Teaching

Fall 2019 and Fall 2016. Mathematical modeling in the biological and medical sciences. Topics include continuous and discrete dynamical systems describing interacting and structured populations, resource management, biological control, reaction kinetics, biological oscillators and switches, and the dynamics of infectious diseases.

Spring 2020, Spring 2017, and Spring 2016. Mathematical models of spatial processes in biology including pattern formation in the embryo and during tissue differentiation, applications of traveling waves to population dynamics, epidemiology, and chemical reactions, and models for neural patterns.

Spring 2018. Random walks, Markov chains, continuous-space Markov processes, Brownian motion, stochastic integration, stochastic differential equations, connections to PDEs, stochastic simulation.

Spring 2019. Analytic functions, complex integration, Cauchy integral theorem, Taylor and Laurent series, residues and contour integrals, conformal mappings with applications to electrostatics, heat, and fluid flow.

Fall 2020 and Fall 2018. Standard and modern topics in applied mathematics, including scaling and dimensional analysis, regular and singular perturbation, calculus of variations, Green's functions and integral equations, nonlinear wave propagation, and stability and bifurcation.

Fall 2017. Classical wave, Laplace, and heat equations. Fourier analysis, Green's functions. Methods of characteristics.

Fall 2021 and Fall 2015. Combinatorial problems, random variables, distributions, independence and dependence, conditional probability, expected value and moments, law of large numbers, and central limit theorems.

Fall 2014. A hybrid course which teaches linear algebra and ordinary differential equations. Linear ordinary differential equations: initial-value problems and behavior of solutions. Euclidean space, linear systems, Gaussian elimination, determinants, inverses, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization.

Spring 2014 and Spring 2013. The course is designed to introduce the basic mathematical methods that are vital to genetics and genomics. Students will use probability, statistics, and matrix algebra to study Mendelian segregation, population allele frequencies, sex-linked traits, genetic recombination, sequence analysis, and phylogenetic trees. In addition to the specific techniques and facts learned, this interdisciplinary course aims to convince students of the importance of mathematics to biology.

Fall 2011. First semester calculus course that utilizes a weekly exploratory lab session. Functions and their graphs, differentiation of polynomial, rational and trigonometric functions. Velocity and acceleration. Geometric applications of the derivative, minimization and maximization problems, the indefinite integral, and an introduction to differential equations. The definite integral and the Fundamental Theorem of Calculus.