the office of student life describes. I don’t have my own passionate pursuit right now. But having a family is sort of a passionate pursuit.
FRANKLY: Are you on campus all of the time?
HOFFMAN: I go home when it gets dark, and I stay there until it gets light again.
But I like to talk to people about math, and I try to make myself available to do so. If people want to talk to me about math, they can find me in the Dining Hall.