Georgia Institute of Technology College of Sciences

This sequence develops the qualitative theory for systems of differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. (2nd of two courses)

Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.

Basic theories of statistical estimation, including optimal estimation in finite samples and asymptotically optimal estimation. A careful mathematical treatment of the primary techniques of estimation utilized by statisticians.

Develops the probability basis requisite in modern statistical theories and stochastic processes. (2nd of two courses)

Graduate level linear and abstract algebra including rings, fields, modules, some algebraic number theory and Galois theory. (2nd of two courses)

Functions, the derivative, applications of the derivative, techniques of differentiation, integration, applications of integration to probability and statistics, multidimensional calculus.

Linear equations, matrices, linear programming, sets and counting, probability and statistics.

The topics covered parallel those of MATH 2551 with a somewhat more intensive and rigorous treatment.

Methods for obtaining numerical and analytic solutions of elementary differential equations. Applications are also discussed with an emphasis on modeling.

Linear approximation and Taylor’s theorems, Lagrange multiples and constrained optimization, multiple integration and vector analysis including the theorems of Green, Gauss, and Stokes.