Special Topics in Stochastic Analysis for Bioengineers
Future offering: 2024
This course is designed for graduate students in engineering and covers advanced topics in cancer modeling. Major course topics include mathematical pre-requisites (probability overview, probabilistic modeling, and mathematical analysis), deterministic modeling of cancer growth, stochastic models of cancer dynamics, Markov chains, Poisson and birth-death processes, branching processes, martingales, Luria-Delbrück fluctuation analysis, stochastic numerical simulations of cancer growth and the Gillespie algorithm, cancer evolution and acquired resistance, cancer evasion and dynamic programming, diffusions, modeling the tumor microenvironment, and cancer dormancy. The course will introduce graduate students to a rigorous and comprehensive treatment of the relevant mathematical tools and their application to contemporary cancer modeling. Problem sets and exams will emphasize key principles and their application to cancer and immunology. In order to prepare students for research in cancer engineering, problem sets will also involve application of concepts to analyze relevant publications in the field. Students are expected to be proficient in undergraduate multivariable calculus, differential equations, linear algebra, and numerical methods (e.g. proficiency in MATLab, Python, or similar computing language).