An Undergraduate Research Program in Combinatorics and Number Theory

The objective of the program is to provide a professional level research experience for eight undergraduate mathematics students. The program provides a unique research community-of-peers setting that emphasizes developing the independence of each student. At Duluth the approach is to treat undergraduate students with extraordinarily high potential for doing significant research as though they are working on a PhD thesis problem where the adviser provides the problem and mentoring but avoids direct involvement in solving the problem. The PI is assisted by three graduate students and many visitors who are program alumni.

Participants work on open problems and conjectures from the recent literature. Topics include pattern-avoiding permutations, combinatorial problems involving words, and problems in combinatorial number theory. Students gain experience in reading research articles, finding insightful examples, asking probing questions, recognizing subtle patterns, writing frequent reports, giving weekly presentations, posing problems and making conjectures, using computational software, working with peers, dealing with setbacks and frustration, and becoming familiar with the publication process. Participants will be integrated in the mathematical research community by giving presentations of their results at meetings and conferences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.