Measure and Integration II
Course Information and Syllabus, Spring 2002
Text:Measure
Theory and Probability by M. Adams and V. Guillemin, Wadsworth &
Brooks, 1996 
Prerequisites: Graduate standing, exposure to advanced calculus and basic course in probability, MTH 535
Exams and Grading:
Course grade will be determined based on homework and
mid-term and final exams:
Homework: 40 %
Exams:
60 %
The exams will be of the take home variety.
The topics that will be covered are:
Application of Measure and Integration Theory to Probability
Theory: Random Variables, Expectations, Independence, and Central Limit
Theorem
Application of Measure and Integration Theory to Fourier
Analysis
Application to Fractal Geometry : Hausdorff Measure and
Dimension
Application to the Analysis of Chaotic Signals
Application to Some Problems in Ordinary Differential
Equations: Existence Problems and Asymptotic Behavior of Solutions
Computer Requirements
The use of computer algebra systems such as MATHEMATICA,
MAPLE,
and Scientific Notebook is encouraged. Some MATHEMATICA
and/or MAPLE notebooks will be provided and demonstrated in the
class.
Some of the problems may need MAPLE or MATHEMATICA
to be solved effectively.
Instructor: Dr. M. Kulenovic,
Phone: 44436
e-mail: kulenm@math.uri.edu
Online information: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm
Office: Tyler 216
Office hours: MWF 11-12 and by appointment. 
Time: Tyler 260
Place:
MW 12:30-1:45