Courses in applied mathematics, computational neuroscience, and mathematical biology. Most courses end with a project on a current research question.
APPM 4370 / 5370
Fall 2026; previously 2024, 2023, 2021, 2020
Introduces mathematical and computational models of neurons, neural networks, and cognition. Topics include single-neuron dynamics, synaptic plasticity, recurrent network models, and attractor dynamics, with numerical simulation throughout and a final research project. I developed this course and have taught it at CU Boulder since 2020.
APPM 4560 / 5560
Fall 2026, 2025
Studies stochastic processes with the Markov property. Topics include discrete- and continuous-time Markov chains, Poisson processes, stationary distributions, and long-run behavior, with applications to models of random systems.
APPM 4390 / 5390
Spring 2026
Introduces mathematical modeling of biological systems. Topics include population dynamics, interacting species, feedback and regulation, and spatial effects, using both analytical and computational methods.
APPM 5470
2024, 2020, 2019, 2018
Covers the theory and solution of partial and integral equations. Topics include classification of equations, analytical solution techniques, and properties of solutions.
APPM 3010
Fall 2021
Introduces the analysis of nonlinear dynamical systems. Topics include stability, bifurcations, limit cycles, and chaos.
APPM 5480
Spring 2021
Covers asymptotic and perturbation methods for problems that cannot be solved exactly. Topics include dominant balance, regular and singular perturbation theory, and reduced descriptions of complex systems.
I organize APPM 8400: Mathematical Biology Seminar, which brings visiting speakers and CU researchers together around mathematical modeling in the life sciences.
I helped redesign APPM 7400: Introduction to Research, and introduced APPM 7400: Graduate Research Seminar, so that journal club and student research presentations are part of the first and second years of the PhD program.