Undergraduate-appropriate summer projects

(updated: now with links to projects)

A friend asked me, in reference to my post about the call for proposals for REU positions from CRA, “What kind of projects did you have them work on?”

Two years ago, I proposed two projects and used one.  (I was to have two students, but sadly the shuttle carrying one student to her local airport crashed and she ended up hospitalized with serious injuries.  Last I heard, many months after the accident, she was recovering very well and CRA had set up a last-minute local project for her to work on.)  I include here the two project descriptions I submitted to CRA:

This summer was spent mostly on experimental work rather than theoretical and I was glad for the experimental plan.

For the OSU Math REU program — now accepting applications! — last summer, I proposed a rough area and at the start of the summer changed my mind (while keeping with the spirit of the original area) so that my two summer students could work with my graduate student on what she had already started.  The summer was very successful, resulting in the completion of a paper in which the undergraduate students proved two main theorems.  I had given a thorough outline for one theorem and very little guidance for the second theorem.  They also experimented with generating examples which I think aided in a feeling of productivity and surely helped them understand the problem at hand better. Their summer project report is available here.

Based on this very limited experience, I have the following advice for theoretical-based REUs:

  • If possible, have two undergraduate students working together.
  • Involve a graduate student.  Even a junior graduate student can help fill-in course-level knowledge and can help advise if you need to travel during the summer.
  • Have an experimental (back-up) component.  If they get stuck, the experimental component can help with a sense of productivity and accomplishment.
  • Seek out math, computer-science double majors.

I’d love to hear what other advice/ideas people have.

Did I mention:  the Oregon State University Math REU Program is now accepting applications!  Math/CS double majors are welcome and highly desired!

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