This course is, first and foremost, an introduction to stochastic processes (models that incorporate randomness) that is equivalent in level, and to a large extent content, to Math 632. However, the applications will be drawn primarily from the biosciences, with a special emphasis on the continuous time Markov chains used to model biochemical and other population processes. Further, as simulation is a large part of how scientists study their models, we will spend considerable time on these methods (such as the well known ``Gillespie Algorithm''). Matlab will be the software package of choice for the course and each homework assignment will incorporate at least one Matlab exercise.
Math 635, 735, 831-832
- Discrete Time Markov Chains.
- Branching processes.
- Continuous time Markov Chains.
- Diffusion processes.
- Applications to biology, especially the continuous time Markov chains used to model biochemical reaction networks.
- Computational/Simulation methods.