a specific form of

factorisation within the school mathematics

Bezivin,

Factorisation de polynomes, unpublished manuscript (in French), 2008, available at http://jp.

These numbers have the property that the sum of the numbers digits is equal to the sum of the digits in its prime

factorisation.

The impact of the elliptic curve method for integer

factorisation (developed by my PhD advisor Hendrik Lenstra) has played a role in introducing elliptic curves to cryptographers, albeit for attacking the underlying problem on which RSA is based (the difficulty of factoring integers)," said David Kohel, convenor of the ESF workshop, from the Institut de Mathematiques de Luminy in Marseille, France.

O'Leary [6] proposes to tackle this problem by rank monitoring of the descent matrix with a QR

factorisation and by discarding dependent vectors.

This book provides such a concrete and visual model, based on simple areas of rectangles, for students to explore: expansion of brackets;

factorisation of algebraic expressions; solution of linear equations using red and blue foam tiles to represent positive and negative quantities; and a square tile representing 'x-squared'.

There are a range of related Demonstrations (dynamic pre-developed Mathematica files) available from Wolfram Research that use this functionality to illustrate aspects of mathematics such as divisibility networks, the Sieve or Eratosthenes, prime

factorisation or the distribution of primes (see: http://demonstrations.

Example 3 is a problem-solving exercise in which

factorisation is involved.

Many secondary mathematics teachers find it a challenge to teach

factorisation of quadratic expressions to students who have weak foundations in algebra.

The

factorisation widget enables students to distribute cups, each containing y bunnies, and separate bunnies onto a given number of plates as a visualisation of an algebraic

factorisation.

Difficulty retrieving multiplication facts directly influences students' ability to engage effectively in

factorisation of quadratics, since

factorisation is a process of finding products within the multiplication table.

Lyashko-Looijenga morphisms and submaximal

factorisations of a Coxeter element.