Instructor: Marc Rieffel
Lectures: MWF 8:10-9:00 am, Room 740 Evans
Course Control Number: 54494
Office: 811 Evans
Office Hours: M 9:00-10:00; W 10:15-11:30, 1:15-2:00
GSI: Diogo Oliveira e Silva, 1075 Evans, office hours Fridays 2-4.
Prerequisites: Math 202A or equivalent preparation in analysis. Notice that some measure and integration will have been covered in Math 202A.
Recommended Texts: Syllabus:
We will continue the study of measure and integration begun in Math 202A.
My treatment of integration will be closer to that given in the text by
Lang than in the text by Knapp.
Topics that will be discussed
include product measures and Fubini theorems, signed measures, the
Radon-Nikodym theorem, measure and integration on locally compact
spaces. This will be followed by an introduction to functional analysis.
Banach spaces, closed-graph theorem, Hahn-Banach theorem and
duality, duals of classical Banach spaces, weak topologies, Alaoglu
theorem, convexity and Krein-Milman theorem.
Grading: I plan to assign roughly-weekly problem sets.
Collectively they will count for 50% of the course grade.
Students are
strongly encouraged to discuss the problem sets and the course content
with each other, but each student should write up their own solutions,
reflecting their own understanding, to turn in.
Comments: Students who need special accomodation for
examinations should bring me the appropriate paperwork, and must tell me
at least a week in advance what specific accomodation they need,
so that I will have enough time to arrange it.
The above procedures are subject to change.
Homework assignments:
They will be posted at Homework as they
are assigned.
Real and Functional Analysis 3rd ed. by Serge Lang, Springer-Verlag
Basic Real Analysis by Anthony Knapp.
Advanced Real Analysis by Anthony Knapp.
Through an
agreement between UC and Springer, chapters of the Knapp texts are available
for free download by students. You can find the chapters
here, and
here.
You may need to use campus computers to authenticate yourself
to gain access.
It is my impression
that, at least on-line, one can purchase the two Knapp books together as
a package at a more attractive price than if they are purchased singly.
In my lectures I will
try to give well-motivated careful presentations of the material.
There will be a final examination on
Monday May 7, 8-11 AM, which will count for
35% of the course grade. There will be a midterm exam
on Monday, March 12, at the regular class time.
It
will count for 15% of the course grade. There will be no early
or make-up final examination. Nor will a make-up midterm exam be
given; instead, if you tell me ahead of time that you must miss the
midterm exam, then the final exam will count for 50% of your course
grade. If you miss the midterm
exam but do not tell me ahead of time, then you will need to bring
me a doctor's note or equivalent in order to have the final exam
count for 50% of your course grade.