Summer Bridge Program
This 3-week summer program covers topics from analysis and probability theory (including metric spaces, linear functional analysis, and measure theory) that will be used or introduced in our introductory graduate-level course in fall. The program also fosters community-building among our incoming graduate students and helps them build a supportive and collaborative environment.
Evidence-based Teaching
I build evidence-based techniques into my teaching, from short in-class active-learning activities to problem-solving workshops in recitations and labs.
Lecture Notes
The following course notes are made available under the CC BY-NC 4.0 license.
- Applied Ordinary Differential Equations (introductory undergraduate-level course)
- Applied Partial Differential Equations (introductory undergraduate-level course)
- Applied Dynamical Systems (advanced undergraduate-level course)
- Nonlinear Dynamical Systems 1 (graduate-level course)
- Nonlinear Dynamical Systems 2 (graduate-level course)
Race and Gender in the Scientific Community
This course examines disparities in representation in the scientific community, issues facing different groups in the sciences, and paths towards a more inclusive scientific environment through texts dealing with the history, philosophy, and sociology of science. We will also explore the specific problems faced by under- and well-represented racial and ethnic minorities, women, and LGBTQ community members.
Introduction to Modelling
Offers an introduction to the mathematical modeling of biological, chemical, and physical processes. We will learn about the typical way in which applied mathematicians approach practical applications, from understanding the research question, creating and analyzing a model, and interpreting the findings.
Applied Ordinary and Partial Differential Equations
This two-semester sequence focuses on how differential equations can be used to solve practical applications, from creating models, solving them using analytical, numerical, or qualitative methods, and interpreting the findings. Theoretical foundations are also covered.
Applied Dynamical Systems
Gives an overview of the theory and applications of dynamical systems modeled by differential equations and maps, including bifurcation theory and chaotic dynamics. Applications to chemical reactions, epidemiology, and phase transitions will be covered.
Nonlinear Dynamical Systems
Provides a rigorous introduction to ordinary differential equations, studied from a dynamical-systems viewpoint. Motivated by examples from ecology, chemistry, mechanics, and physics, we will study the existence and uniqueness of solutions and the dynamical behavior near equilibria and periodic orbits.