In my own research, I enjoy collaborating with other mathematicians. Discussing problems and ideas for solutions is a great stimulus for the creativity mathematics often requires. Most of the upper division courses I teach are small, typically with fewer than ten students. This gives everyone, myself included, the opportunity to ask a lot of questions and take time to discuss the concepts at hand. I encourage my students to work together on homework and assignments. I frequently ask students to work on individual projects on a related topic of their choice. Students sometimes pick topics that are unfamiliar to me; together we learn something new.
Part of the reason I decided to come to the University of the Pacific is that this is a place where students and teaching come first. Because of my own undergraduate experience, I wanted to work in an environment where professors work closely with students in the classroom and during office hours. Because I like discussing mathematics with students, even in larger classes of 35-40 students, I try to find ways to make this happen. Many of us in the math department, myself included, like to lecture in class and then give time for students to break into groups of 2 or 3 to work on problems. This gives students the chance to talk about the concepts at hand and ask questions. It also gives me the chance to work with more students individually.
For me, the epitome of collaboration with students is working on unsolved problems that arise in my own research. Fortunately, my research field is reasonably accessible: the student must have knowledge of some graph theory and an understanding of the techniques of proof. One of my goals in guiding undergraduate research is to work with students as I would with any other colleague, achieving publishable results. Another goal is to have fun working on challenging problems.
Selected research includes:
- Factor, Merz, and Sano. The (1,2)-Step Competition Number of a Graph. Under revision.
- Factor and Merz. The (1,2)-Step Competition Graph of a Local Tournament. In preparation.
- Langley and Merz. The Set Chromatic Number of a Digraph. In preparation.
- Factor and Merz. The (1,2)-step competition graph of a tournament. Discrete Applied Mathematics 159:100-103, 2011.
- Albertson, Harris, Langley, and Merz. Domination parameters and Gallai-type theorems for directed trees. Ars Combinatoria 81:201-207, 2006.
- Fisher, Guichard, Lundgren, Merz, and Reid. Domination graphs with 2 or 3 nontrivial components. The Bulletin of the Institute for Combinatorics and its Applications 40:67-76, 2004.
- Langley and Merz. The number of alpha-dominating sets in tournaments. Congressus Numerantium 162:183-192, 2003.
- Fisher, Guichard, Lundgren, Merz, and Reid. Domination graphs of tournaments with isolated vertices. Ars Combinatoria 66:299-311, 2003.
- Merz and Stewart.Gallia-type theorems and domination in digraphs and tournaments. Congressus Numerantium 154:31-41, 2002.
- Langley, Merz, Stewart, and Ward.Alpha-domination in tournaments and digraphs. Congressus Numerantium 157:213-218, 2002.
- Fisher, Guichard, Lundgren, Merz, and Reid. Domination graphs with nontrivial components, Graphs and Combinatorics 17(2):227-236, 2001.
- Fisher, Lundgren, Merz, and Reid. Connected domination graphs of tournaments, The Journal of Combinatorial Mathematics and Combinatorial Computing 31:169-176, 1999.
- Fisher, Lundgren, Merz, and Reid.The domination and competition graphs of tournaments, The Journal of Graph Theory 29:103-110, 1998.
- Langley, Lundgren, McKenna, Merz, and Rasmussen. The p-competition graphs of strongly connected and Hamiltonian digraphs, Ars Combinatoria 47:161-172, 1997.
- Lundgren, McKenna, Merz, and Rasmussen. The p-competition graphs of symmetric digraphs and p-neighborhood graphs, The Journal of Combinatorics, Information and System Science 22(2), 1997.
- Langley, Lundgren, Merz, and Rasmussen. Posets with interval or chordal strict upper and lower bound graphs, Congressus Numerantium 125:153-160, 1997.
Professor of Mathematics