Goals:
The goals of this course are to give the students the
mathematical preparation to pass written exams in real analysis and/or
pursue a master's theses in which prior knowledge into real analysis is
required.
Texts (required):
- An Introduction to Lebesgue Integration and Fourier
Series, Howard J. Wilcox and David L. Myers, Dover
Publications.
- Measure and Integral: An Introduction to Real
Analysis, Richard L. Wheeden and Antoni Zygmund, Dekker.
This course will cover
- W&Z Chapters 3,4,5 and part of 6
- W&M Chapters 2,3,4,5 and 6
Assignments:
Homework: Expect daily homework
assignments. I plan to assign exercises from the
texts as well as assignments in which you read, understand and discuss
material from the two texts. The homework assignments will be
graded subject to the following rules:
- A problem
completed correctly and on time will receive 10 points.
- A problem
completed correctly and up to
one week late
will receive 8 points. (I really want
you to do the homework!!)
- An incorrect
problem (one which is either mathematically wrong or written poorly)
will receive partial credit and may be corrected and resubmitted within a
week from when it
is returned for up to 8 points. (In
fact, I really want
you to do the homework correctly!!
Even if you need help or more time.)
Tentative schedule
of topics:
|
1
|
Introduction
|
|
2
|
Outer measure
|
|
|
3
|
|
Lebesgue
measurable sets
|
|
4
|
|
|
5
|
Measurable functions
|
|
6
|
Catch-up and Exam 1
|
|
7
|
Lebesgue integral
|
|
8
|
|
9
|
Convergence Theorems
|
|
10
|
|
|
Spring Break
|
|
11
|
|
|
12
|
Exam 2
|
|
13
|
Fubini’s Theorem
|
|
14
|
|
|
15
|
|
Exams:
Grades:
Distributions.
Homework
|
40% |
| Midterm 1 |
20% |
| Midterm 2 |
20% |
| Final Exam |
20%
|
|