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 very fast pace. We will cover a lot of material and applications, and you are required to read the book before the lecture. Whenever possible we will prove all results and theorems.
Format: lecture. Evaluation will be based primarily on homework, classwork, writing and exams. 
Prerequisites: Multivariable Calculus and Linear Algebra, or permission of instructor. No enrollment limit (expected: 40). 

CONTACTING ME: You can reach me in Bascom 106D (if I'm there it's probably office hours), email sjm1@williams.edu, or anonymously through ephsmath@gmail.com (password 1793williams; it used to be the first eight Fibonacci numbers but annoyingly  someone hacked the account and changed it, and Google wouldn't let me restore it).

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.

TEXTBOOK/SYLLABUS: The textbook is The Probability Lifesaver. This book is designed to supplement any standard class, or be used as a stand-alone book. Tentatively we will cover most of the first 20 chapters, chapter 23, and additional topics as time permits; due to time constraints we may not do some of the topics (such as Chapter 6). There will also be programming assignments (you may use any language). There will be a weekly lunch series (if you do not have a meal plan lunch will be provided) to discuss additional topics if there is student interest; though in parallel to that course, these meetings are optional and have no impact on the course grade. You are expected to have read the corresponding material before class; if you have any questions you should email me beforehand.  I strongly urge you to pick up an additional book for the class (almost any book is fine, feel free to grab one from the library). It is a valuable skill to learn how to read and discern the relevant information from a variety of sources.  Here are a few particularly good books: (1) Probability and Random Processes by Geoffrey R. Grimmett and David R. Stirzaker (third edition). Excellent text, used it a few years ago, lots of great additional topics. (2) Probability by Lawrence M. Leemis. Not as high level as Grimmett and Stirzaker and not as many advanced applications, but extremely well written, friendly, and has lots of comments on how to attack the problems in R. (3) A nice read is Impossible?: Surprising Solutions to Counterintuitive Conundrums by Julian Havil (this is a suggested book for the class for those who want to see some additional fun problems; this book is not required for the course, and anything we use from the book will be explained completely in class).

GRADING POLICY: Homework: 15%. Preparing for class: 5%. Midterm: 40% (if there are two exams only best counts). Final exam: 40%. You may also do a project for 10% of your grade (which reduces all other categories proportionally). Exams are black tie optional. Homework is to be handed in on time, stapled and legible. Late, messy or unstapled homework will not be graded. I encourage you to work in small groups, but everyone must submit their own homework assignment. Extra credit problems should not be included in the general homework, but handed in separately. Very little partial credit is given on these problems.

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!