The department offers the following basic courses at a current rate of one course every one or two semesters.

• MATH 582
  Introduction to C*-Algebra Theory
  Basic properties of C*-algebras, representation theory, group C* algebras and crossed products, tensor products, nuclearity and exactness
 
• MATH 583
  Introduction to K-Theory
  K-theory groups for compact spaces and C*-algebras. Long exact sequences, Bott periodicity, index theory and the Pimsner-Voiculescu theorem.
 
• MATH 584
  Introduction to von Neumann Algebras
  Comparison of projections, traces, tensor products, ITPFI factors and crossed products, the Jones index, modular theory, free probability.

In addition, topics courses of direct interest to students in operator algebras, noncommutative geometry and related areas are quite often offered. Most recently (Fall 2008) we offered a course on the Atiyah-Singer index theorem.