Kevin Hastings’ Introduction to Probability with Mathematica adds computational exercises to the traditional undergraduate probability curriculum without cutting out theory. The computation exercises illustrate the theory but are not used to replace it; no “proof by simulation” here. If one were to ignore all references to Mathematica, the book would still include more material than most courses would cover.
The computational exercises use standard features of Mathematica 7 as well as custom functions from a library distributed with the book. Introduction to Probability with Mathematica woud be a good textbook for a class with a strong emphasis on hands-on experience with probability. A student who goes through these exercises will have much stronger intuition for probability and its applications than a student working through a purely theoretical textbook. On the other hand, a student who does not go through the exercises will have a more difficult time reading this book than one that does not interrupt the presentation with code examples.
One interesting feature of the book is that each set of exercises includes a few problems taken from actuarial exams. No doubt this will comfort students who are taking a probability course in hopes that it will prepare them for an actuarial exam. Another interesting feature is the discussion of the Central Limit Theorem. The book goes into an interesting discussion of the history of the theorem and hints at extensions to the theorem that are beyond the book’s scope.
John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.