Math 241 Calculus, part IV: This is an undergraduate course where we study the physical background, mathematical techniques and numerical methods related to the heat equation, the wave equation and Laplace’s equation. If time permits, we also perform some numerical computations related to these physical models. This course is typically offered in both the Fall and Spring semesters.
Math 290 Undergraduate Research in Mathematics: In this course, students will do a research project on a topic of current interest in mathematics. They will also write a report subject to revision and give an oral presentation of their work. The projects to be selected from are drawn from many areas of mathematics including dynamical systems, number theory, fluid mechanics, geometry, optimization and probability. This course is typically offered in the Spring semester.
Math 320 Computer Methods in Mathematical Sciences: This is an undergraduate course where we will write programs in MATLAB to solve problems in numerical integration, equation solving, linear algebra and differential equations. We will also study theoretical and computational aspects of the methods along with error analysis. Prior programming experience will be helpful but isn’t necessary. This course is typically offered in the Fall semester.
Math 432 Game Theory: This course will be an introduction to game theory. Specifically, we will learn how to use mathematics to study various questions which arise when playing games between two players (tic-tac-toe, chomp, Nim, hex, go, chess, penalty kicks, military pursuit games, etc). We will also study ways that multiple self-interested agents interact. These situations arise when considering topics such as bargaining, fair division, auctions, voting, and network formation. Finally, we’ll identify some applications of these ideas in economics, business, biology, and the social sciences. This course is typically offered in the Fall semester.
Math 530 Mathematics of Finance: This an undergraduate/graduate course involving mathematical modeling in finance. The core material customarily involves the Black–Scholes option pricing model. However, we will usually discuss additional topics and students will write a paper based on another mathematical model in finance. This course is typically offered in the Spring semester.
Math 608/Math 609 Analysis I/Analysis II: This is a two-semester, graduate sequence in mathematical analysis. The first third of the course covers complex analysis (Cauchy’s theorem, meromorphic functions, singularities, entire functions, conformal mappings); the second third covers real analysis (measure theory, integration, product measures, Lebesgue-Nikodym theorem, differentiation of measures, BV functions); and the last third covers functional analysis (inner product spaces, normed linear spaces, Hahn-Banach theorem, open mapping and closed graph theorems, weak topologies and dual spaces, topological vector spaces, L^p spaces).
Math 644 Partial Differential Equations: This is a graduate course on theory for partial differential equations (PDE). We usually start with theory related to linear elliptic, parabolic and hyperbolic equations, and then move on to nonlinear PDE arising in the calculus of variations, gradient flows, and optimal control. Along the way, we will discuss connections to physics, optimization, engineering, and other areas of mathematics. This course is typically offered in the Fall semester.