A course on spatial stochastic (Monte Carlo) simulations of molecular processes in living cells. The course might be of interest to those who took one or both semesters of Mathematical Systems Biology in the past years. However, this course is meant to be self contained, and pre-requisite knowledge is some familiarity with dynamical systems, basic multivariate calculus and probability. We will spend a few classes on basic models in systems biology and (a superficial) summary of chemical reaction systems. The core course focuses on the connection between the continuum picture (reaction-diffusion systems represented by PDE) and the behavior of individual particles. The ideas behind these simulation methods are quite general, and might be useful in other applications. Students proficient in programming will have the option of choosing projects that center on writing simulation programs.
This course is generally offered every other year, alternating with the Matroids sequence. This is a full-year course, with research-level topics in the spring.
This course is offered in alternate years, alternating with Math 751 Functional Analysis. It is intended to be followed in the spring with Math 758 and so would be suitable for either a minor sequence or as part of a major area in differential equations for Ph.D. students. Some background in differential equations and analysis, such as Math 564 and Math 551, respectively, is needed.
This course will follow in the Spring with Math 783. Math 683/783 can be used as a minor in Set Theory in the Ph.D. program. In some cases it may be appropriate for Ph.D. students to combine Math 783 and advanced algebra into a major area.
This course is offered about every other year and provides a graduate-level introduction to Number Theory. Depending on interest, there is sometimes a second semester of Number Theory, Math 645, offered in the spring.
