### MAT 544 Problem Sets Real Analysis I

Fall 2011

There will be 10 problem set. Problems due one week will often practice material covered in previous weeks. It is important to do the problems in a timely manner; do not postpone problems until the last minute.

### UNDER NO CIRCUMSTANCES WILL LATE HOMEWORK BE ACCEPTED.

In exceptional circumstances such as a documented medical absence, etc., the instructor will drop the missing problem set and compute the problem set total using the remaining problem sets.

You are encouraged to work with other students in the class, but your final write-up must be your own and must be based on your own understanding. Moreover, write-ups must be legible, etc. Write-ups which prove too difficult to read may be marked incorrect or may be returned to the student to be rewritten. All questions regarding grading of a problem set should be addressed to the instructor in a timely fashion.

In the assignments below, please work through all problems. Please direct any questions regarding problem sets to your instructor.

• Problem Set 1 is here. This problem set is due Thursday, September 8th. The solutions to the problem set are here.
• Problem Set 2 is here. This problem set is due Thursday, September 15th. The solutions to the problem set are here.
• Problem Set 3 is here. This problem set is due Thursday, September 22th. The solutions to the problem set are here.
• Problem Set 4 is here. This problem set is due Thursday, October 6th. The solutions to the problem set are here.
• Problem Set 5 is here. This problem set is due Thursday, October 13th. The solutions to the problem set are here.
• Problem Set 6 is here. This problem set is due Thursday, October 20th. The solutions to the problem set are here.
• Problem Set 7 is the following 5 exercises from Folland.
p. 24: Exercise 4.
p. 27: Exercises 11, 12, 13.
p. 32: Exercise 17.
This problem set is due Thursday, October 27th.
• Problem Set 8 is the following 5 exercises from Folland.
p. 32: Exercises 18, 19.
p. 39: Exercises 29, 30.
p. 48: Exercise 3.
This problem set is due Thursday, November 10th.
• Problem Set 9 is the following 5 exercises from Folland.
p. 48: Exercises 4, 7.
p. 52: Exercises 14, 15 (do not simply cite the Dominated Convergence Theorem).
p. 59: Exercise 19.
This problem set is due Thursday, November 17th.
• Problem Set 10 is the following 5 exercises from Folland.
p. 59-60: Exercises 22, 23, 26.
p. 63: Exercises 32, 42.
This problem set is due Thursday, December 1st.

Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr