This course examines concepts in finance from a mathematical viewpoint. It includes topics such as the Black-Scholes model, financial derivatives, the binomial model, and an introduction to stochastic calculus. Although the course is mathematical in nature, only a background in calculus (including Taylor series) and basic probability is assumed; other mathematical concepts and numerical methods are introduced as needed.

This course is a continuation of MATH-431. It concentrates on differentiation, integration (Riemann and Riemann-Stieltjes integrals), power series, and sequences and series of functions.

This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.

This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.

This course serves as a bridge course that builds the mathematical foundations needed for the IDAI-620 course, Mathematical Methods for Artificial Intelligence, a course introducing the mathematical background for AI systems in the MS in AI program. It focuses on the basic constructions, structures, and results in four key areas: (1) linear algebra (vectors, matrices, and their operations) (2) optimization theory (multivariable functions and their calculus) (3) probability and statistics (basic combinatorics, elementary statistics) and (4) numerical analysis (basic notions of approximation).

This is the first course in a sequence that examines mathematical and statistical models in finance. By taking a mathematical viewpoint the course provides students with a comprehensive understanding of the assumptions and limitations of the quantitative models used in finance. Topics include probability rules and distributions, the binomial and Black-Scholes models of derivative pricing, interest and present value, and ARCH and GARCH time series techniques. The course is mathematical in nature and assumes a background in calculus (including Taylor series), linear algebra and basic probability. Other mathematical concepts and numerical methods are introduced as needed.

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

Independent Study