MTH 536
Measure and Integration II

Course Information and Syllabus, Spring 2003

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:

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.

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
 

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:

Place: