WMC-REU-2015

Today, we wrapped up the REU (on-site, anyway). Each group gave their final presentations, and then we had a final round of root beer floats and games. It’s been a lot of work to be an REU mentor, but it’s been equally fun. In the next week, I’ll wrap up a few thoughts about the REU and post a link to our final product. But for now, it’s time to get to the airport and start my trip back to Hamilton.

Let’s be blunt: I’m not good at giving feedback. I tend to lay things out with little (read: zero) padding. My former linear algebra* students will understand what I mean immediately. Did you include a meaningless sentence? Did you try to prove linear independence and instead show me that 0 = 0? Here’s what I think of that:

  I’m lucky to have an REU group that takes my criticism in stride.

There are only two and a half weeks left of the REU. How did that happen?! My REU students are still making progress. We established that the active writing will commence (and thus the research will end) on Monday. My students assure me that they’ll work on tying up the loose research ends on over the weekend.* They know that I’d like to see one more theorem from them by the end of the week, and I think they’re slightly afraid of me.

The two other REU mentors, Erin McNicholas and Colin Starr, are incredible people. Erin is one of the PIs for the grant that’s funding the REU for the next three years. Colin has had this role in the past, too. Aside from the obvious responsibilities that come with that job, there are hidden mountains of paperwork and bureaucracy to summit. Erin is a portrait of productivity. She’s doing the extra work on top of mentoring her algebraic voting theory group, learning new math alongside them, organizing the occasional picnic or outing, and keeping up with her research agenda!

I had resolved myself to the idea that we might not prove our theorem in full generality. I accepted that we’d settle for writing a paper where we made a conjecture about the general case and wrote proofs for, I don’t know, up through n = 6 or something. Note-to-Gibbons: You shouldn’t doubt your incredible REU group like that! We riffed on the general ideas in our proof and about 10 minutes ago, we proved the general case!

I’ve had a few people ask me what I was looking for when I read through REU applications.  I thought I’d describe my process and my reasons, which you can take to be my rubric for putting together an excellent application.  As with all advice on this blog, these are my opinions.  You should gather a few other ideas for a complete picture, especially since this is my first time as an REU mentor.  Now, disclaimers aside, follow the jump to my advice.

We’re pretty close to Theorem 1. When I started designing my REU project, I worried that I was either too narrow or too ambitious. I thought the students might finish in week 1…or not get anywhere at all. After all, my experience mentoring student research has been with the amazing and talented Robert Huben. On some days, I felt like I should be happy with less from Robert, and on other days, I thought I should push for more.

Mike Orrison, of Harvey Mudd, visited the REU on Wednesday and talked about the generalized Condorcet criterion and the underlying linear algebra used to prove a surprising result. The Condorcet criterion is said to hold for a voting system if it guarantees that, if a candidate would win each head-to-head election, then that candidate would win the election. In our usual voting system, we only ask voters to vote for their first choices.