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
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:
Basic Construction of Lebesgue Measure. Lebesgue Integrals. Convergence in measure. Various Limiting Theorems.
Application of Measure and Integration Theory to Probability Theory: Random Variables and Expectations. Laws of Large Numbers.
Application of Measure and Integration Theory to Fourier Analysis
Application to Some Problems in Ordinary Differential
Equations: Existence Problems and Asymptotic Behavior of Solutions
The use of computer algebra systems such as MATHEMATICA,
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,
Online information: www.math.uri.edu/courses or www.math.uri.edu/~kulenm
Office: Tyler 216
Office hours: MWF 11-12 and by appointment.
Theory at Harvard University