Schedule (subject to change, last updated 10/13/21)

As of October 13, we’re one class meeting behind the schedule below.

Required readings are from Jacod and Protter, Probability Essentials, 2nd edition (2004).

Class meeting	Date	Notes	Topics	Readings (required)	Readings (supplemental)	Assignments (out)	Assignments (due)
1	9/8		Intro & logistics; big picture	Ch. 1
2	9/13		Axioms	Ch. 2
3	9/15		Basic probability	Ch. 3-4		Assignment 1
4	9/20		Random variables on countable spaces	Ch. 5
5	9/22		Construction of a probability measure	Ch. 6		Assignment 2	Assignment 1
6	9/27		Construction of a probability measure on the real line	Ch. 7
7	9/29		Random variables	Ch. 8		Assignment 3	Assignment 2
8	10/4		Integration and expectation - part 1	Ch. 9
9	10/6		Integration and expectation - part 2	Ch. 9			Assignment 3
-	10/11		No class
10	10/13		Independent random variables	Ch. 10		Assignment 4
11	10/18		Probability distributions on the real line, R	Ch. 11
12	10/20		Probability distributions on Rn	Ch. 12		Assignment 5	Assignment 4
13	10/25		Probability distributions continued, review
14	10/27		TBD, midterm (take-home)				Assignment 5
15	11/1		Characteristic functions and sums of random variables	Ch. 13-15
16	11/3		Gaussian random variables	Ch. 16		Assignment 6
17	11/8		Convergence of random variables	Ch. 17
-	11/10		No class
17	11/15		Weak convergence	Ch. 18
18	11/17		Weak convergence and characteristic functions, laws of large numbers	Ch. 19-20		Assignment 7	Assignment 6
19	11/22		Central Limit Theorem	Ch. 21
20	11/24		L2 and Hilbert spaces	Ch. 22		Assignment 8	Assignment 7
21	11/29		Conditional expectation! - part 1	Ch. 23
22	12/1		Conditional expectation! - part 2	Ch. 23			Assignment 8
23	12/6		Conditional probability, Markov kernels, etc.	tbd