Detailed Lecture Schedule:


	1. Fundamentals 

Sep 06	1.1 Overview 
Sep 09	1.2 Measure
Sep 13	1.3 Lebesgue integral
Sep 16	1.4 Random variables and independence

	2. Weak Laws  

Sep 20	2.1 L^2 weak law
Sep 27	2.2 Triangular arrays, truncation, and classical weak law

	3. Almost Sure Convergence

Sep 30	3.1 Borel Cantelli 
Oct 07	3.2 Strong Law
Oct 14	3.3 Convergence of Random Series

	4. Large Deviations

Oct 18	4.1 Upper bound
Oct 18	4.2 Radon-Nikodym derivatives
Oct 21	4.3 Lower bound 
Oct 21	4.4 Condition on a large deviation for the sum
Oct 21	4.5 Multidimensional large deviations

	5. Convergence in Distribution

Oct 25	5.1 Two equivalent definitions
Oct 25	5.2 Tightness/compactness
Oct 25	5.3 Metrizability

	6. Characteristic Functions

Oct 28	6.1 Definition, properties and examples
Oct 28	6.2 Inversion
Nov 01	6.3 Tighness and continuity theorem
Nov 01	6.4 Moments and derivatives

	7. Central Limit Theorems

Nov 04	7.1 Classical CLT: IID finite variance
Nov 04	7.2 Triangular arrays (Lindeberg-Feller):
Nov 08	7.3 Local CLT for lattices
Nov 08	7.4 Further statements: non-lattice CLT, Berry-Esseen
Nov 08	7.5 Multivariate CLT

	8. Poisson convergence and Poisson processes

Nov 11	8.1 Poisson convergence
Nov 11	8.2 Total variation distance
Nov 11	8.3 Arratia-Goldstein-Gordon-Chen-Stein bounds (time permitting)
Nov 15	8.4 Poisson processes
Nov 15	8.5 Poissonization (time permitting)

	9. Summed Poisson processes

Nov 18	9.1 Adding up the points
Nov 22  9.2 Infinitely divisible processes and Levy processes
Nov 25	9.3 Stable laws

	10. Random walks and stopping times

Dec 02	10.1 Stopping times
Dec 06	10.2 Wald's identity
Dec 06	10.3 Recurrence and transience
Dec 09	10.4 Occupation results in one dimension