Fall 2018 MATH 202A 001 LEC

Introduction to Topology and Analysis
001 LECMoWeFr 09:00AM - 09:59AMEvans 60Marc A Rieffel22409
UnitsEnrollment Status
Additional Information: 

Prerequisites:  Math 104 and considerable experience with other upper-division mathematics courses and with writing proofs. Math 105, 142 and 185 give especially useful preparation. I have no restrictions on enrollment by undergraduates. See Math department staff advisors for any needed enrollment codes.

Description: This course and Math 202B are "tool courses", in that they cover some basic mathematical concepts that are of importance in virtually all areas of mathematics and its applications. In Math 202A these include: Metric spaces and general topological spaces, compactness, theorems of Tychonoff, Urysohn, Tietze, locally compact spaces; an introduction to general measure spaces and integration of functions on them, with Lebesgue measure on the real line as a key example; function spaces and the very beginnings of functional analysis. In Math 202B most of these topics will be developed further, especially measure and integration, and functional analysis.

Office: 811 Evans Hall

Office Hours: TBA

Recomended Texts: 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,

The Lang text gives a presentation of the material that is somewhat closer to that which I will give than the other texts. My understanding is that through an agreement between UC and the publishers, chapters of the Lang text, the Knapp texts, and the Pedersen text are available for free download by students. You may need to use campus computers to authenticate yourself to gain access.  

Grading and Homework: 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, which will count for 35% of the course grade. There will be a midterm exam, at the regular class time, 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.

Course Webpage: There is a link to the course webpage on my homepage: math.berkeley.edu/~rieffel