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.
My personal web page can be found here: http://www1.pacific.edu/~smerz
Associate Professor of Mathematics