Case studies, visiting lecturers from financial institutions, student group projects of an advanced nature, and student reports, all centered around quantitative and computational finance. Crosslisted with ISYE and MGT 6785.
Fundamental methods of enumeration and asymptotic analysis, including the use of inclusion/exclusion, generating functions, and recurrence relations. Applications to strings over a finite alphabet and graphs.
Fourier analysis in Euclidean space. Basic topics including L^1 and L^2 theory; advanced topics such as distribution theory, uncertainty, Littlewood-Paley theory
Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, SVD, eigenvalue problems. Crosslisted with CSE 6643.
Discrete time Markov chains, Poisson processes and renewal processes. Transient and limiting behavior. Average cost and utility measures of systems. Algorithm for computing performance measures. Modeling of inventories, and flows in manufacturing and computer networks. (Also listed as ISyE 6761)
Mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization. Concepts from probability and mathematics are introduced as needed. Crosslisted with ISYE 6759.
Introduction to the implementation and analysis of numerical algorithms for the numerical solution of the classic partial differential equations of science and engineering.
