Spring 2012 MATH 202B 001 LEC

Introduction to Topology and Analysis
Schedule: 
SectionDays/TimeLocationInstructorCCN
001 LECMWF 8-9A 740 EVANSRIEFFEL, M A54494
Units/CreditFinal Exam GroupEnrollment
41: MONDAY, MAY 7, 2012 8-11ALimit:35 Enrolled:21 Waitlist:0 Avail Seats:14 [on 05/03/12]
Additional Information: 

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.