Sarah Merz
PhD, University of Colorado at Denver, 1995
MS, University of Colorado at Denver, 1994
BA, Whitman College, 1991
Teaching is the most important aspect of my job as college professor. I love my research; it fuels my passion for mathematics. But wanting to work with students is the reason I sought a position in a strictly undergraduate department rather than one with a graduate program. Service to the University can be important and rewarding, but teaching is what motivates me. The desire to teach undergraduates is why I am at 91成人导航.
Because I have been involved in many faculty searches in the math department, I have read hundreds of teaching statements by faculty candidates. These statements are often puzzling: the authors often seem confident in their philosophy in spite of relatively little experience. Having taught at 91成人导航 since 1995, I am experienced in teaching courses that range from General Education to courses targeting science and engineering majors to math major courses.
I've worked with all kinds of students: from the math phobic to some of our most mathematically gifted students. Given this breadth and depth of experience, I'm surprised to find how much more difficult it is to formulate my teaching philosophy now as compared to when I first entered the job market. I have guiding principles I bring to the classroom: be well prepared and have a map for your intended accomplishments. But ultimately, I believe that in order to be an effective teacher, we must recognize when our methods must change to suit the needs of our students. This is the core of my teaching philosophy.
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My research is in the field of graph theory. Specifically, I have worked on problems involving competition and domination in digraphs. Competition graphs were introduced in the study of food webs. A food web can by modeled by a directed graph wherein each vertex represents a species in the food web. An arc is directed from one vertex to another provided the species associated with the initial vertex preys on the species associated with the subsequent vertex. The competition graph of this directed graph is then constructed by creating a new graph with the same vertex set, but with an edge between two vertices provided their corresponding species share common prey. A common thread in my research is the characterization of the competition graphs of different classes of digraphs (e.g., interval digraphs and tournaments).
