Georgia Institute of Technology College of Sciences

An advanced course in Linear Algebra and applications.

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (1st of two courses in sequence)

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.

Introduction to large scale-system design to support computational finance for options, stocks, or other instruments.

Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

Fourier analysis on the torus and Euclidean space.

Basic theories of testing statistical hypotheses, including a thorough treatment of testing in exponential class families. A careful mathematical treatment of the primary techniques of hypothesis testing utilized by statisticians.

Basic unifying theory underlying techniques of regression, analysis of variance and covariance, from a geometric point of view. Modern computational capabilities are exploited fully. Students apply the theory to real data through canned and coded programs.

The study of zero sets of polynomials: algebraic varieties, regular and rational map, and the Zariski topology.

Introduction to the mathematical theory of partial differential equations covering the basic linear models of science and exact solution techniques.