Georgia Institute of Technology College of Sciences

Core topics in differential and Riemannian geometry including Lie groups, curvature, relations with topology.

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.

Geometry, convergence, and structure of linear operators in infinite dimensional spaces. Applications to science and engineering, including integral equations and ordinary and partial differential equations.

The three course series MATH 6579, 6580, and 6221 is designed to provide a high level mathematical background for engineers and scientists.

This course is equivalent to MATH 6338. Students should not be able to obtain credit for both MATH 6580 and MATH 6338.

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.

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.

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.