1. Heaviside’s operational method has for some time been in fairly general use among engineers for solving problems in circuit theory, and appears in most of their textbooks. The average man who has read these seems able to manipulate the “expansion theorem” and to solve problems in which E.M.F is applied to an initially “dead” circuit, but he is not at all clear about the foundations or correctness of the theory and apt to be worried by any slightly more complicated problem, such as cases in which the circuit is not initially dead or problems involving switching operations (which are usually dealt with in the textbooks by artifice). It is now pretty well recognised that the Laplace transformation provides a satisfactory approach to the operational methods, but it is not perhaps fully realised just how simple it is and how extremely easy to teach.

The following notes arose from a talk given by Professor Halberstam to the South West Wales branch of the Association. In the marriage bureau problem we imagine that n boys and n girls are to be paired off in marriage, that we are able to establish preference lists for each boy of all the girls and vice versa. These preference lists may be displayed in a table such as that given below, which shows the rankings for four boys α, β, γ and δ, and for four girls A, B, C, and D. The boys’ rankings are the first members of the number pairs, in rows, and the girls’ are the second members, in columns.

Although the approximation of elementary functions is a well-researched area of mathematics, very little has been published on built-in routines in any particular calculator or computer. Computer manufacturers are, understandably perhaps, reluctant to publicise details about their algorithms. Hewlett-Packard have been less secretive than most and allowed an occasional glimpse behind the scene in their own Journal and various other sources. The following square root routine for one of their machines, the now extinct 2000F series, has appeared in an Open University text on numerical computation [1]. The process of evaluating √x is carried out in four steps:

The Royal Statistical Society and the Institute and Faculty of Actuaries have published a report, written by Roger Porkess [1], which draws urgent attention to the issue of statistical education: is it fit for purpose? Statistics is an ever-present part of real life, and there can be no doubt that for most pupils it is statistics that will be the most directly used part of their mathematical education.

The report follows an investigation into the perceived statistical needs of various subject ‘communities’, and is a follow-up to The future of statistics in our schools and colleges [2] by the same author and publishers. It is aimed at a wide readership, from policy-makers through curriculum providers and teachers (fairly low in the pecking order!) to authors and other providers of resources. There is no doubt that all such interested parties should be considering the issues covered by this study, and it should be read widely. The title of the report implies suggestions for cross-curricular work, but it is more essentially a plea to rethink the role of statistical education – a plea articulated more fully in [2]. It is the purpose of this article to further the debate.

Notation. By (x/y, X/Y) = a1.a2a3 … are let it be understood that after a vulgar fraction X/Y has been converted into a continued fraction (CF.), a1.a2a3 … are the partial quotients, and x/y is the penultimate convergent. The point placed after a1 is intended to show that, in the case of a proper fraction, the first partial quotient must be taken as zero.

In an earlier paper in the Gazette the authors of define what it means for a matrix in a set M of n × n matrices to be prime, namely if it is not the product of two matrices in M, neither of which is the identity. They then showed that there are exactly two primes in the set M2 of 2 × 2 matrices with non-negative integral entries and unit determinant, namely