We teach a number of courses in mathematical biology including:
Computational Modeling of Biological Systems
Fundamental models that arise in biology and their analysis through modern scientific computing. Discrete and continuous-time dynamics, in deterministic and stochastic settings, with applications from molecular biology to neuroscience to population dynamics. Statistical analysis of experimental data. MATLAB or R programming taught from scratch.
Prerequisites:Either a course in differential equations or permission of the instructor Course Web Page (Winter 2013)
Mathematical Analysis in Biology and Medicine
This course focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications are drawn from many branches of biology and medicine. Students will gain experience in applying differential equations, difference equations, and dynamical systems theory to biological problems.
Prerequisites:Either courses in differential equations and probability and statistics, or permission of the instructor Course Web Page (Spring 2013)
Focuses on the construction and analysis of mathematical models for infectious disease transmission and control. Emphasizes evaluation and comparison of vaccination programs. Applications are presented for a variety of diseases such as measles, rubella, smallpox, rabies, etc.
Prerequisites:AMATH 351 or equivalent
Mathematical Theory of Cellular Dynamics
Biological cells are biochemical systems that obey the laws of physics. This course develops a coherent mathematical theory for processes inside living cells. It focuses on analyzing dynamics leading to functions of cellular components (gene regulation, signaling biochemistry, metabolic networks, cytoskeletal biomechanics, epigenetic inheritance) using deterministic and stochastic models.
Prerequisites:Either courses in dynamical systems, partial differential equations, and probability, or permission of the instructor Course Web Page (Autumn 2012)
Mathematics of Genome Analysis and Molecular Modeling
Genome analysis, i.e., bioinformatics, and molecular modeling in terms of molecular dynamics (MD) and Brownian dynamics are now fast growing areas of applied mathematics in molecular biology. This course introduces the fundamentals of these approaches in terms of discrete probability, classical mechanics, theory of diffusion, and Monte Carlo simulations.
Prerequisites:Either Amath 506 or permission of the instructor
Neural Control of Movement
This class provides a comprehensive view of how the brain controls movement. It brings together elements of biomechanics and muscle physiology, neuroanatomy and neurophysiology of the motor system, sensorimotor psychophysics and kinesiology, and movement disorders. Empirical data are interpreted in the context of control-theoretic models whenever possible.
Prerequisites:Vector calculus, linear algebra, MATLAB, or permission of the instructor
Dynamics of Neurons and Networks
Mathematical analysis and computational modeling on three interconnected scales \(em neurons, networks, and populations \(em including (1) oscillations and synchrony, (2) role of network structure and symmetry, (3) statistical mechanics tools for large-scale models, (4) bifurcation and reduction methods for biophysical models. Emphasizes links between system dynamics and signal processing.
Prerequisites:Eithr CSE/NBB 528 or permission of the instructor
This course considers models, methods, and issues in population ecology. Topics include the effects of density dependence, delays, demographic stochasticity, and age structure on population growth; population interactions (predation, competition, and mutualism); and applications of optimal control theory to the management of renewable resources.
Prerequisites:Either a course in differential equations or permission of the instructor Course Web Page (Spring 2011)
Spatial Models in Ecology and Epidemiology
This course considers models for the growth and dispersal of biological populations. Topics include population persistence, climate-induced range shifts, and rates of spread of invading organisms. We will consider reaction-diffusion equations, integrodifference equations, branching random walks, and other relevant classes of models.
Prerequisites:Either a course in partial differential equations or permission of the instructor Course Web Page (Spring 2012)