One subject, two cultures

These two introductory textbooks on numerical analysis differ essentially only in the cultural style in which similar material is presented. Alastair Wood's new book is thoroughly "British", with occasional humour and exercise questions of the style: "A goat is tethered by a rope of length x...". The more well-known book by Ward Cheney and David Kincaid is typical of a North American text in its professional, utterly comprehensive, but rather uniform style.

Numerical analysis is an often under-represented subject which, because it describes mathematical techniques used on computers, finds its home in mathematics or computer science departments. The fact that it underpins computer simulation tools used in many areas of science, engineering, social science and medicine - and thus enables that third investigative approach alongside theoretical analysis and experimentation - is obviously not lost on publishers. In their first 300 or so pages, both books cover much the same material as books suitable for a first course in numerical analysis for first or second-year mathematics, science or engineering undergraduates. They differ in their explicit use of examples and exercises in symbolic computer language: Wood uses Derive while Cheney/Kincaid use Maple and the excellent Matlab as well as generic "pseudocode".

Wood attempts only to cover introductory material whereas Cheney and Kincaid (being approximately twice as long) has chapters on data smoothing, Monte Carlo methods, boundary value problems for ordinary differential equations and partial differential equations and so might additionally be suitable for a second course or simply a longer course covering more than one term.

Introduction to Numerical Analysis is well designed, attractively laid out and only mildly flawed by such irksome references as "Table ??" (on page 71) which seem to be a feature of first editions nowadays: whatever happened to copy editors? I liked the brief biographical references and the unanticipated chapter five on "iteration", which introduces some nice material on recurrence relations. The brief summaries at the end of each chapter are also helpful and there are reasonable pencil and paper exercises. Less good is the occasional scant treatment of important principles: for example, the first time a uniqueness result is needed (for the Lagrange interpolating polynomial), it is relegated to an unhelpful footnote.

Numerical Mathematics and Computing is similarly well laid out and has a set of "computer problems" as well as "problems" for each chapter. As one would expect from well-known specialists, there seems little room for improvement in this new edition, but I did get the impression that much had already been added "up front" to earlier editions in an attempt to satisfy too many criteria: the numerical analysis does not start until page 90. Following this line, I checked to see where the trapezium rule for integration (a topic familiar in school mathematics) was first introduced and was horrified to discover that in Cheney and Kincaid it was on page 195 and in Wood on page 209. I hope there are correspondingly succinct books around, for if I were learning numerical analysis now, I might be worn out before I got to appreciate the practicality and beauty of my subject.

Andrew J. Wathen is reader in numerical analysis, University of Oxford.