Mathematical Modeling

This course introduces students to methods of mathematical modeling. The emphasis is on ways to analytically represent and study todays complex modeling problems, with cases from the natural and social sciences. Topics include the model building process, mathematical models of systems, and modeling data to discover properties and hidden characteristics. The calculus of finite differences and solutions to classes of difference equations will serve as the core mathematical theory taught in this course. The dynamics of certain linear and nonlinear models will be explored from various domains (e.g., population models, economic models, Markov models). The course will conclude with an introduction to mathematical graph theory and its application to modeling interacting and interdependent systems and networks.