A. Gardiner – författare

Mathematical Olympiad competitions started in Hungary at the end of the nineteenth century, and are now held internationally. They bring together able secondary school pupils who attempt to solve problems which develop their mathematical skills. Olympiad problems are unpredictable and have no obvious starting point, and although they require only the skills learnt in ordinary school problems they can seem much harder. The Mathematical Olympiad Handbook introduces readers to these challenging problems and aims to convince them that Olympiads are not just for a select minority. The book contains problems from the first 32 British Mathematical Olympiad (BMO) papers 1965-96 and gives hints and outline solutions to each problem from 1975 onwards. An overview is given of the basic mathematical skills needed, and a list of books for further reading is provided. Working through the exercises provides a valuable source of extension and enrichment for all pupils and adults interested in mathematics.

What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math­ ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro­ logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex­ amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students'' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this­ including teachers, teachers in training, students in their last year at school, and others interested in mathematics.