Georgia Institute of Technology College of Sciences

Develops the probability basis requisite in modern statistical theories and stochastic processes. Topics of this course include measure and integration foundations of probability, distribution functions, convergence concepts, laws of large numbers and central limit theory. (1st of two courses)

Graduate level linear and abstract algebra including groups, rings, modules, and fields. (1st of two courses)

Fundamentals, connectivity, matchings, colorings, extremal problems, Ramsey theory, planar graphs, perfect graphs. Applications to operations research and the design of efficient algorithms.

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.

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.

An introduction to multivariable calculus through vectors in 3D, curves, functions of several variables, partial derivatives, min/max problems, multiple integration. Vector Calculus not covered.

This is an intensive course on linear algebra, taught at a sophisticated and abstract level.

Linear algebra through eigenvalues, eigenvectors, applications to linear systems, least squares, diagonalization, quadratic forms.