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 (ISBN13: 9783319067278)
Recommended text:
B. Hall, Quantum Theory for Mathematicians, Graduate Texts in Mathematics 267,Springer, 2013 (ISBN13: 9781461471158)
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, WileyInterscience 2002
 Wikipedia topics pages:
 Matlab/Octave codes:

schedule version 3 May 2020
Day 
Week/
Chapter 
Topic 
Assigned/
Due 
1/131/17 
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: finitedim. 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: finitedim. 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) 

3/93/13 
9 
no lecture
Spring Break 

3/163/20 
10 
no lecture
more Spring Break ... coronavirus 

M 3/23 
11 
cont.
video Lecture323 

W 3/25 

cont.
video Lecture325part1
video Lecture325part2 

F 3/27 

cont.
video Lecture327
review: A Hilbert space alphabet 
A #6 due 
M 3/30 
12
Chapter 11 
Banach spaces
video Lecture330 
Assignment #7 
W 4/1 

HahnBanach theorem
video Lecture41 (recording failed midway)
Midterm 2 description
skeleton slides (LaTeX source)
skeleton slides (PDF) 
Midterm 2 (takehome) assigned 
F 4/3 
Chapter 13 
Banach algebras
video Lecture43 
A #7 due 
M 4/6 
13 
power series
video Lecture46 

W 4/8 
Chapter 14 
spectral theory
video Lecture48part1
video Lecture48part2 

F 4/10 

types of spectrum
video Lecture410 
Midterm 2 due 5pm
Assignment #8 
M 4/13 
14 
6 examples of operator spectrum
video Lecture413 

W 4/15 

compact operators and their spectra
video Lecture415 
Assignment #9 
F 4/17 
Chapter 15 
normal operators, unitary operators, C* algebras
video Lecture417 
A #8 due 
M 4/20 
15 
spectral theorem for compact, normal operators
video Lecture420 

W 4/22 

quantum mechanics
video Lecture422 

F 4/24 

spectral theorem for bounded, normal operators
video Lecture424 
Final Exam assigned
A #9 due 
M 4/27 
16 
functional calculus and unitary groups
video Lecture427 
A #9 due 
F 5/1 

Final Exam
due at 5:00 pm 
Final Exam due 
