Math 992, Topics in Analysis
                             Professor Fang
                              Spring 2007

There will be no book.. I will type up course notes. 
Prerequisite for the course is complex analysis 

Along with standard theorems, the course will include:
1) a crash course in functional analysis, explaining how to use some typical
   theorems by examples.
2) The Spectral Theorem
3) compact operators
4) "baby" index theory, (i.e., on the circle)
5) Toeplitz operators
6) trace theory

Instead of specializing in one direction in operator theory, I will choose topics 
of wide interests in analysis and beyond. This course does not depend on my Fall '06 
MATH 992 course, but complements it.