The renowned mathematical physicist Pierre-Simon, Marquis de Laplace wrote in his opus on probability in 1812 that “the most important questions of life are, for the most part, really only problems in probability”. His words ring particularly true today in this the century of “big data”.
This introductory course takes us through the development of a modern, axiomatic theory of probability. But, unusually for a technical subject, the material is presented in its lush and glorious historical context, the mathematical theory buttressed and made vivid by rich and beautiful applications drawn from the world around us. The student will see surprises in election-day counting of ballots, a historical wager the sun will rise tomorrow, the folly of gambling, the sad news about lethal genes, the curiously persistent illusion of the hot hand in sports, the unreasonable efficacy of polls and its implications to medical testing, and a host of other beguiling settings. A curious individual taking this as a stand-alone course will emerge with a nuanced understanding of the chance processes that surround us and an appreciation of the colourful history and traditions of the subject. And for the student who wishes to study the subject further, this course provides a sound mathematical foundation for courses at the advanced undergraduate or graduate levels.