Math 154 - Probability Theory

Math 154 - Probability Theory - Spring 2009

Lectures: Tuesday and Thursday 1-2:30pm (Exam group 15, 16) in Science Center 110

Lecturer: Lauren Williams (office Science Center 432, e-mail lauren@math.harvard.edu)

Office Hours: Tuesday 2:30-4:00pm (and by appointment)

Course assistants: Yi Sun (yisun@fas) and Charles Chen (chen33@fas)

Yi Sun's office hours: Wednesday, 4pm, Science Center 103b

Note: Yi Sun will have special office hours on Monday, March 2: they will be from 4-5pm in Science Center B-10.

Course description

This class is an introduction to probability theory. Topics will include: discrete and continuous random variables; distribution and density functions for one and two random variables; conditional probability; generating functions; weak and strong laws of large numbers; the central limit theorem; geometrical probability; random walks; Markov processes.

Click here to see what section you are in. Note that sections begin on Monday February 9.

Here is a syllabus for the course. Here is a survey for the first day of class. And here is a sectioning form, to be handed in during class on February 5.

Texts:

Probability and Random Processes, Grimmett and Stirzaker, third edition, Oxford University Press, 2002, ISBN# 0-19-857222-0.
One Thousand Exercises in Probability, Grimmett and Stirzaker, Oxford University Press, 2002, ISBN# 0-19-857221-2.

Lectures

Lecture 1 (Jan. 29): Countability and uncountability

Lecture 2 (Feb. 3): Sets and probability

Lecture 3 (Feb. 5): Infinite unions and infinite series

Lecture 4 (Feb. 10): Combinatorics, bridge, and poker

Lecture 5 (Feb. 12): Conditional probability

Lecture 6 (Feb. 17): Independent events, Simpson's paradox

Lecture 7 (Feb. 19): Random variables, law of averages

Lecture 8 (Feb. 24): Discrete random variables, expectations

Lecture 9 (Feb. 26): Variance

Quiz 1 (March 3): In-class quiz

Lecture 10 (March 5): More on discrete random variables

Lecture 11 (March 10): Conditional expectation

Lecture 12 (March 12): Simple random walks and Gambler's ruin

Lecture 13 (March 17): Ballot theorem and the reflection principle

Lecture 14 (March 19): Arc sine laws for random walks

Spring break (March 24): No lecture

Spring break (March 26): No lecture

Lecture 15 (March 31): Continous distributions and random variables

Lecture 16 (April 2): Functions of random variables

Quiz 2 (April 6): 7 to 9pm

Lecture 17 (April 7): Bivariate normal distribution and Buffon's Needle

Lecture 18 (April 9): Change of variables; convolution.

Lecture 19 (April 14): Start geometric probability (Bertrand's paradox, Crofton's method).

Lecture 20 (April 16): Finish geometric probability.

Casino Night (April 16): 9-11pm in the Quincy House Senior Common Room

Lecture 21 (April 21): Probability generating functions

Lecture 22 (April 23): Random walks via generating functions.

Lecture 23 (April 28): Central limit theorem, Strong law of large numbers

Lecture 24 (April 30): Markov processes. How many shuffles does it take to get a deck of cards random?

Final Exam (May 19): Good luck! (9:15am in Science Center E)