*A useful text for a wide range of disciplines*

According to the cover blurb, *Mathematics for Physical Chemistry* is a text for chemistry undergraduates with emphasis on preparation for physical chemistry courses. As such, it contains the usual exposition, examples and problems, but also may be useful as a review to those in a variety of other fields. The author wisely begins simply; reviewing numbers, symbols and algebraic equations before proceeding to calculus, differential equations, series, matrices and (gasp) group theory. The formal sections end with a valuable chapter on handling experimental data, followed by appendices with physical constants, formulas and tables of integrals and derivatives. Exercises are freely sprinkled throughout the chapters and are given without answers or solutions (a wise choice although it’s sometimes helpful to work backwards from answers or to have partial solutions and hints).

Although written so as to be useful for self-study, the author points out that the book is not a substitute for traditional mathematical training (like we all taught ourselves calculus, right?!). He correctly opines that many students will not wish to write their own programs to perform the more complex or tedious calculations, so he defaults to (Excel) spreadsheets and Mathematica. These should both be readily available to all undergraduates. The text may be used for review, supplement and reference.

As with many modern texts, communication of ideas is stressed by prefacing each chapter with sections on core ideas and objectives. This may appear as overly simplistic, but such a good job is done at summary and clarity that, if the student has any fear or trepidation as to what will follow, those notions are soon corrected. Frequently used equations are set apart from the text and enclosed in boxes for easy identification and retrieval. Among the more important examples of repetition and clarity in the text are examples of incorrect usage and inclusion of important explanations of why certain precedents need be followed. For example, at the undergraduate level, stressing such concepts as numbers of significant digits and inclusion of units with every measurement irritated many of us. It almost seemed akin to splitting hairs. Here, the author takes pains to point out that carrying units through a calculation may be paramount to proper numerical conversion, and significant digits are vital to accuracy. Rules of thumb, always a valuable inclusion (but rarely used in most texts), are sometimes woven-in to assist with actual applications of technique. Each chapter is concluded with a short summary and problem set, also without solutions.

Special sections such as ‘Problem Solving and Symbolic Mathematics’ are treasures to the professional who took mathematics courses several decades ago. At that time, further explanation of any concept was relegated to more equations, and the infamous ‘the student can easily fill in the steps’ was seen or implied on almost every page. Here, the author offers sage advice on approaches to the oft-encountered ‘word problems,’ where the analytic steps are not specified and may not be obvious. Helps such as this become even more valuable as the student begins to apply the reasoning. Of course, the approach to word problems should be stressed in grammar school, but many times may not be related in the student’s mind to scientific problems.

Perhaps the most demanding test of quality in any text of this sort lies in the ease with which it can clarify the complex topics of advanced (at least to the non-math major undergraduate) mathematics, such as calculus. Again, the text stresses clarity as concepts are first introduced: the symbols are graded as the student is eased from algebra to ‘change with respect to…,’ a brief review of functions and graphics and, finally, the concept of derivatives. All of this is richly illustrated with graphs to demonstrate the nature and magnitudes of the changes, as well as the relationship between the numbers and the changes. Throughout these chapters, concepts are always developed and explained. The much-dreaded integral is gradually introduced by the concept of finding a function that possesses a certain derivative. Similar illuminating devices are applied to operators, matrices and, finally, group theory, *and each area is related to the chemistry where it will ultimately be used.*

The text is a fairly easy read, well laid-out, and laced with examples that illustrate several concepts at once, thus obviating the necessity of hundreds more. The student will derive benefit from the clarity, and the professional from a concise compilation of techniques stressing application rather than theory. As such, this book will be useful to a wide range of physical scientists and engineers, as well as to the interested life scientist.

My summary: *Recommended.*

##### Availability

*Mathematics for Physical Chemistry, 3rd ed.*, by Robert G. Mortimer. Elsevier Academic Press; 416 pp. (2005); paperback $41.95

*John Wass is a statistician with GPRD Pharmacogenetics, Abbott Laboratories. He can be reached at sceditor@scimag.com.*