COURSE DESCRIPTION: While probability began with a study of games, it has grown to become a discipline with numerous applications throughout mathematics and the sciences. Drawing on gaming examples for motivation, this course will present axiomatic and mathematical aspects of probability. Included will be discussions of random variables, expectation, independence, laws of large numbers, and the Central Limit Theorem. Many interesting and important applications will also be presented, including some from coding theory, number theory and nuclear physics. NOTE: this course will move at a good pace. We will cover a lot of material and applications. Whenever possible we will prove all results and theorems.
Format: lecture. Evaluation will be based primarily on homework, classwork, and exams.
Prerequisites: Mathematics 211 --OR-- 251 or permission of instructor. No enrollment limit (expected: 21). 

OBJECTIVES: There are two main goals to this course: to explore probability theory and see the connections between various problems, and to learn problem solving skills. We will constantly emphasize the techniques we use to solve problems, as these techniques are applicable to a wide range of problems in the sciences. For a fuller statement as to the objectives of this course, please click here. This includes some fascinating videos with some thought provoking comments about what you should get out of your education.

COURSE NOTES: Below are scanned copies of my lecture notes for the course (click here for additional comments from each day's lecture). Skimming these notes is a good way to prepare for lecture and to review the material; however, it is not the case that everything said in lecture will be in these notes for two reasons: (1) I hope to have a lot of class discussion, and these comments will undoubtably influence which direction we pursue; (2) detailed explanations of many arguments are given in the book, so often I have just jotted down notes to remind myself of what I wanted to mention.

• General introduction to the course (slides from first lecture)
• Lecture notes for chapter 1 of our book
• Lecture notes for chapter 2 of our book
• Lecture notes for chapters 3 and 4 of our book (much in common b/w the two chapters, so we'll do them at the same time)
• Notes for chapter 5 (from moment generating functions to the Central Limit Theorem)
• Notes taken by Aom Kitichaiwat: Part 1    Part 2    Part 3

    Slides and programs:

• slides from the first lecture (9/10/2009)
• slides of lecture 2 (9/15/2009) are available here   
• slides of lecture 3 (9/17/2009) are available here.
• slides of lecture 4 (9/22/09) are available here.
• slides of lecture 5 (4/24/09) are available here        and     click here for a template specific for writing homework problems.
• slides of lecture 6 (9/29/09) are available here.
• slides of lecture 8 (10/6/09) are available here
• slides of lecture 9 (10/8/09) are here;                    Mathematica programs: 3x+1 iterates and counting prime factors
• slides of lecture 10 (8/15/09);                               Mathematica program for Monte Carlo integration of the n-dimensional sphere's volume.
• slides of lecture 11 (8/22/09);                               Mathematica program for generalized prize problem;     here is more info on the three hats problem.
•  

COURSE DISCLAIMER: I may occasionally say things such as `Probability is one of the most useful courses you can take' or 'If you know probability, stats and a programming language then you'll always be able to find employment'. I really should write `you should always be able to find employment', as nothing is certain. Thus, please consider yourself warned and while you may savor the thought of suing me and/or Williams College, be advised against this! I'm saying this because of the recent lawsuit of a graduate who was upset that she didn't have a job, and sued her school!

• Article from the NYPost on the lawsuit.
• Another article, which notes that she misspells 'tuition'.
• You can view her motion here.