Math 563 - Topics

The nominal text for the course is Probability : theory and examples by Durrett. The following is my best guess at the start of the semester of what we will cover.

The number in parentheses is the corresponding section in Durrett.

Basic defs - probability measures, distributions (1.1)
Random variables (1.2)
Expected value (1.3)
Independence (1.4)
Weak law of large numbers (1.5)
Borel-Cantelli lemma (1.6)
Strong law of large numbers (1.7)
Large deviations (1.9)
Weak convergence (2.2)
Characteristic functions (2.3)
Central limit theorem (2.4)
Poisson convergence (2.6)
Conditional expectation (4.1)
Central limit theorem in R^d (2.9)
Stable laws (2.7)