Mathematics 242: Functional Analysis (Fall 2002)
Instructor
Tom Beale
Description
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. Notions of
convergence and topologies are important in infinite dimensions. This
subject is fundamental background for most rigorous analysis, especially in
partial differential equations. The course would also be useful to
students studying geometry who will be using analytic tools. Topics
include Hilbert spaces, Banach spaces, bounded and unbounded operators,
compact operators and their spectra, the spectral theorem, and connections
with differential equations.
Prerequisites
Math 241 (Real Analysis) or consent of instructor
Text(s)
The text is likely to be
- Methods of Modern Mathematical Physics, Vol I: Functional Analysis,
by M. Reed and B. Simon.
This is a tentative choice, subject to change. We will cover most of
Chapters 1 through 8; see the book to get some idea of the material.
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Last modified: 16 March 2002