The “Very Short Introduction” series from Oxford University Press is a collection of over 300 books on a wide variety of topics ranging alphabetically from “Advertising” to “Writing and Script”. (Mathematical topics on the list include game theory, logic, and statistics, as well as mathematics itself.) The books are designed as quick entries into new fields for curious readers, and this work on probability comes in at under 130 pages while hitting all of the most significant ideas without requiring any advanced mathematical prerequisites.
John Haigh is well-suited for this task, having previously written the much longer Taking Chances on the same subject and for approximately the same audience. His exposition draws on familiar circumstances where probability is applied, including airplane overbooking, medical testing, and surveys, and does so without either drowning in formulas or skimping on mathematics. The normal distribution and Central Limit Theorem both appear in their proper level of rigor but at the same time accessible to newcomers.
In teaching elementary probability, one invariably confronts the differences among theoretical, experimental, and subjective probability — and usually rapidly explains away the last as less important, because it’s far less amenable to mathematical description. Haigh chooses to place somewhat more emphasis than that on subjective probability, which is probably a wise move for a general audience. Someone wishing to learn what probability is about but who is concerned about their mathematical background will be well-served by this book, and perhaps will be interested enough to investigate the subject further. Since that’s what this series is all about, Probability: A Very Short Introduction has hit its target.
Mark Bollman (firstname.lastname@example.org) is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.