Ed Bueler
elbueler@alaska.edu
Office: Chapman 306C ( hours)
Class times and room:
MWF 10:30 -- 11:30 pm
Bunnell 410
Chapman 204
ONLINE!
CRN: 35419
Required text:
J. Muscat, Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras, Springer, 2014 (ISBN-13: 978-3319067278)
Recommended text:
B. Hall, Quantum Theory for Mathematicians, Graduate Texts in Mathematics 267,Springer, 2013 (ISBN-13: 978-1461471158)
Links:
- LaTeX materials:
- a LaTeX .tex template for your one "LaTeX problem" per assignment
- the PDF result of running pdflatex on the template
- Beginning LaTeX by David Maxwell
- the LaTeX book at Wikibooks
- LaTeX installation guides by David Maxwell:
- If you are using Linux and need installation help just let me know.
- Overleaf allows you to LaTeX, and share projects, online.
- Texts I could have chosen for this course, but which are perhaps too complete and/or advanced:
- M. Reed & B. Simon, Functional Analysis, Methods of Modern Mathematical Physics I, Revised and enlarged edition, Academic Press 1980
- P. Lax, Functional Analysis, Wiley-Interscience 2002
- Wikipedia topics pages:
- Matlab/Octave codes:
|
schedule version 3 May 2020
| Day |
Week/
Chapter |
Topic |
Assigned/
Due |
| 1/13--1/17 |
1
Chapters 1,2,3,4,5,6 |
no lecture
Bueler at conference |
Assignment #1 |
| M 1/20 |
2 |
no lecture
Alaska Civil Rights Day |
|
| W 1/22 |
Chapter 7 |
vector spaces |
|
| F 1/24 |
|
what is functional analysis? |
Assignment #2
A #1 due |
| M 1/27 |
3 |
normed vector spaces |
|
| W 1/29 |
|
cont. |
|
| F 1/31 |
|
slides: finite-dim. spectral theory I |
A #2 due |
| M 2/3 |
4 |
cont. |
Assignment #3
A #2 due |
| W 2/5 |
Chapter 8 |
continuous linear maps |
|
| F 2/7 |
|
cont. |
|
| M 2/10 |
5 |
integral operators |
Assignment #4
A #3 due |
| W 2/12 |
|
cont. |
|
| F 2/14 |
|
Y Banach => B(X,Y) Banach |
|
| M 2/17 |
6 |
projections, Riesz theorem |
Assignment #5
A #4 due |
| W 2/19 |
Chapter 9 |
sequence spaces |
|
| F 2/21 |
|
Lebesgue theory |
|
| M 2/24 |
7 |
cont. |
|
| W 2/26 |
|
dual spaces |
|
| F 2/28 |
|
slides: finite-dim. spectral theory II |
A #5 due |
| M 3/2 |
8 |
Midterm 1
in class |
Midterm 1 |
| W 3/4 |
|
slides cont. |
Assignment #6 |
| F 3/6 |
Chapter 10 |
Hilbert spaces
Jordan & von Neumann 1935 (parallelogram law ==> inner product) |
|
| 3/9--3/13 |
9 |
no lecture
Spring Break |
|
| 3/16--3/20 |
10 |
no lecture
more Spring Break ... coronavirus |
|
| M 3/23 |
11 |
cont.
video Lecture-3-23 |
|
| W 3/25 |
|
cont.
video Lecture-3-25-part1
video Lecture-3-25-part2 |
|
| F 3/27 |
|
cont.
video Lecture-3-27
review: A Hilbert space alphabet |
A #6 due |
| M 3/30 |
12
Chapter 11 |
Banach spaces
video Lecture-3-30 |
Assignment #7 |
| W 4/1 |
|
Hahn-Banach theorem
video Lecture-4-1 (recording failed midway)
Midterm 2 description
skeleton slides (LaTeX source)
skeleton slides (PDF) |
Midterm 2 (take-home) assigned |
| F 4/3 |
Chapter 13 |
Banach algebras
video Lecture-4-3 |
A #7 due |
| M 4/6 |
13 |
power series
video Lecture-4-6 |
|
| W 4/8 |
Chapter 14 |
spectral theory
video Lecture-4-8-part1
video Lecture-4-8-part2 |
|
| F 4/10 |
|
types of spectrum
video Lecture-4-10 |
Midterm 2 due 5pm
Assignment #8 |
| M 4/13 |
14 |
6 examples of operator spectrum
video Lecture-4-13 |
|
| W 4/15 |
|
compact operators and their spectra
video Lecture-4-15 |
Assignment #9 |
| F 4/17 |
Chapter 15 |
normal operators, unitary operators, C* algebras
video Lecture-4-17 |
A #8 due |
| M 4/20 |
15 |
spectral theorem for compact, normal operators
video Lecture-4-20 |
|
| W 4/22 |
|
quantum mechanics
video Lecture-4-22 |
|
| F 4/24 |
|
spectral theorem for bounded, normal operators
video Lecture-4-24 |
Final Exam assigned
A #9 due |
| M 4/27 |
16 |
functional calculus and unitary groups
video Lecture-4-27 |
A #9 due |
| F 5/1 |
|
Final Exam
due at 5:00 pm |
Final Exam due |
|