Fall 2018
Meetings: TR 1PM2:15PM, Van Hise 115
Instructor: David Anderson
Office: 617 Van Vleck
Email: anderson@math.wisc.edu
Office hours: W 1:00PM2:00PM or by appointment
I will use the class email list to send out
corrections, announcements, please check your wisc.edu email
from time to time.
If you try to register, you may find the class full. In that case sign up for the waitlist. Waitlisted students will typically find a place in the course eventually, and you may also attend lectures in the meantime (assuming there is space in the classroom).
Measure theory is a basic tool for this course. A suitable background can be obtained from Math 629 or Math 721. Chapter 1 in Durrett covers the measure theory needed. We will very briefly review some measure theory at the beginning of the semester. Prior exposure to elementary probability theory could be useful.
Foundations, properties of probability spaces 
laws of large numbers 
Characteristic functions, weak convergence and the central limit theorem 
Conditional expectations 
Martingales 
Markov chains (time permitting) 
Course grades will be based on biweekly (once per two weeks)
homework assignments (30%), a midterm exam (30%) and the final
exam (40%). We will have an evening midterm exam on Monday,
October 29th, 7:15pm8:45pm. In exchange, the class on
Tuesday, October 30th will be canceled. The room
for the first exam is B239 in Van Vleck Hall.
Final exam: Saturday, December 15, 10:05am  12:05pm, room is
Psychology 107.
We will use the software Gradescope, which is already being succesfully tested in other courses here at UWMadison. The advantages for you are the following:
Covered
topics 
Suggested
reading for next week 

Week
1. 9/6 
Introduction and
Probability space. Sections 1.1. 
Sections
1.1  1.7 
Week
2. 9/11, 9/13 
Finish
chapter 1. Sections 1.11.7. 
Sections 2.1 
Week
3. 9/18, 9/20 
Finish chapter 1.
Begin Independence Tuesday: Finish chapter 1. Thurs: Independence (Section 2.1) 
Section 2.2 
Week
4. 9/25, 9/27 
Independence and the weak
law of large numbers Sections 2.1 and 2.2 
Sections
2.3, 2.4, and 2.5 
Week
5. 10/2, 10/4 
Weak law and
BorelCantelli, strong law if time Sections 2.2, 2.3, and 2.4 
Sections 2.4  2.7 
Week
6. 10/9, 10/11 
Strong law of large
numbers, renewal theory or large deviations(?) Sections 2.4  2.7 
Sections 3.1  3.2 
Week
7. 10/16, 10/18 
Weak convergence Sections 3.1 and 3.2 
Section 3.3 and 3.4 
Week
8. 10/23, 10/25 
Characteristic functions
and CLTs Sections 3.3 and 3.4 
Sections
3.3 and 3.4 
Week
9. 10/29, 11/1 
midterm
(Monday night), 10/30 class canceled, Central limit theorem, LindebergFeller Sections 3.3 and 3.4 
Section 3.4
and 3.6 and 3.7 
Week
10. 11/6, 11/8 
Finish LindebergFeller,
Poisson convergence Section 3.4, 3.6 
Section 3.7 
Week
11. 11/13, 11/15 
Poisson processes Sections 3.7 + extra material 
Section 4.1 
Week
12. 11/20 
Conditional
expectation. Thanksgiving (no
class Thursday) Section 4.1 
Sections 4.1  4.3 
Week
13. 11/27, 11/29 
Conditional expectation,
Martingales, and convergence Sections 4.1, 4.2, and 4.3 
Section 4.4 and 4.5 
Week
14. 12/4, 12/6 
Doob's inequality, square
integrable Martingales Sections 4.4 and 4.5 
Sections 4.6, 4.7, and 4.8 
Week
15. 12/11 
UI, Backwards Martingales,
Optional Stopping Sections 4.6, 4.7, and 4.8 
N.A. 