**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