MATH 6337 Real Analysis I
Spring 2014
TTh 12-1:30 Skiles 170
Office Hours: TTh 2:00-3:00 in Skiles 224
If you have problem to meet me during the scheduled or
email me to set an appointment.
Prerequisite
MATH 4317, 4318 (Analysis I, II)
Textbook
Gerald B. Folland, "Real Analysis", Wiley Inter-Science, 2nd Edition.
Will cover chapter 1, 2, and 3 from the book plus other argument using prof. Heil notes and other material.
Material available on line
Professor C. Heil material for Math6337.
Grading
I will collect HW every 2 weeks for a total of 5/6 HW. On top there will be two in class midterms and a in
class final. Midterms and final will be cumulative. The possibility of personal project will be discussed
later during the class. The grading scheme will be 25% HW, 35% midterms and 40% final.
First Midterm: February 18 Second Midterm: March 25
First week
- Material covered
- 0.1-0.6 Prologue
- 1.1 Measure: introduction
- 1.2 Sigma Algebras
- Exercises
Second week
- Material covered
- Exercises
First HW collection on Tuesday January 21nd. Solution set for the first HW.
Third week
- Material covered
- (1.4) Outer Measure: Carathéodory's Theorem
- (1.5) Borel Measure on the Real Line
- Exercises
- (1.4) 18, 19
- (1.5) 28, 32, 33
Fourth week
- Material covered
- (1.5) Borel Measure on the Real Line (continued)
- Exercises
Second HW collection on Thursday February 6th.
Fifth week
- Material covered
- (2.1) Measurable Functions
- (2.2) Integration of Nonnegative Functions
- Exercises
Seventh week
- Material covered
- (2.3) Integration of Nonnegative Functions
- (2.4) Mode of Convergence
- Exercises
- (2.3) 19, 23, 27
- (2.4) 37, 43
First midterm on February 25th.
Practice material 1 and 2 for the Midterm.
Solution set for the first midter.
Third HW collection on Tuesday March 11th.
Eighth week
- Material covered
- (2.5) Product Measures
- (2.6) The n-dimensional Lebesgue Integral
- (2.7) Integration in Polar Coordinates
- Exercises
- (2.5) 47, 50
- (2.6) 56, 59
- (2.7) 64
Fourth HW collection on Teusday April 1st.
Tenth week
- Material covered
- (3.1) Signed Measures
- (3.2) The Lebesgue-Radon-Nikodym Theorem
- Exercises
- (3.1) 3, 6, 7
- (3.2) 8, 12, 17
Last HW collection on Tuesday April 15th
Solution set for the second midter.
Take home midterm due on April 22.