Math 242: Functional analysis
Instructor: M. Stern

	
This course is an introduction to functional analysis. In this general
approach to analysis, we treat functions as points in vector spaces and work
with the properties of these spaces and operators on them. Much of the
emphasis is on linear operators as generalizations of what we know from
linear algebra in finite dimensions, including the spectrum of such an
operator. These ideas were fundamental in the development of quantum
mechanics. Notions of convergence and topologies are important in infinite
dimensions. This subject is fundamental background for most rigorous
analysis, especially in partial differential equations. Topics include
Hilbert spaces, Banach spaces, bounded and unbounded operators, compact
operators and their spectra, the spectral theorem, and connections with
differential equations.