Mathematics for Physical Chemistry: Opening Doors
Author: Donald McQuarrie
Publisher: University Science Books
Authors: Allan Blackman, Steven Bottle, Siebert Schmid, Mauro Mocerino and Uta Wille
Publisher: John Wiley & Sons Australia
Chemistry: A Guided Inquiry
Authors: Richard Moog and John Farrell
Publisher: John Wiley & Sons
The subtitle of Donald McQuarrie's Mathematics for Physical Chemistry, "Opening doors", is really what matters. It springs from a remark by James Caballero that the author quotes with approval: "I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors."
Mathematics is the mountain range that chemistry students see they must climb if they are to be successful, if not in the whole of chemistry then certainly in its most quantitative domain, physical chemistry, the interface between physics and chemistry and where its fundamental principles lie. McQuarrie concurs with the view of most chemists that the mountain range gives way to swamps if chemists are taught mathematics by mathematicians, whose correct concern for rigour can overwhelm the practicalities of the language. The aim of this volume is to present chemistry undergraduates with the mathematics that they need for reasonably advanced courses in physical chemistry, particularly in thermodynamics and quantum theory, and to do so in a manner that is appropriate to their inclinations and tastes.
We have seen much of it before. The material is taken in large part from the "MathChapters" of an advanced physical chemistry text that McQuarrie published some years ago and from another text on quantum chemistry. He has also written a text on thermodynamics and a much heftier volume on mathematical methods for scientists and engineers. As such, he is well placed to judge what is appropriate for chemists. These other texts tend to be just a little too high for the corresponding market in the UK, with its decaying mathematical infrastructure, and, like the book under review, are better suited to the US market, where for reasons related to the structure and sequence of courses, students are better equipped to cope with mathematics by the time they get to serious physical chemistry.
Taken on its own terms, however, the book is very good indeed. It covers just about every topic that a physical chemist is likely to need. A structural advantage is that its 345 pages are divided into 23 short chapters: the constraint of brevity entails that focus is maintained on the essentials, which students will welcome. They will also welcome the numerous worked examples that occur throughout the text and will recognise in most places the relevance of the topic to their subject. The topics covered include differentiation, integration, complex numbers, Fourier series and transforms, operators, matrices, vectors and, in its closing chapters, introductions to probability, statistics and numerical methods.
Allusions throughout are made to using various mathematical software packages to eliminate the drudgery of many of the manipulations. That is certainly the best way to develop skill in this wonderful language. In short, this focused, short, authoritative text is a useful contribution to the quantitative education of a chemist.
I have alluded to structural reasons why students in the US can approach physical chemistry at a higher level than their UK counterparts: their freshman year is largely introductory physical chemistry, so they reach physical chemistry more prepared for tougher topics. There are numerous freshman texts, but they often have difficulty travelling to other parts of the world because they underemphasise organic chemistry. In response, texts that resemble American freshman texts but are developed to match local requirements are starting to appear. One such is Chemistry by Allan Blackman et al, which is targeted at the Australian market. It has its roots in Wiley's US stable, for it is in essence an extensively revised and colourful adaptation of two of Wiley's US freshman texts spiced with a considerable infusion of one of its introductory inorganic chemistry texts with numerous allusions to Australian examples.
Chemistry by Richard Moog and John Farrell is a very different kettle of fish. Written at an introductory level and published as a low-budget ancillary text, it focuses on another feature characteristic of US freshman chemistry instruction: the group activity. "Guided inquiry" is a way of developing understanding by group interaction, including the sharing of understanding between peers and the deepening of one's own understanding under the pressures of that sharing. Some have found this approach highly effective, and as the entry level of our own undergraduates sinks to the level typical of American freshmen, frustrated teachers in the UK might find inspiration in its pages. Currently, though, it remains more appropriate to A-level students than to undergraduates.