MATHEMATICS 515-Fall, 2008
Real Analysis
Carver 268
Instructor: Howard A. Levine , Department of Mathematics, 410 Carver
Office Hours: or by appointment
Textbook: Royden: Real Analysis
Other References:
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.) . (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.
I expect the solutions to be written up in some version of TEX and
solutions e-mailed to me in .pdf format. 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 of this course is part of the
real analyisis qualifing examination. Therefore we will strictly
adhere to the following syllabus.
Real Analysis
A detailed daily syllabus can be found at common syllabus.
1. Chapter 1, sections 4-9
2. Chapter 2, parts of sections 4,5,7
3. Chapter 3, Lebesgue measure
4. Chapter 4. The Lebesgue integral
5. Chapter 5. Differentiation and Integration
6. Chapter 6. The Classsical Banach Spaces
7. Chapter 7. Metric Spaces
Homework problem sets are given below. All
files are in pdf format. Due dates for each set
are at the top of each page. Late homeworks carry a 20% penalty.
Problem sets will be added to the list from time to time. Check back frequently.
Problem set 1. Problem set 2. Problem set 3 .
Problem set 4. Problem set 5. Problem set 6.
Problem set 7, Problem set 8. Problem set 9.
FINAL EXAMINATION INFORMATION:
For Math 515: TBA