Spring 2020 MATH 202B 001 LEC

Introduction to Topology and Analysis
Schedule: 
SectionDays/TimesLocationInstructorClass
001 LECTuTh 09:30AM - 10:59AMCory 241Marc A Rieffel20484
UnitsEnrollment StatusSession
4Open2020 Spring, January 21 - May 08
Additional Information: 

Prerequisites: Math 202A or equivalent. I have no restrictions on enrollment by undergraduates. See Math department staff advisors for any needed enrollment codes. Students who did not take Math 202A last Fall and want to enroll in this Math 202B should have a solid understanding of the following parts of the Lang text listed below: Chapter II, Section 3 of Chapter III, and Sections 1-8 of Chapter VI.

Office: 811 Evans 

Office Hours: TBA 

Description: This course, and Math 202A, are "tool courses", in that they cover some basic mathematical concepts that are of importance in virtually all areas of mathematics and its applications. Our Math 202B will follow on from where we left off at the end of Math 202A. The topics we will discuss include: The Hahn-Banach Theorem, duals of Banach spaces and weak topologies, Krein-Milman Theorem, Hilbert spaces, the Radon-Nikodym Theorem, Stone-Weierstrass Theorem, signed measures, Radon measures, operators on Banach and Hilbert spaces, additional topics as time allows. 
In my lectures I will try to give careful presentations of the material, well-motivated with examples.

Recommended Texts:  (available free on line for UCB students): See course web page, including for the Lang text.  

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 Wednesday May 13, 11:30-2:30 PM, which will count for 35% of the course grade. There will be a midterm exam, which 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 try to avoid a score of 0.

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

Using TEX: I encourage students to write up their problem-set solutions in TEX, more specifically LATEX. This 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. For more information about this see the course web page.

Comment: The above procedures are subject to change.

Course Webpage: math.berkeley.edu/~rieffel