Problems you can't ignore

THE MATHEMATICAL OLYMPIAD HANDBOOK: An Introduction to Problem Solving. By Tony Gardiner. Oxford University Press Pounds 14.95

MORE MATHEMATICAL CHALLENGES: Problems from the UK Junior Mathematical Olympiad 1989-95. By Tony Gardiner. Cambridge University Press Pounds 6. 95

Tom Roper enjoys compelling questions

I wasn't expecting to enjoy these books. Collections of mathematics problems tend to look boring and may well be boring. I also find maths competitions difficult to come to terms with, although I have set them myself. We don't have a History Olympiad or a Junior Geography Challenge. This is not to decry the element of competition: but in maths it has always been between me and the problem , not between me and a colleague.

In the end, the two books proved irresistible. As I flicked through the pages, problems caught my eye, out came the piece of scrap paper and pencil. Doodles, scrawls, half-remembered formulae were shaped into convincing proofs and arguments. Frustration was eased, perhaps too easily, through the readily available hints.

Looking up the solutions (even if you know it's correct, you like to see whether you agree with the back of the book), I found I had not always seen the problem and attacked it as the solution seemed to imply that I ought. I then needed to wrestle with the two solutions and reconcile the approaches. All of which, I guess, is exactly what the author expected.

The intended reader is not somebody like me though, but the student of maths in secondary school who needs something beyond what the normal curriculum and textbooks can offer. The books will only become accessible to students if their teachers take them up, read them as I did and realise that there is a lot of material here to enjoyed, to be grappled with and, as Tony Gardiner points out in one of them, taken and adapted.

However, in preparing the reader for the content of the books, Gardiner pulls no punches in putting over his own view of maths: that it is hard, exacting and exact, but very rewarding.

A further complication in The Mathematical Olympiad Handbook is a section headed, "A little useful mathematics", at the start of the book. Tony Gardiner is quick to warn readers in the preface that they should not read this section but get stuck into the problems and use it only for necessary reference. In my experience, few people read prefaces and the very positioning of this lump of mathematics might well encourage many of the intended readers to plough through it and fail to reach the jewels beyond.

Tom Roper lectures in mathematics education at the University of Leeds

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