Teaching

I have taught many courses during my career. I have taken on different roles including the coordination of several large courses at the University of Toronto. These experiences occurred across a range of institutions: University of Toronto, Georgian College, Wake Forest University, and Wofford College.

Fall 2024

During the Fall 2024 semester I will be teaching the following courses:

• MATH 210A Multivariable Calculus: MWF 8:30-9:20 in Olin 210
• MATH 210B Multivariable Calculus: MWF 13:00-13:50 in Olin 210
• MATH 446A Partial Differential Equations: MWF 9:30-10:20 in Olin 210

Undergraduate Research Projects

I have supervised a number of research projects with undergraduate students and I am always open to suggestions for projects. Here are some of the projects I’ve supervised in the past.

Relativistic Walks and the Relativistic Heat Equation (with H. Wages)

The heat equation that we learn about in a standard course in partial differential equations is nonrelativistic in the sense that the speed of propagation is infinite for the heat flow. In this project we looked at an attempt at formulating a relativistic heat equation that begins by considering random walks. (This was an Honors Thesis project at Wofford College.)

Quantum Graphs and a Model of the Nervous System (with D. Couch)

Quantum graphs provide a structure for considering phenomena that are described by differential equations on a network. In this project we considered a model of the nervous system posed as a variation of the heat equation on a quantum graph. (This was an Honors Thesis project at Wofford College.)

A Statistical Analysis of “Big Brother” (with J. Cohen)

This project was focused on trying to determine the best possible strategy for contestants on the reality television show “Big Brother.” We divided the contestants into different archetypes and carried out a statistical analysis of their various levels of success. (This project began as an independent project for Wofford College’s Interim term and continued as an independent study during the following Spring semester.)

The Multilinear Correction Algorithm and Conservation Laws for the Korteweg-de Vries Equation (with R. Dougherty, joinly supervised with F. Moore)

The multilinear correction algorithm can be seen to provide a way of constructing conservation laws for the KdV equation. We were focused on trying to show that all of the conserved quantities at integer regularities can be obtained from this algorithm. An interesting connection between the terms in the conservation laws and certain combinatorial structures developed in the course of the work. (This was part of an undergraduate thesis at Wake Forest University and was jointly supervised by Frank Moore.)

The Inverse Scattering Transform and Scale Invariant Lax Pairs (with J. Byrum)

The inverse scattering transform provides a powerful way of solving certain nonlinear partial differential equations by converting them to linear problems. Lax pairs are one way of formulating the inverse scattering machinery. In this project we considered the problem of finding scale invariant Lax pairs. (This was part of an undergraduate research project that took place at Wake Forest University.)