I am currently an Assistant Professor in the Developmental Mathematics department at Utah Valley University. Before beginning at Utah Valley University, I completed my Ph.D. at the University of Notre Dame in philosophy. My focus is in philosophy of mathematics and my dissertation, The Explanatory Value of Category Theory, considers the role of explanation in contemporary mathematics with a specific focus on category theory and algebraic topology. Before studying at Notre Dame I completed a B.A. in philosophy and mathematics, and an M.A. in mathematics at SUNY Potsdam.
My primary research interests are in philosophy of mathematics with particular focus on contemporary mathematics, mathematical practice, and mathematical explanation and understanding. I am specifically interested in category theory and algebraic topology and explanations as they appear in these areas. My dissertation has two primary aims. First, to develop accounts of mathematical explanation and understanding, as well as to analyze the relation between the two and the roles that each play in contemporary mathematics. Second, to demonstrate that category theory plays an explanatory role in contemporary mathematics. These two points contribute to my over-arching research goal of bringing more philosophical attention to contemporary mathematics and its practice.
I also have research interests in mathematics education, specifically in the role that definitions play in introducing students to new concepts and how the presentation and formulation of definitions can affect student success. I am also interested in strategies for maximizing the effectiveness of homework assignments, specifically, in how opportunities to revise and reflect on homework assignments can increase their effectiveness.
AOS: Philosophy of Mathematics
AOC: Epistemology, Logic, Philosophy of Science
Developmental Mathematics Department
Utah Valley University