Each offering of this course presents an advanced subfield (application area or technique) of applied mathematics. One topic from the following list will be covered.
Mathematical Finance
In this offering, we present the classical underpinnings of the framework of mathematical finance. We will discuss asset pricing and the development of continuous (Black-Scholes) and discrete (binomial tree) models for option pricing. Interest-rate models, fixed-income products, and portfolio theory will be discussed as time permits.
Industrial Mathematics
The type of mathematics used to solve industrial problems varies widely depending on the problem at hand. In this course, students will work in teams on industrial problems presented at various industrial and modeling camps and workshops over the years. Students will apply the skills they learn in MATH 347 to model the underlying processes, and perform analytical, statistical, and computational analysis as appropriate. Students will also develop additional marketable skills by presenting their results in oral and written form.
Introduction to Optimal Control
This offering provides an introduction to the theory and computational techniques of optimal control. Mathematical models are powerful tools for predicting how systems evolve in time. Controlled models allow some parameters to be chosen by the modeler in order to influence the behavior of the system. Optimal control is the study of how to choose parameters to optimize the behavior of the system according to some specified objective. The course will cover dynamic programming methods for deterministic stochastic discrete systems and an introduction to continuous-time optimal control. Problems will be chosen based on real-world relevance, and the course will discuss both computational methods and theoretical results.