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The quadratic equation is a central topic in high school algebra. It provides the simplest generalisation of the familiar linear equation, and finding its roots introduces students to a non-trivial problem that requires the application of new techniques, such as completing the square and/or factorisation into linear factors involving the roots. It also introduces the student to the phenomenon of repeated roots, which opens the door to a discussion of multiplicities of roots. Furthermore, it naturally exposes the student to the case where the equation has no real roots, a phenomenon that could also be used to introduce the student to complex numbers.

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Using high school algebra for a natural approach to derivatives and continuity

REAL SUBMANIFOLDS IN COMPLEX SPACE AND THEIR MAPPINGS (Princeton Mathematics Series 47) By M. SALAH BAOUENDI, PETER EBENFELT and LINDA PREISS ROTHSCHILD: 404 pp., £42.50, ISBN 0 691 00498 6 (Princeton University Press, 1999).

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Using high school algebra for a natural approach to derivatives and continuity

REAL SUBMANIFOLDS IN COMPLEX SPACE AND THEIR MAPPINGS (Princeton Mathematics Series 47) By M. SALAH BAOUENDI, PETER EBENFELT and LINDA PREISS ROTHSCHILD: 404 pp., £42.50, ISBN 0 691 00498 6 (Princeton University Press, 1999).