Undergraduate Research

I have supervised a number of successful undergraduate research projects over the years. I was a co-director of a National Science Foundation sponsored Research Experience for Undergraduates in mathematics at the University of Notre Dame in Summer 2002 and Summer 2003. The REU at Notre Dame has an informative website.

If you are an undergraduate mathematics major and you are interested in working on a research project, please come talk to me.  I would also be happy to advise you on applying for summer research programs.

I used to give projects to undergraduates almost entirely in the fields of graph theory and combinatorics. Lately, this has changed significantly. Certain aspects of my current research projects lend themselves to undergraduate research, and my recent undergraduate research projects have fallen into the category of classical algebra.

Here is a list of undergraduate students that have worked with me:

1. S. Bratek, The Brain puzzle and the reflected Gray code, honors thesis, 2008.
   
2. S. Yeakel, Eigentheory and Cayley-Dickson algebras, 2006.
3. C. Zin, Computing annhilators in Cayley-Dickson algebras, 2005.
4. M. Buckman, Wayne State University, Comparing the Hopf-Stiefel and the Atiyah function, 2004.
5. A. Shkembi, Wayne State University, Comparing the Hopf-Stiefel and the Atiyah function, 2004.
6. A. Sondhi, Wayne State University, Computing the Hopf-Stiefel function, 2004.
7. D. Brown, University of Arizona, Counting pseudographs, 2003.
8. B. Ginsberg, Yale University, Hamiltonian circuits in Cayley digraphs, 2003.
9. K. Harwood, University of Notre Dame, Hamiltonian circuits in Cayley digraphs, 2003.
10. A. Rupinski, University of Notre Dame, Counting pseudographs, 2003.
11. V. Barone, University of Notre Dame, Hamiltonian circuits in Cayley digraphs, 2002.
12. C. Jankowski, University of Notre Dame, K_*-homogeneous graphs, 2002.
13. M. Mauntel, University of Notre Dame, Hamiltonian circuits in Cayley digraphs, 2002.
14. M. Miller, Bowdoin College, Hamiltonian circuits in Cayley digraphs, 2002.
15. S. Proctor, California State University at Fullerton, K_*-homogeneous graphs, 2002.

Here is a list of papers written as a result of undergraduate research projects that I have supervised:

1. V. Barone, M. Mauntel, and M. Miller, Hamiltonicity of the cartesian product of two directed cycles minus a subgroup, AKCE Int. J. Graphs Comb. 3 (2006) 39--43.
2. D. Brown and A. Rupinski, Counting a certain type of pseudograph with given Euler characteristic.
3. B. D. Ginsberg and K. S. Harwood, Hamiltonicity of subgroup-deleted Cayley digraphs.
4. D. C. Isaksen, C. Jankowski, and S. Proctor, On K_*-ultrahomogeneous graphs, Ars Combinatoria 82 (2007) 83--96.
5. M. Miller, Hyperhamiltonicity of the cartesian product of two directed cycles, Ars Combin. 79 (2006) 269--275.
6. C. Zin, Notes on computing dimensions of annihilators in Cayley-Dickson algebras .

For many years, I have been involved in the REU run by Joe Gallian at the University of Minnesota, Duluth. In Summer 1993 I participated as an undergraduate student, where I wrote an article about graph theory. In Summer 1994, 1995, and 1996, I worked as a graduate research advisor in Duluth. During this time I coauthored with David Moulton the paper

D. C. Isaksen and D. P. Moulton, Randomly planar graphs, Discrete Math. 175 (1997) 265--269.

Since 1997, I have visited Duluth every summer except for Summer 2000. During that time, I coauthored the paper

D. C. Isaksen and B. Robinson, Triangle-free polyconvex graphs, Ars Combin. 64 (2002) 259--263.

In 2006 I participated in the conference Promoting Undergraduate Research in Mathematics in Rosemont, Illinois.  I contributed the following two articles to the conference proceedings of that conference.

Assessment methods for undergraduate research programs, in Proceedings of the Conference on Promoting Undergraduate Research in Mathematics, ed. J. A. Gallian, Amer. Math. Soc. (2007) 307-310.

Graduate students as mentors in mathematics REUs, in Proceedings of the Conference on Promoting Undergraduate Research in Mathematics, ed. J. A. Gallian, Amer. Math. Soc. (2007) 285-287 (with S. G. Hartke and P. Matchett Wood).

Student mentors in the Duluth mathematics REU, Council on Undergraduate Research Quarterly 19, no. 4, 163--167, June 2000 (with D. K. Biss).

The Tanglewood of mathematics, Math Horizons, September 1997.

This is a short piece, more or less in the style of a newspaper article, about the Research Experience for Undergraduates summer program run by Joe Gallian at the University of Minnesota, Duluth.