Georgia Institute of Technology College of Sciences

Mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization. Concepts from probability and mathematics are introduced as needed. Crosslisted with ISYE 6759.

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, fixed point methods, Newton quasi-Newton, updating, gradient methods. Crosslisted with CSE 6644.

Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, SVD, eigenvalue problems. Crosslisted with CSE 6643.

Introduction to the implementation and analysis of numerical algorithms for the numerical solution of the classic partial differential equations of science and engineering.

Applied mathematics techniques to solve real-world problems. Topics include mathematical modeling, asymptotic analysis, differential equations and scientific computation. 

The differential topology of smooth manifolds.

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

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. No student may obtain credit for both MATH 6579 and MATH 6337. 

This sequence develops the qualitative theory for systems of ordinary differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, normal forms. (1st of two courses)