Book Review: Essential Mathematics and Statistics for Science

Here isa book review I wrote for the Mathematical Association of America's website:

What is a good way to learn and compute statistics? Is it to pick-up one book, read it, and apply the algorithms to one's problem? Should one have a single book for his/her work or many books? How much theory should one know? Lastly, how can one use the world-wide web with a text book?

Drs. Currell and Dowman have written a statistics textbook for students and researchers. Their book provides brief discussions, formulas, worked examples, and exercises (with short answers in the back) to illustrate topics and usage. In addition to the text itself, there is a well-organized and useful web site for the book (http://eu.wiley.com//legacy/wileychi/currellmaths/ or http://www.wileyeurope.com/go/currellmaths). The web site provides supplementary help, in-depth solutions, and study resources, among other topics. The text and web site complement one another and are excellent at giving the reader a workable grasp of the material.

The text begins with a gentle discussion of statistics, data, and numbers. It discusses units, conversion between units, and then measurements. The discussion and topics are a solid introduction for the beginning student. The book then guides the reader through manipulation of equations, relationships between variables (such as linear, quadratic and exponential) and discusses probability distributions such as normal, binomial, and Poisson. In the final chapters the book discusses statistical tests: F-test, t-test, Chi squared, and non-parametric tests. All these topics are highly relevant to researchers, well presented, and easy to follow. The multitude of examples clarifies the text.

The authors state in the first sentence that the book is for "biological, environmental, chemical, forensic, and sport sciences." This is important because the book, which presents the material at that level, is not the most appropriate for mathematicians, physicists or engineers—anyone with a deeper mathematical background or interest. I was, in fact, struck by the oftentimes cook-book nature of the discussion.

I would have liked more discussion of the mathematics behind the ideas. For example, the method of linear fit is given without any theory such as derivatives. The text shows how to find the parameters with Excel but not what the Excel routines do. Many readers probably have Excel and for those who just want the answer, that may be all they need. (One note: While Excel is popular I urge authors to look at OpenOffice software, www.openoffice.org, in the future. It is free, easy to use, and not proprietary.)

What about using the world-wide web? The authors employ the web for detailed solutions and supplementary help for the reader. This is indeed a plus. Obviously, other web sites can provide details on any topic one desires. But, I believe that having a text book with the web site is the better way to use the web. The reader sees a consistent presentation of each topic both on his paper page and his screen page. The textbook gives the researcher an easy to navigate source of topic, explanation, example, without having to load pages, or search multiple sites for details. Thus this book with its companion web site are all the better.