Math 426A/576A: Fundamental Concepts of Analysis III

Spring 2009

Instructors: Zhen-Qing Chen

Phone: (206) 543-1907 (Office)
Fax: (206) 543-0397
Office: Padelford Hall, Room C525
Email: zchen at math.washington.edu

Teaching Assistant: Mauricio Duarte, maduarte at math.washington.edu (Office hours: Wednesdays 2:30-3:30 pm. and Thursdays 10:30-11:30pm at Math Lounge in PDL across the main office of the Mathematics Department. Effective from May 11, 2009)

Lectures: MWF 11:30 a.m.-12:20 p.m. at GLD 435.

Office Hours: Mondays and Wednesdays: 4:00-4:50 pm. at Padelford C-525.

Prerequisites:

2.0 or better in MATH 425/M575.

Course Outline:

This course continues Math 424/574-425/575 and provides an introduction to measure theory and integration. The following is a tentative plan.

Weeks 1-2: Introduction, Measurable Functions, Measures (Chapters 1-3)
Weeks 3-4: Generation of Measures, Lebesgue Measure (part of Chapters 9, 11-17)
Weeks 5-6: Integral, Integrable Functions (Chapters 4-5)
Weeks 7-8: Lebesgue Spaces $L^p$, Modes of Convergence, Decomposition of Measures
Weeks 9-10: Product Measures (Chapter 10), Review

Some adjustment may be made as the course goes.

Homework:

There will be weekly homework assignments throughout the quarter. The most important function of the homework is to help you to internalize concepts, develop problem solving skills and the ability to write mathematically rigorous proofs. Homework problems will be collected at the beginning of the Friday's class. A selective of the homework problems will be graded by a TA. Homework will count for 30\% of the final grade of this course. No late homework will be accepted. However the homework set with lowest score will be dropped in calculating the final grade. Please write legibly and staple your homework and clearly mark it with your name.

Examinations:

During the quarter, there will be one take-home midterm exam and one comprehensice final exam. No makeup exams will be given . For documented illness or real emergency, it will be treated on a case by case basis. Malfunctioning alarm clocks and missed buses are not such emergencies. So please plan ahead.

Examination Dates:

Take-home Midterm Exam: Given on Monday, May 4, 2009 and due at the beginning of the class on Friday, May 10, 2009.
Final Exam: Wednesday, June 10, 2009, 2:30--4:20 pm. at GLD 435.

Grading Policy:

Homework (30%), Take-home Midterm Exam (30%), and Final exam (45%). Your grade for this course will be based on the sum of these scores.