Mathematical Sciences Courses

MA 590: Special Topics: Stochastic Control and Optimization - Professor Gu Wang

(offered Fall 2024)

This course discusses the theory of optimal decision making in a dynamic and random environment. It starts with an introduction to stochastic process and analysis, and then discusses classical stochastic control techniques in continuous-time optimization models. The topics include dynamics programming principle, Hamilton-Jacobi-Bellman equations, viscosity solutions, duality and martingale methods, and optimal stopping, and the application to reinforcement learning. Recommended prerequisite: Probability, Stochastic Processes

MA 4891: Special Topics: Number Theory - Professor Brigitte Servatius

(offered D-Term 2025)

Number theory is about integers. And integer valued functions. Number theory exists in three mutually supporting varieties. Elementary Number Theory, Analytic Number Theory, and Algebraic Number Theory, with Elementary Number Theory the necessary introduction to the other two. This course will introduce elementary number theory (which, according Paul Erdos is all but elementary) and end by pointing toward topics and problems in analytic/algebraic number theory. We will discuss prime numbers, modular arithmetic, quadratic reciprocity and Diophantine equations. Proof techniques as well as computer techniques will be practiced and applications, in particular to cryptography, explored.