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 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!