There's no way out of it. The preface to Mathematics for Economists is correct in quoting economist Paul Krugman's belief that "the nerds won". As a discipline, we are now faced with the question of not whether but how to teach mathematical techniques in economics.
Both these texts offer a comprehensive presentation of the maths required at undergraduate level, and indeed for much of the material in MSc economics courses. The coverage of the volume by Michael Hoy et al is, however, slightly more extensive, including a useful and intuitive introduction to optimal control theory.
An objective of both books is to emphasise the relevance of maths for economics, and, to a large extent, both are successful. The strategy of Hoy et al is to bombard the reader with worked examples and exercises, frequently consisting of the economic models encountered in undergraduate courses.
Extensive use of some well-produced diagrams enhances the learning experience. An abbreviated answer set, an instructor's manual and a student solution manual are available. The principal strength of the end product is that the reader is made as self-sufficient as possible, thereby reducing the workload of the instructor.
Malcolm Pemberton and Nicholas Rau do a better job of integrating the maths with the economics. Nowhere is maths included except soon after a relevant economic application. For example, matrix algebra is introduced as it is required, rather than in one hit. An impressive explanation of circular functions and complex numbers sensibly precedes the chapter on higher order dynamic equations. The chapters are short, and formal material is judiciously appended when necessary. This organisation is complemented by a relaxed but informed writing style; the reader is warned when the going is about to get tough, and the speed of progress is proportionate to the difficulty of the material. Like Hoy's book, full recourse is made to core economic models, reflected in examples and problems to which answers are available.
Both texts achieve their mission statement, and choice of one over the other is a matter of taste. Hoy's is more extensive and less personal and as such it also works well as a reference text. Pemberton and Rau's may possibly work better as a teaching device for students who are more maths-averse. In any case, nerds across the world may rejoice.
Andrew Pickering is lecturer in economics, University of Bristol.
Mathematics for Economists: An Introductory Textbook
Author - Malcolm Pemberton and Nicholas Rau
ISBN - 0 7190 3341 1
Publisher - Manchester University
Price - £14.99
Pages - 613