Math 629, Spring 2020 - Introduction to Measure and Integration

Instructor: Joris Roos
Office hours: Friday 10-11 am 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 22-24: Introduction
Week 2, Jan 27-31: Measures, premeasures & outer measures (Ch. 6.1.1, 6.1.3, also see Ch. 1.1-1.3)
Week 3, Feb 03-07: Extension theorem, metric exterior measures (Ch. 6.1.3, 6.1.2, also see Ch. 1.1-1.3)
Week 4, Feb 10-14: Properties of Lebesgue measure, simple functions, measurable functions (Ch. 6.2, also see Ch. 1.4)
Week 5, Feb 17-21: Measurable functions, definition of integral (Ch. 6.2, also see Ch. 1.4, 2)
Week 6, Feb 24-28: Definition of integral, convergence theorems (Ch. 6.2, also see Ch. 2)
Week 7, Mar 2-6: Lp spaces (Notes), product measures (Ch. 6.3.1, also see Ch. 2.3)
Week 8, Mar 9-11: Fubini's theorem, polar coordinates (Ch. 6.3.1, Ch. 6.3.2, also see Ch. 2.3)
Week 9, Mar 23-27: Differentiation of the integral: Hardy-Littlewood maximal function, Vitali covering lemma (Ch. 3.1)
Week 10, Mar 30-Apr 3: Lebesgue differentiation theorem, approximation of identity (Ch. 3.1, 3.2)
Week 11, Apr 5-9: Approximation of identity, Fourier transform (Ch. 3.2, 2.4)
Weeks 12, 13, Apr 13-24: Hilbert spaces (Ch. 4)
Week 14, Apr 27-May 1: Ergodic theory (Ch. 6.4) - not relevant for the final exam


Prerequisites: Basic analysis (Math 521, 522).
Number of credit hours: 3 (three 50-minute class periods every week)

Effective Monday, March 23, instruction will happen online. See e-mail for invitation link.

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
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: Friday, March 13 in class.
Final: Sunday, May 3, 2:45pm-4:45pmonline

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: there is an automatic grace period. Late homework may be turned in at the latest on the Wednesday following the respective due date (in class). No late homework will be accepted after that time!

Homework will be graded for completeness and one or two selected problems on each sheet will be graded for correctness.

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!).