# Spring 2012 MATH 202B 001 LEC

Section | Days/Time | Location | Instructor | CCN |
---|---|---|---|---|

001 LEC | MWF 8-9A | 740 EVANS | RIEFFEL, M A | 54494 |

Units/Credit | Final Exam Group | Enrollment |
---|---|---|

4 | 1: MONDAY, MAY 7, 2012 8-11A | Limit:35 Enrolled:21 Waitlist:0 Avail Seats:14 [on 05/03/12] |

**Office:** 811 Evans

**Office Hours:** TBA

**Prerequisites:** Math 202A or equivalent preparation in analysis. Notice that some measure and integration will have been covered in Math 202A.

**Recommended Reading:**

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.

**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. In my lectures I will try
to give well-motivated careful presentations of the material.

**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.

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**.
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.

**Homework:**They will be posted at Homework as they are assigned.

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

The above procedures are subject to change.