MATHEMATICS 515-Fall, 2005

Real Analysis

Carver 196

Instructor: Howard A. Levine , Department of Mathematics, 410 Carver

Office Hours: M-W 10-10:50 AM,  Tu 1-1:2 or by appointment

Phone 515-294-8145, e-mail: halevine@iastate.edu

Textbook: No official textbook. 

Other References:

Royden:  Real Analysis
Rudin:  Real and Complex Analysis
Titchmarsh: The Theory of Functions
Halmos: Measure Theory
Munroe: Measure and Integration
Bartle: The Elements of Integration
Friedman: Foundations of Modern Analysis
Depree and Schwartz: Introduction to Real Analysis

Grading: Homework: 40%, Midterm 20% and Final: 40%

The grade will be determined from, homework, (200 pts.) the mid term, (100 pts.) and the in class final (200 pts.) and the homework assignments (200 pts.). (There will be about eight to ten such assignments each consisting of four or five problems.) Half of the homework assignments are to be regarded as "take home exams" for which you may consult other (non human) sources. (Those that are to be so regarded will be clearly marked as such.) For the remaining homework assignments, you are encouraged to engage in discussions with your classmates although the final write up must be in your own words.

NOTE: Although each problem set will have as many as five or six problems, I will only grade one or two from each set. I will determine which of them after I collect the sets.


While I expect the solutions to be written up in AMS-TEX. Failure to do so after the first two problem sets will result in a ten percent reduction in points on the offending sets.

Content of the Course


The content for this course is to be found in in Titchmarsh (10-13) and Rudin (Chapters 1-9). I have not placed Titchmarsh on reserve but there is a copy or two in the Math Reading Room. Please do not remove them from there so that all may share.

The material for these two courses will come: from Titchmarsh:

Chapter 10. The theory of measure and the Lebesgue Integral (515)
Chapter 11. Differentiation and Integration(515)
Chapter 12. Further Theorems on Lebesgue Integration(515)


and from Rudin:

Chapter 1. Abstract Integration(515)
Chapter 2. Positive Borel Measures(515)
Chapter 3. Lp Spaces(515)


as well as supplemental material on metric space topology (515) to be given in class lectures. 


Homework problem sets are given below. All files are in pdf format. Due dates for each set are at the top of each page.

Problem sets will be added to the list from time to time. Check back frequently.

Math 515 Problem sets.

Problem Set 1.
Problem Set 2.
Problem Set 3.
Problem Set 4.
Problem Set 5.
Problem Set 6.
Problem Set 7.
Problem Set 8.



Here is the link to the mid term exam for Math 515. No books except class texts, no internet and no human sources allowed!
Take Home Midterm for 515




 

FINAL EXAMINATION INFORMATION:



For Math 515:  TBA