Math 629, Spring 2019 - Introduction to Measure and Integration
Instructor: Joris Roos
Office hours: Friday 1-2pm in Van Vleck 513
E-Mail: jroos at math...
Lectures: MWF 12:05pm-12:55pm in Van Vleck B115
Course content: Measure and integration theory.
Textbook:
This course will mostly follow the textbook Real Analysis by E. M. Stein and R. Shakarchi.
- Week 1 (Jan 23): The problem of measure & motivation (Introduction, Ch. 1.1)
- Week 2 (Jan 28): Exterior/outer measure (Ch. 1.2)
- Week 3 (Feb 04): Measurable sets (Ch. 1.3)
- Week 4 (Feb 11): Measurable functions (Ch. 1.4)
- Week 5 (Feb 18): The Lebesgue integral (Ch. 2.1)
- Week 6 (Feb 25): L^p spaces (Lecture notes)
- Week 7 (Mar 04): Fubini's theorem (Ch. 2.3)
- Week 8, 9 (Mar 11): Differentiation of the integral (Ch. 3.1, 3.2)
- Week 10, 11, 12 (Apr 01): BV functions (Ch. 3.3)
- Week 13, 14 (Apr 22): Hilbert spaces, L^2 (parts from Ch. 4 & 5), Review
Prerequisites: Basic analysis (Math 521, 522).
Number of credit hours: 3 (three 50-minute class periods every week)
Piazza: Piazza is an online Q&A platform for discussions among students and instructors, click here.
Please refrain from discussions of grades or grading policies on Piazza. Talk to me directly if you have any questions on grading.
Canvas: You will be able to look up your homework and exam scores on Canvas: click here.
Grading
Your grade will be determined based on your performance on
- homework assignments (30%),
- one midterm exam (30%),
- and the final exam (40%).
Grading errors: If you believe that there has been a grading error, please come talk to me after class. Verify in a timely manner that your grades are being entered correctly into learn@uw.
Honors students: There will be extra honors problems included in the homework assignments. You are expected to at least make an attempt at solving each of them.
Exams
Midterm: Wednesday, March 13 in class.
Final: Tuesday, May 7, 2:45pm-4:45pm, Room: VV B115
If you know of conflicts with any of the exam dates, notify me immediately. There will be no makeup examinations, except in justified cases.
Cheating will not be tolerated.
Homework
Homework will be assigned weekly and is to be turned in on the due date in class. There will be no makeup assignments. Late homework is not accepted. Homework will be graded for completion and one or two selected problems on each sheet for accuracy.
You are encouraged to work in small groups, but each student must hand in the solution written neatly and in their own words. Please staple your solutions and write your name on the top of every page.
Cite all sources that you used (books, internet resources). Copying a solution from a peer, a book or the internet is cheating. Give appropriate credit to everyone that helped you with the solution (including your peers!). Citing and giving credit will not affect your grade negatively (but not doing so will if discovered!).
- Homework 1 Due Monday, 2/4
- Homework 2 Due Monday, 2/11
- Homework 3 Due Monday, 2/18
- Homework 4 Due Monday, 2/25
- Homework 5 Due Monday, 3/04
- Homework 6 Due Monday, 3/11
- Homework 7 Due Monday, 3/25
- Homework 8 Due Monday, 4/1
- Homework 9 Due Monday, 4/8
- Homework 10 Due Monday, 4/15
- Homework 11 Due Monday, 4/22