Teaching

Description:
Mathematical modeling is of increasing importance in the biological and medical sciences. This course focuses on various models of biological
processes using ordinary differential equations and probabilistic techniques. We will look at  models in molecular and cell biology, physiology, neuroscience, ecology and epidemiology. Topics covered include the Hodgkin-Huxley model ofelectrical activity, Michaelis-Menton theory, continuous and discrete population interactions, biological oscillators, aspects of network theory, and the dynamics of infectious diseases.

MATH 6397: Stochastic Models in Biology - Fall 2009

Description:
While deterministic models of biological systems can offer valuable insights into their function and behavior, they do not fully capture the effects of randomness and variability which are fundamental features of nearly all biological systems. In this course we will apply the theory of probability and stochastic processes to models of biological systems. Students taking the course should be comfortable with multivariate calculus, differential equations and linear algebra.

Topics to be covered include: a review of probability, including numerical techniques for generating random samples, Markov processes with discrete and continuous space vari-ables, diffusion processes, Wiener and Ornstein-Uhlenbeck processes, point processes, Gillespie's algorithm and other algorithms for simulating stochastic processes and their application in biology, statistical analysis of time series, power spectra of random processes. A portion of the course will be devoted to numerical simulations of stochastic systems using MATLAB.

Previous Semester Courses