**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: 50 %

Exams:
50 %

The exams will be of the take home variety.

The topics that will be covered are:

L^{1 }and L^{2 }
theory, Geometry of Hilbert spaces

Application of Measure and Integration Theory to Probability
Theory: Central Limit
Theorem

Application of Measure and Integration Theory to Fourier Analysis: Fourier series

Application to Fractal Geometry : Hausdorff Measure and Dimension, IFS

Application to Ergodic Theory: Invariant Measures, Birkhoff Ergodic Theorem

Application to Some Problems in Ordinary Differential Equations: Existence Problems and Asymptotic Behavior of Solutions

The use of computer algebra systems such as
** MATHEMATICA, MAPLE**
is encouraged. Some

Some of the problems may need

Here is a sample of images that can be easily produced by the software that will be used in this course. See also Dynamica.

**Useful links**:

Measure Theory at Harvard University

S.
Zakeri collection of solved problems

**Instructor**: Dr. M. Kulenovic,

Phone: 874-4436

e-mail: kulenm@math.uri.edu
**Online information**: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm

**Office: **Tyler 216
**Office hours**: MTW 1-2 and by appointment.

**Time**: MW 3-4:15

**Place**: