Instructor: Marc Rieffel
Lectures: MWF 11:10-12:00 am, Room 60 Evans
Course Control Number: 54758
Office: 811 Evans
Office Hours: M 10-10:50, 1:15-2; W 8:15-8:50; F 10-10:50
GSI: Michael Hartglass
Prerequisites: Math 104 or equivalent preparation in analysis. Further experience with upper-division mathematics courses, including writing proofs, is strongly recommended.
Required Text: Basic Real Analysis by Anthony Knapp. Recommended Text: For Math 202B next Spring I will
probably require
Advanced Real Analysis by Anthony Knapp. 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.
You can find chapters to download
here.
Syllabus:
We will cover basic mathematical concepts that are of
importance in virtually all areas of mathematics. These
include: Metric spaces and general topological spaces. Compactness and connectedness. Characterization of compact metric spaces. Theorems of Tychonoff, Urysohn, Tietze. Complete spaces and the Baire category theorem. Function spaces; Arzela-Ascoli and Stone-Weierstrass theorems. Partitions of unity. Locally compact spaces; one-point compactification. Introduction to measure and integration. Sigma algebras of sets. Measures and outer measures. Lebesgue measure on the line. Construction of the integral.
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.
This page was last updated on 10/08/2009
Through an
agreement between UC and Springer, chapters of the text are available
for free download by students. You can find the chapters
here. You may need to use campus computers to authenticate yourself
to gain access.
In my lectures I will
try to give well-motivated careful presentations of the material.
There will be a final examination on
Saturday December 12, 12:30-3:30 PM, which will count for
35% of the course grade. There will be a midterm exam
on Friday, October 30, 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.