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 590-S02: Special Topics: Statistical Methods for Social and Behavioral Science - Professor Adam Sales

Social and behavioral scientists, including economists, psychologists, education, policy, and public health researchers, and others, are increasingly looking to data to describe the human world and to test their theories. This class will be a survey of popular methods across quantitative social and behavioral sciences, with a focus on application. Topics will include data visualization, linear and generalized linear models, techniques for causal inference from experiments and observational studies, measurement modeling, and multilevel modeling. Prerequisite: MA511 or familiarity with the basics of multiple linear regression and hypothesis testing.

This course will count as a Statistics elective for students in the Applied Statistics MS or Statistics PhD program.

MA 590-S03: Special Topics: Principles of Epidemiology - Professor Charlotte Fowler

Epidemiology studies the historical pattern of disease in populations to describe and identify distributions of diseases and opportunities for intervention. This course serves as a cornerstone for the quantitative aspects of global health and focuses quantitatively on the distribution and determinants of health in human populations and communities. The goal is to provide a scientific and engineering foundation that seeks for evaluating both to reduce risk factors and interventions and to improve health in a population through a strong quantitative analysis of causation, problem-solving, and analytic reasoning. The study of epidemiology evaluates the multifactorial etiology and pathophysiology of chronic and infectiousc diseases and applies criteria for identification, prevention and control of infectious agents. The discipline also contributes to public health practice and policy and is designed to introduce students to the principles and methods of health investigations. Specific topics include biomedical study design (experiment, cohort, case-control, cross sectional, ecological), appropriate measures of disease burden and association (prevalence, cumulative incidence, rate ratio, odds ratio), and considerations for efficacy and precision (selection bias, confounding, effect modification, measurement error, and random variation). The course also provides a framework for understanding and evaluating biomedical research publications, causal inference, and rudimentary infectious disease modeling.

This course will count as a Statistics elective for students in the Applied Statistics MS or Statistics PhD program. 

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.