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AMS 691  Topics in Applied Mathematics

Varying topics selected from the list below if sufficient interest is shown. Several topics may be taught concurrently in different sections: Advanced Operational Methods in Applied Mathematics, Approximate Methods in Boundary Value Problems in Applied Mathematics, Control Theory and Optimization Foundations of Passive Systems Theory, Game Theory, Mixed Boundary Value Problems in Elasticity, Partial Differential Equations, Quantitative Genetics, Stochastic Modeling, Topics in Quantitative Finance.


AMS 691.01 & .30: Topics in Applied Mathematics: Epidemiology Modeling
Almost everyone globally has been impacted by the on-going COVID-19 pandemic; are you interested in learning how mathematical modeling approaches shape how society responds to these crises?
Mathematical models lie at the heart of both understanding the dynamics of how infectious diseases spread through a population and how we can respond to minimize their impact. In this class we will introduce the key modeling approaches used in modern epidemiology. Topics covered will include classical compartment models (such as the widely used SIR and SEIR models), stochastic simulation methods, statistical models, and how to address heterogeneity in populations. Additionally, we will discuss some of the challenges in dealing with epidemiological data.

The class will draw heavily on work from the primary literature, with a particular emphasis on using real data from the COVID-19 pandemic, and will have a significant hands-on component using Matlab and R. All students will participate in a term group-project addressing some aspect of the pandemic. 

This class is suitable for both graduate students and advanced undergraduates with a reasonable background in mathematics and some exposure to computing. Undergraduates should have completed AMS 210, AMS 261 and a course in computing OR both AMS/BIO 332 and AMS 333. Graduate students should have taken at least one undergraduate course in each of Linear Algebra, Multivariate Calculus, and Computing. Students that have questions about their preparation for the class, or who would like to request an exception to the prerequisites, should contact the instructor for permission.
3 credits
ABCF Grading

Course Materials:

No required text.  Suggested readings will be recommended.