Posts Tagged ‘Undergraduate Research’

Undergraduate Reseach: Jump Before Looking

May 7, 2014

I talked about my plan for undergraduate research last week. This week, I invited my linear algebra class to join a research team I am forming.

The class is roughly half sophomores and half first-years. They have had calculus and linear algebra. My plan is to come up with a research question based around either finite fields or group actions on cyclic groups. I feel like I have some questions at the appropriate level that have come up in my own research, although I cannot explicitly state them right now. I had better be able to by next fall if any students decide to join the research team.

Draft of an Undergraduate Research Philosophy

April 30, 2014

I am working on establishing a sustainable undergraduate research program. I want to record some ideas that I have here.

First, I think that this might mean a shift toward searching for problems that undergraduates can understand the research question. This is actually pretty close to what I have been doing anyway, although I hope to more consciously seek out easily-understood problems. I had lunch last weekend with Andy Rundquist (#brag), and he told me that he changed his research focus so that it would be easier for undergraduates to work with him. Fortunately for me, he did this in part because of non-academic considerations (lasers are expensive), but I understand that his main focus was to allow students to work with him immediately after their freshman year. I still will study group theory, although I will see if there are questions that students could quickly understand after just having had one or two semesters of calculus. In particular, I might start learning something about finite fields, which I think could be accessible (it is just like the real numbers, only there are only a finite number of points!).

If I can find good questions (that is part of my goal for my sabbatical next spring), then I would like to form a research group. I hope to work with several students at once. The model I have in mind is that each student will work on solve the research question for a specific case—likely a specific family of groups. The students will be able to talk to each other, since each knows the question being asked, although not every student will know the structure of each, say, particular group.

Essentially, these students would be working on the examples that I would do myself if I were trying to solve the problem on my own. After the students complete their work, they perhaps write a thesis on the problem and I see if I can use their work to solve the entire problem.

This gives students a chance to do undergraduate research, gives them a chance to do it in a more collaborative manner (they get to work with a research team), and it gives me a chance to kill two birds with one stone—the undergraduate research is actually supporting my own research, so time spent with undergraduates is really time spent on my own research.

Do you have anything thoughts on this model? Do you have any alternative models for undergraduate research that work?