Probability Theory

Department: 
MATH
Course Number: 
3235
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Fall and Spring Semesters; Some Summers

This course is a mathematical introduction to probability theory, covering random variables, moments, multivariate distributions, law of large numbers, central limit theorem, and large deviations.

MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses. 

Prerequisites: 

(MATH 2551 or MATH 2X51 or MATH 2561 or MATH 2401 or MATH 24X1 or MATH 2411 or MATH 2605 or MATH 2550) AND (MATH 2106 or CS 2051 or MATH 3012)

Course Text: 

G. Grimmett and D. Welsh, Probability: An Introduction.

Topic Outline: 

Topics will include the following basic results and methods of both discrete and continuous probability theory:

  • The probability framework

  • Conditional probability

  • Bayes’ theorem

  • Independent events

  • Random variables

  • Joint distributions

  • Expectations, variance, covariance

  • Convergence in probability and in distribution

  • Law of Large Numbers

  • Central Limit Theorem

  • Large deviations

Instructors may cover additional topics including but not restricted to:

  • The arcsine law

  • Galton-Watson processes

  • Order statistics