Instructor: Sebastien Vasey

Office: Science Center 321H

Email: `sebv (at) math (dot) harvard (dot) edu`

Office hours: MF 4PM-5PM, SC 321H

Lectures: MWF 12PM-1PM, SC 221

Course assistant: Stefan Gramatovici

Email: `sgramatovici (at) college (dot) harvard (dot) edu`

Problem session: *cancelled*, due to not enough people showing up. If you would like it to start again, please let me know.

Office hours: During math night, M 8PM-10PM, Leverett House Dining Hall

Canvas page (for administrivia, hw solutions)

Do not forget to evaluate the class on the Q!

- April 27, 2018: The final is graded, and solutions are on Canvas. I will have office hours 4-5PM today, feel free to swing by to look at your final.
- April 23, 2018: I am pushing the due date for assignment 12 and the extra credit homework: you have until Friday, 1pm.
- April 20, 2018: I will have additional office hours on Tuesday April 24, 3-4pm (in SC 321H). Stefan will have additional office hours on Tuesday, April 24, 4-5pm (in the math lounge).
- April 18, 2018: Assignment 12 is out.
- April 16, 2018: The extra credit assignment is now due on the last day of class.
- April 11, 2018: Assignment 11 is out.
- April 4, 2018: An extra credit homework has been posted (more on this on Friday).
- April 4, 2018: Assignment 10 is out.
- March 28, 2018: Assignment 9 is out.
- March 26, 2018: Notes on the limit theorems (to be discussed starting Friday) have been added.
- March 21, 2018: Assignment 8 is out.
- March 9, 2018: The midterm has been graded. Your score, as well as the midterm solutions, should be on Canvas.
- March 7, 2018: Assignment 7 is out.
- March 5, 2018: Notes on the two envelopes problem (to be discussed on Wednesday) have been posted.
- March 5, 2018: I will have additional office hours on Wednesday, March 7, 4-5PM in SC 321H. Stefan will also hold office hours this Wednesday 5-6PM, in SC 304.
- March 5, 2018: The midterm is online. It is due Tuesday, before 1pm.
- March 2, 2018: Solutions to assignments 4-5 and the sample midterm are on Canvas.
- February 28, 2018: Assignment 6 and Notes on building probability spaces have been posted.
- February 23, 2018: Information on the midterm and a sample midterm are available.
- February 21, 2018: Assignment 5 is out.
- February 16, 2018: Because of President's day, I will
*not*have office hours on Monday, Feb. 19. Instead, I*will*have office hours on Wednesday, Feb. 21, 4-5PM in SC321H. - February 14, 2018: Assignment 4 is out.
- February 12, 2018: Notes on the "mad secretary" are online.
- February 7, 2018: Assignment 3 is out.
- February 2, 2018: A small correction to question (7) on assignment 2 was made: the second inequality also holds for negative real numbers.
- January 31, 2018: Assignment 2 is out.
- January 31, 2018: Since these are not really discussed in Grimmett-Stirzaker, I have added notes on the birthday paradox and the Monty Hall problem.
- January 26, 2018: The reading for next week has been posted. Also, please welcome our CA, Stefan Gramatovici! You are all encouraged to come to his problem session (see above).
- January 24, 2018: Assignment 1 has been posted.
- January 24, 2018: My office hours are now announced: they will be held MF 4-5 in SC 321H, starting this Friday.
- January 10, 2018: This webpage is online, hurray! Please read the syllabus.

- Final exam
*(Solutions are now on Canvas)*. - Information on the final.
*(Updated April 18, 2018: made more precise the material in 6.1-6.2 that will be covered)*. - Sample final exam
*(Solutions are now on Canvas)*. - Information on the midterm.
*(Updated March 2, 2018: added personal notes as allowed documents).* - Sample midterm exam
*(Solutions are now on Canvas)*. - Midterm exam
*(Solutions are now on Canvas)*.

- Assignment 1 (due Wednesday, January 31).
- Assignment 2 (due Wednesday, February 7).
*A small correction to (7) was made on February 2*. - Assignment 3 (due Wednesday, February 14).
- Assignment 4 (due Friday, February 23).
- Assignment 5 (due Wednesday, February 28).
- Assignment 6 (due Friday, March 8).
- Assignment 7 (due Wednesday, March 21).
*Updated on March 9: a small mistake in 4b was fixed.* - Assignment 8 (due Wednesday, March 28).
- Assignment 9 (due Wednesday, April 4).
- Assignment 10 (due Wednesday, April 11).
- Assignment 11 (due Wednesday, April 18).
- Assignment 12
*(now due Friday, April 27)*. - Extra credit assignment
*(now due Friday, April 27)*.

Assignment solutions are posted regularly on Canvas.

Chapter and page references refer to Grimmett and Stirzaker, Probability and random processes, third edition.

For the week of Jan. 22-Jan. 26: Sections 1.1-1.7.

For the week of Jan. 29-Feb. 2: Sections 1.7, 2.1-2.4, and section 9 (p.54-64) of the following lecture notes.

For the week of Feb. 5 to Feb. 9: Sections 2.4-2.6, 3.1-3.3, and 3.5.

For the week of Feb. 12 to Feb. 16: Sections 3.4-3.9 and the notes on the probabilistic method and Ramsey's theorem.

For the week of Feb. 20 to Feb. 23: Sections 3.9-3.10 and the notes on solving linear difference equations.

For the week of Feb. 26 to Mar. 2: Sections 1.6, 4.1-4.4, and the notes on building probability spaces.

For the week of Mar. 5 to Mar. 9: Sections 4.4-4.8 and the notes on the two envelopes problem.

For the week of Mar. 19 to Mar. 23: Sections 4.7, 4.8, 5.1-5.3.

For the week of Mar. 26 to Mar. 30: Sections 5.2-5.4 and Sections 1-4 of the notes on the limit theorems.

For the week of Apr. 2 to Apr. 6: The notes on the limit theorems and Example 5.9.6 in Grimmett-Stirzaker.

For the week of Apr. 9 to Apr. 13: The last section of the notes on the limit theorems, the notes on Stirling's formula, and sections 6.1-6.4 in Grimmett-Stirzaker.

For the week of Apr. 16 to Apr. 20: Sections 6.3-6.4 in Grimmett-Stirzaker.

For the week of Apr. 23 to Apr. 25: No reading! Come relaxed!

- Notes on Stirling's formula.
- Notes on the limit theorems (updated April 6, 2018).
- Notes on the two envelopes problem.
- Notes on building probability spaces.
- Notes on solving linear difference equations.
- Notes on the probabilistic method and Ramsey's theorem.
- Notes on the "mad secretary".
- Notes on the Monty Hall problem.
- Notes on the birthday paradox.
- Course syllabus (updated April 4, 2018) .
- Tentative schedule (updated April 23, 2018).

Here are the references on probabilistic algorithms that were used for the last two lectures:

- Chapter 7 of Arora and Barak,
*Computational complexity*, Cambridge University Press (2009). - Michael O. Rabin,
*probabilistic algorithm for testing primality*, Journal of number theory, vol. 12, no. 1 (1980), pages 128-138. Publisher version.

If you are struggling with proofs, my Concepts of Mathematics lecture notes (taken from a class I taught in 2014 at Carnegie Mellon University) could be helpful.