Graduate Basic Course List

Course #   Course Title   Semester   Description
60210   Algebra I   Fall   Groups, rings, modules
60220   Algebra II   Spring   Fields, Galois theory, and topics chosen from modules, multilinear algebra, homological algebra, commutative algebra, and noncommutative algebra
60350   Real Analysis I   Fall   Calculus, Lebesgue measure, general measure theory

Real Analysis II

  Spring   Functional Analysis or topics chosen at the discretion of the instructor
60370   Complex Analysis I   Fall   Analytic functions, Cauchy integral theorems and formulas, applications.
60380   Complex Analysis II   Spring   Topics from complex manifolds, Riemann surfaces, ...
60330   Basic Geometry & Topology   Fall   Quick review of point set topology, fundamental groups and covering spaces, manifolds.
60440   Basic Topology II   Spring   Algebraic topology, homology, cohomology, duality theorems
60510   Logic I   Fall   Model theory and some set theory.
60520   Logic II   Spring   Computability theory and more set theory.
60610   Discrete Mathematics       Enumeration, graph theory, error correcting codes, and other topics at discretion of the instructor
60620   Optimization       Convex sets, theorems of Caratheodory, Radon,  Helly, and Krein-Milman.  Facial structure of convex sets. Extreme points. Separation Theorem. Optimality conditions for convex programming problems. Introduction to subdifferential calculus. Chebyshev approximations.
60650   Basic PDE       Linear partial differential equations, including transport, Laplace, heat, and wave equations.  Nonlinear differential equations.
60670   Basic Differential Geometry   Spring   Connections, Riemannian geometry, topics chosen from Kahler geometry, symplectic geometry, contact geometry.