Many teachers know that mathematics can be taught thematically, and that their choice of theme will depend upon the age and experience of the students. For the very youngest, this could be based upon favourite toys, children’s games, the cost of keeping a pet, and so on. Later on, the range of themes could be broadened to include ‘mathematics and art’, ‘maths and music’ and, indeed, maths and almost anything.

The justification for this approach is that students are more likely to engage with mathematics if it emerges from familiar contexts. For continuous or longish-term adherence to this philosophy, a large amount of time is required to plan the associated teaching programme and to devise assessment of learning outcomes. On the other hand, thematic teaching may be employed for short lesson sequences. Either way, this book on *Mathematics and Sports* constitutes a very good exemplar to the thematic approach to the study of mathematics, and it could well inspire teachers to adopt it on a wider basis.

The book is described as ‘an eclectic compendium of essays solicited for the 2010 Mathematics Awareness Month web page. All of the articles are accessible to college level mathematics students and some to the general reader. The articles are twenty-five in number. Each article commences with an explanatory abstract and many provide a summary and/or suggestions for further research. Overall, there is a compatibility of style and a high level of expository writing and mathematical precision.

With a title such as the one assigned to this book, the problem is what sports to include and what to omit. Here, the sports are predominantly American, and they include baseball (4 articles), basketball (3 articles), football (4 articles) and NASCAR. More universally popular sports include golf (4 articles), tennis (2 articles) and track and field events (5 articles), but there is only one article on the world’s most widely played sport (soccer).

Given the interesting content and readability of each of the articles, it might be invidious to select any one of them for particular discussion, but there are two particular articles that characterise the total selection. Firstly, the opening article, on the sabermetrics of baseball, is the most mathematically accessible and perhaps represents the infimum of the book’s mathematical content. Secondly, in the article on the teaching of mathematics and statistics using tennis, the author closely aligns aspects of this sport to a series of teaching objectives, and he provides a range of exploratory activities and illustrative exercises for the elicitation of probabilistic ideas and modelling. He thereby indicates how such an open-ended topic can be structured for teaching purposes.

The required mathematical knowledge ranges between high school mathematics and the lower undergraduate level, but follow-up study of many of the topics could invoke higher levels of mathematical analysis. However, although ideas on statistics and probability feature in many of the articles, the overall mathematical content of the book is quite wide. For example, the article on the swerve of a soccer ball introduces the Navier-Stokes equations, which are made digestible by the accompanying narrative and appealing illustrations. This ties in quite nicely with the paper that discusses the science of the golf swing. Another article examines the application of the matrix techniques of the Colley method to the problem of college football rankings. But an opportunity for the inclusion of geometrical ideas has been missed due to the lack of mention of pool — or its superior sibling, snooker.

Despite no mention of snooker, and little coverage of soccer, I really enjoyed reading these articles. I don’t know much about baseball, but the coverage of that sport in this book has engendered my curiosity. Moreover, the sort of analysis used to discuss aspects of that game can be applied to other sports, such as cricket. And that goes for some of the other themes in the book. Overall, this book is a very welcome addition to the body of mathematical literature, and I know of no other like it.

Over the years, **Peter Ruane **has keenly participated in a range of sports, including soccer, swimming, cycling, squash, badminton, golf and chess. But, judging by his empty trophy cabinet, the degree of his enthusiasm has been far in excess of the level of his expertise. (Actually, he doesn’t even have a trophy cabinet.)