Math 154 Probability theory (Spring 2018)
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!
News / Announcements
- 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.
Assignments
- 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.
Reading assignments
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!
Other course documents
Other resources
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.