Skip to content
The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem
Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces
Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.
Topics from complex function theory, including contour integration and conformal mapping
Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n
Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series
Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices
Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing
Simple random walk and the theory of discrete time Markov chains
This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.
Georgia Institute of TechnologyNorth Avenue, Atlanta, GA 30332Phone: 404-894-2000