My research is mathematical biology, with a focus in spatial ecology. Mathematical models include nonlinear partial differential equations, integrodifference equations and related stochastic spatial processes. Biological problems include modeling the process of territorial pattern formation in wolves, predicting population spread in biological invasions, calculating optimal strategies for biocontrol, and assessing the effect of habitat fragmentation on species survival. A significant part of my research involves the formulation and verification of quantitative models, in collaboration with biologists. Mathematical approaches include analytical methods for dynamical systems, perturbation theory, and computational methods.
Formulation, analysis, parameterization, and validation of quantitative models for ecological processes. Applications include population dynamics, species interactions, movement, and spatial processes. Approaches include classical hypothesis testing, computer simulation, differential equations, individual-based models, least squares, likelihood, matrix equations, Markov processes, multiple working hypotheses, and stochastic processes. The lab covers computer simulation methods. Prerequisite: consent of Instructor. Offered in alternate years.Winter Term 2021
The derivative as a rate of change. Differentiation of elementary, trigonometric, exponential, and logarithmic functions. The definite integral as a summation. Integration. The Fundamental Theorem of Calculus. Applications in the context of the life sciences. Prerequisite: Mathematics 30-1. Note: Credit can be obtained in at most one of MATH 100, 113, 114, 117, 134, 144, 154 or SCI 100.Fall Term 2020