Achievement

Mark Adler (Mathematics) and Paul Miller (Biology) developed and taught an applied version of the Mathematics course "Introduction to Stochastic Processes" in a manner appropriate to IGERT trainees, six of whom participated. The course was based on the textbook of the same name by Lawler, but with careful selection of topics to allow for more applications and for training in writing computer code. Mathematical topics covered were Finite and Countable Markov Chains, Branching Processes, Poisson Process, Birth and Death Processes, Optimal Stopping and Brownian Motion. Applications included Basic Cell Genetics, Population Extinction, Hidden Markov modeling for data analysis, the Gillespie algorithm, statistics of Neural Spiking and probabilistic Decision Making. Students learned how to generate the statistics of these processes by simulating single-trial trajectories according to Langevin equations, or to solve for the dynamics of the probability distribution via the diffusion equation.