Mathematics 242: Functional Analysis (Fall 2003)
Instructor
Leslie Saper
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 or number theory 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
- Methods of Modern Mathematical Physics, Vol I: Functional Analysis,
by M. Reed and B. Simon.
We will cover most of Chapters 1 through 8; see the book to get some idea
of the material.
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