MATH 726 Introduction to Functional Analysis
Instructor: Kevin McLeod
Office: EMS E481 (229-5269)
Office hours: By appointment
e-mail:
kevinm@uwm.edu
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Text: Reed and Simon, Methods of Modern Mathematical
Physics, vol.I
Class meeting time: MW 11:00 am-12:15 pm, EMS E416
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Course description
Since its beginnings around the turn of the century, functional
analysis has become
a vital tool in applied mathematics and mathematical physics,
as well as a central area in pure mathematics.
The basic topics--infinite-dimensional vector spaces and linear
operators in them--were first developed by mathematicians, but
it was soon realised (by von Neumann in particular) that these
abstract ideas were exactly what was needed to put the new
quantum theories of Heisenberg, Schrödinger and Dirac on a
firm mathematical footing.
For the above reasons, this course will be taught as
`Mathematical Physics in Disguise': we will cover the central
ideas of functional analysis, but the topics will be chosen
with applications to quantum theory in mind. Several of these
applications will be covered in class. We will certainly
cover the two basic examples which are done in every quantum
mechanics class: the harmonic
oscillator and the basic model of the hydrogen atom.
If time permits, we will also discuss the Zeeman and Stark
effects in hydrogen, and/or the HVZ Theorem (which describes
the spectra of arbitrary atoms).
This semester will
cover basic functional analysis and applications to quantum
mechanics. The second semester (Math 825) will cover a
selection of more advanced topics, chosen at least partly
according to students' interests.
Evaluation
Your grade for the course will be based on the following factors:
- Homework You will be assigned homework after each class
period, some of which will be collected and graded.
10%.
- Class participation 10%.
- Exams There will be two exams, each of which will
have both in-class and take-home parts. Each of the four
parts will count for 20% of the grade.
80%.
Students with disabilities
If you feel you are a student with a disability, please feel free
to contact me early in the semester for any help or accommodation
you may need.
Kevin Mcleod
8/31/2006