**Fall 2024**

**Instructor:** Marc Rieffel

**Lectures:** MWF 10:10-11:00, Etcheverry 3108

**Course Control Number:** 22022

**Office:** 811 Evans

**Office Hours:**TBA

** GSI:** TBA

**Office:** TBA

**Office Hours:** TBA

**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 "enrollment guidelines".

**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 by Nicolas Bourbaki (a classic. Read "Advice to the reader".)

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, the texts by
Lang, Knapp, Pedersen, Halmos and Bourbaki are available
for free download by UC students. You can find the
the Lang text
here,
and the Knapp texts
here, and
here, and the Pedersen text
here, and the Halmos text
here, and the Bourbaki text
here.
You may need to use campus computers to authenticate yourself
to gain access.

Links for the five free on-line books are:
Bass Real Analysis,
Bass Functional Analysis,
Kelley 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.

The above procedures are subject to change.

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 or Linux, go to
Latex-project.

The best way to start learning TEX is not by trying to compose the long header
that is needed, 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 04/28/2024