There are two principal forms of interaction between different disciplines. One occurs by comparing and sharing, the other is where one discipline, finance for example, is totally dependent on the applied tools and methodology of another, such as mathematics; and could not exist without it.

The second form of interaction is illustrated by this excellent new book. The authors set out clearly in the preface the philosophy of their approach, what they intend to do and how. Remarkably they comply with it throughout the book.

The layout is good and clear, so is the style of notation; the extraction of technical points makes the reading easier and more interesting and the supply of exercises confirms that this is indeed a student book and not an author's self-indulgence. The pointers in "Further reading" genuinely encourage the reader to further his or her studies, unlike the typical uninspired bibliography.

Overall this is an excellent tool for both mathematicians interested in the world of finance as well as finance practitioners keen to rebuild the foundations of their empirical knowledge.

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The joint authorship surely helps. The book neither attempts to promote any particular pet theory, nor tries to write beautiful maths just for the sake of it. This is a book for users.

I compared its approach with that of a recent German text, covering a related field. The latter starts characteristically with a philosophical quotation from Wittgenstein. The Cambridge University Press text, however, while pursuing deliberately a practical and informal approach, does not seem to compromise scientific rigour.

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The authors cite chapter three as the "most important in the book", which covers the derivation of the original Black-Scholes partial differential equation and boundary conditions for the value of an option.

I suspect, however, that many readers will find chapters eight through ten covering numerical methods very useful.

A final reason to recommend this book is that part of the royalties will be used to fund a graduate scholarship at the Oxford Centre for Industrial Applied Mathematics. By the time the reader has finished the exercises appended to all the 18 chapters, he may just qualify for it.

Rudi Bogni, former chief executive of the Swiss Bank Corporation, London, is currently on a sabbatical at the Centre for Quantitative Finance, Imperial College, London.

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