# Fall 2014 MATH 202A 001 LEC

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

001 LEC | MWF 1-2P | 20 BARROWS (effective 09/05/14) | RIEFFEL, M A | 54419 |

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

4 | 12: WEDNESDAY, DECEMBER 17, 2014 7-10P | Limit:71 Enrolled:58 Waitlist:0 Avail Seats:13 [on 10/09/14] |

**Prerequisites:** 104 or equivalent preparation in analysis. Further experience with upper-division mathematics courses such as Math 142 or 185, including writing proofs, is strongly recommended.

**Syllabus:** Metric spaces and general topological spaces. Compactness and connectedness. Quotient topologies. Theorems of Tychonoff, Urysohn, Tietze. Complete spaces and the Baire category theorem. Function spaces; Arzela-Ascoli and Stone-Weierstrass theorems. Partitions of unity. Locally compact spaces; one-point compactification. Introduction to measure and integration. Sigma algebras of sets. Measures and outer measures. Lebesgue measure on the line and Rn.

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

**Office:** 811 Evans

**Office Hours:** TBA

**Required Text:** None

**Recommended Reading:**

The two texts whose treatment is closest to my approach to the topics of the course are:

Topology, 2nd Ed., J. R. Munkres, Prentice Hall, 2000

Real and Functional Analysis, 3rd Ed., S. Lang, Springer-Verlag, 1993

Students may also find useful the classic text General Topology by J. L. Kelley.

**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 **WEDNESDAY, DECEMBER 17, 2014 7-10PM**, 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.

**Course Webpage:** http://math.berkeley.edu/~rieffel/202AannF14.html