**Fall 2021**

**Instructor:** Marc Rieffel

**Lectures:** TTh 9:40-11:00 pm, Valley Life Sciences 2040.

**Course Control Number:** 22271

**Office:** 811 Evans

**Office Hours:** Tuesdays 11-12, 1-2; Thursdays 11-12

** GSI:** Eric Jankowski

**Office for office hours:** 939 Evans

**Office Hours:** Mondays 10:30-12; Wednesdays 12:30-2

**Prerequisites:** Math 104 and considerable experience
with other upper-division mathematics courses in dealing with quite
abstract concepts and with constructing somewhat complicated proofs.
Math 105, 110, 142 and 185
give especially useful preparation. I have no restrictions on enrollment
by undergraduates. But undergraduates must fill out a form that
can be found by going from the department home web page
to "courses", then "enrollment" then "availability updates".

**Recommended Texts (available free on-line):**

Real and Functional Analysis 3rd ed. by Serge Lang, Springer-Verlag

Basic Real Analysis by Anthony Knapp, Birkhauser.

Advanced Real Analysis by Anthony Knapp, Birkhauser.

Analysis Now by Gert K. Pedersen, Springer-Verlag.

Measure Theory by Paul Halmos, Springer-Verlag (a classic).

Real Analysis for Graduate Students by Richard F. Bass.

Functional Analysis by Richard F. Bass.

General Topology by John L. Kelley (a classic).

General Topology, Chapters 1-4, by N. Bourbaki (the original classic)

Measure, Integration & Real Analysis by Sheldon Axler

Real Analysis by Bruce Blackadar. This is a preliminary version of a remarkable book-in-progress.

The Lang text gives a presentation
of the material that is somewhat closer to that which
I will give than do the other texts.

My understanding is that through an agreement
between UC and the publishers, chapters of the texts by
Lang, Knapp, Pedersen and Halmos are available
for free download by students. You can find the chapters
of the Lang text
here,
and chapters of the Knapp texts
here, and
here, chapters of the Pedersen text
here,
and chapters of the Halmos text
here.
You may need to use campus computers to authenticate yourself
to gain access.

Links for the six free on-line books are:
Bass Real Analysis,
Bass Functional Analysis,
Kelley Topology,
Bourbaki General Topology,
Axler Measure Integration Real Analysis, and
Blackadar Real Analysis.
The link for ancient lecture notes of mine on measures and integration
can be found at the bottom of my home web page.

**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.
Even more, if students collaborate in working out solutions,
or get specific help from others, they should explicitly acknowledge
this help in the written work they turn in.
This is general scholarly best practice. There is no penalty for acknowledging
such collaboration or help.

There will be a **final examination**, on **Tuesday, December 14,
from 3 to 6 pm**,
which will count for
35% of the course grade. There will be a **midterm exam**,
at the regular class time,
on **Tuesday, October 19**.
It will count for 15% of the course grade.
Here is a sample midterm exam.
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 persuasive doctor's note or equivalent in order to try to avoid a score of 0.

**Comments:** Students who need special accommodation for
examinations should bring me the appropriate paperwork, and must tell me
somewhat more than a week in advance of each exam what accommodation
they need for that exam,
so that I will have enough time to arrange it.

**Problem sets:**
We will use GradeScope for posting
the problem sets and for uploading the solutions.

The above procedures are subject to change.

**Using TEX:** I encourage students to write up their problem-set solutions in TEX,
more specifically LATEX. (But I do not require this.)
LATEX is a powerful mathematical typesetting program which is widely
used in the sciences, engineering, etc., for documents that use a lot of mathematical symbolism.
Thus learning to use TEX is a valuable skill if you work in such fields.

You can freely download versions of TEX onto your computer.

If you use Mac OS, you can find it at MacTex.

If you use Windows, you can find it at proTeXt.

The best way to start learning TEX is not by trying to compose the long header, but rather by
having a file that already has a header, and then gradually modifying that file as you learn how TEX works.

To obtain such a TEX file with a header, click LATEX-sample .
Make a copy to play with, once you have downloaded TEX onto your computer.
At first, don't modify anything above "\begin{document}".
Since the output from TEX is a PDF file that can be directly uploaded to GradeScope,
this would eliminate the need to scan pages of paper for uploading to GradeScope.

This page was last updated on 09/01/2021