Elementary Probability with Applications

In the UK, most formal introductions to the subject of probability are made via one or two chapters of larger books on pre-university mathematics. But the subject is informally introduced to children as young as six or seven, and it forms a continuous thread through the school mathematics curriculum up to the age of about sixteen.

This book, however, focuses entirely upon discrete probability and is based upon notes used by the author for a one-semester course intended for non-math and non-science students. Pre-requisite knowledge is assumed to be a grounding in high school algebra.

As stated in the preface, the treatment is informal and there is no reference to theorems (or proof) since the author believes that 'students learn from examples rather than theory', which is true for an introductory course for this sort of readership. The seven chapter headings don't suggest an innovatory approach to probability but the novelty value of the book is deemed to lie within the provision of an abundance of non-routine problems.

The chapters, in turn, cover basic concepts, conditional probability, multiplication and addition rules, random variables, distributions, expected values, sampling with and without replacement and simple statistical tests. The prose evinces both clarity and liveliness and there are very many well-explained examples.

Regarding the supposed emphasis on applications, one has to say that the vast majority of the problems involve the modelling of hypothetical situations that may prepare students for the process of probabilistic simulation. This, of course, is only to be expected in a first course designed for non-math majors, but readers will gain a good impression of the range of possible real-world uses.

The problems are graded from fairly straightforward to very challenging and the book is, for this reason at least, a welcome addition to the literature. If you teach this sort of material, try an inspection copy at least.

Peter Ruane (ruane.p@blueyonder.co.uk) has been involved with the teaching of mathematics at many levels since 1966. He has taught children from five to eighteen years old and he was employed in the field of mathematics education of teachers for over 25 years. Prior to his career in mathematics education he was variously employed, for a period of twelve years, as a docker (stevedore), slaughterman, bartender, farm labourer, hotel worker, shop assistant, etc.