Teaching Portfolio

"The stringent precision attainable for mathematical thought has led many authors to a mode of writing which must give the reader an impression being shut up in brightly illuminated cell where every detail sticks out with same dazzling clarity but without relief. I prefer the open landscape under a clear sky with its depth of perspective, where the wealth of sharply defined nearby detail gradually fades away towards the horizon." ~Hermann Weyl

Welcome to my teaching portfolio. Here you will find my teaching philosophy, a summary of my experience both in the classroom and as a mentor for undergraduate research, and some thoughts on pedagogy. Expanding the sections below, you will also find links to sample course materials for classes on applied topics as well as proof-based courses.

Philosophy

In my view, the task of the teacher is to lead the students on a clear and efficient path through the given subject. The tour should not only be informative, but also entertaining. The route should be easy to navigate, allowing those students who lag behind the group a chance to catch up, yet novel enough to give those wanting to move ahead of the pace the opportunity to explore intriguing side roads. Read More...

Experience

Both as a visiting assistant professor at the University of Notre Dame and as a graduate student at the University of Arizona, spanning some eight years in total, I have served as the instructor of record for a variety of courses ranging from a proof-based honors calculus course to vector calculus with applications, various versions of calculus, and elementary algebra. Each class level presents its own set of pedagogical challenges and I have enjoyed tackling those challenges time and time again. Read More...

Mentoring

I have had the privilege of directing the undergraduate research and senior theses of three honors mathematics students over the past five years, two at the University of Notre Dame, and one at the University of Arizona. Two have continued on to graduate study in mathematics and one is pursuing a graduate degree in education. Work with such students is much more than regular meetings to discuss readings, it is an opportunity to expose them to the fascinating world of my profession and help them shape their post-collegiate future. Read More...

Course Design

This is an arena in which I have experimented thoroughly and which is centrally important to my effectiveness as a teacher. From classroom interaction via ConcepTests, to problem design, to syllabus scheduling, to lecture and examinations, every component my course reveals a part of the story I am trying to tell. Read More...