Basic Courses

Click here for rules regarding basic courses

Forms:

 

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
60360

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.
60850 Probability   An introduction to probability theory, including elements of measure and integration, random variables, central limit theorems, and other topics.
70220 Lie Groups and Lie Algebras Spring