Crossing the maths Rubicon

The Association for Science Education recently held its annual meeting here in Leeds. A major theme was the transition from school to university. In the chemistry group, much of the discussion focused on students'' preparation at school, not just for the university chemistry syllabus but perhaps even more in relation to their background in mathematics and physics. At the school of chemistry in Leeds we have now crossed a sort of Rubicon, with more than half of our intake having lower than a grade C at A-level mathematics, and probably an equal proportion having no physics A level. Such a change, which is common to almost all UK universities, has major implications for the teaching of the more quantitative aspects of chemistry and for physical chemistry in particular. Increasingly, we have to address not so much students'' lack of ability in mathematics as their lack of confidence in using mathematics and in being able to see beyond the boardfuls of equations to the molecular behaviour - the chemistry - that we are trying to explain.

These two books are firmly in the area of "hard" physical science and both recognise that they have to provide mathematical support within the text. Molecular Thermodynamics addresses the area of chemical and statistical thermodynamics, one of the cornerstones of physical chemistry courses. This book is derived from the same authors'' comprehensive Physical Chemistry and shares with it the ambitious approach of building purposely on a fundamental molecular basis. I reviewed Physical Chemistry for The THES a year ago: it is a pleasure to acknowledge that my qualified appreciation has been modified by a successful trial with our second-year students in 1999, who found it very accessible. The new text is more than simply an abstract of the appropriate chapters from the earlier book. It starts with an introduction to quantum-mechanical ideas, in particular the existence of allowed energy levels, and builds from there. The authors have a neat route to the Boltzmann equation that avoids the use of undetermined multipliers, which can always appear as a sleight of hand. An energy-levels approach allows the more attractive statistical interpretation of entropy, rather than relying on the Clausius interpretation, but the authors made less of this possibility than I had expected. The "maths support" arises in the form of "MathChapters" interspersed between the main chapters, which work well and, importantly, come at the right time. I have some minor reservations. I prefer to introduce the reaction quotient and equilibrium constant with ratios of partial pressures to the standard pressure shown explicitly, rather than apparently relying on the latter having the value of unity when expressed in bar; for one thing this prevents well-trained students forever asking "where have the units gone?". In common with other texts, there is an overemphasis on small molecules and the gas phase. Nevertheless, this book can provide a very sound basis for thermodynamics courses, probably from year two onwards.

Chemical Modeling by Alan Hinchliffe is a book of a different colour. The attitude here is definitely mathematical, not just in the direct use of equations but also in the way many of the associated explanations are cast. A "mathematical toolkit" is provided as an appendix and this provides a helpful reference point. The book is certainly no "how to" manual, but instead sets out to describe the fundamental science underlying the processes used in molecular modelling and molecular dynamics. The underlying theme is the explanation of properties of materials, building from inter-molecular and intra-molecular potentials and quantum-mechanical principles. The author is explicitly unapologetic for including "substantial chapters" on introductory material such as states of matter, equations of state and thermodynamics. Personally, I found the sheer extent of these did rather hold up the story - it seemed frustrating still to be reviewing basic material in chapter nine and then again in later chapters - but the book gets into full swing from chapter 15 onwards. Any undergraduate taking a module in molecular modelling would do well to read this book.

Stephen K. Scott is professor of mathematical chemistry, University of Leeds.