Over the past few years more and more schools have been able to gain access to computers. Many have their own terminals, and can work on-line, others send their material to a centre for batch processing. This article looks at some examples of the way such computing facilities can be used in the teaching of statistics. Clearly much more work can be done with interactive programs carried out on-line, but a great deal can be done with off-line facilities. Two difficulties with statistics are that experiments can take a long time and that the resulting computations can become tedious. In both cases the main statistical ideas can get lost in the sheer drudgery involved. One undeniable advantage of a computer is that it does things quickly. It is putting these two facts together that can make computers a useful tool in the teaching of statistics.

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

Teachers of elementary Mathematics are generally very glad to find some unfamiliar field into which they can turn their pupils to exercise themselves in elementary processes. The following is a suggestion of a method of approaching certain theorems in connection with the Geometry of the Triangle which, although well known to Mathematicians, are not, as a rule, studied as part of a school course, except perhaps by specialists. The Brocard Points and Circle are generally approached, via the theory of Isogonal Conjugates (see Casey’s Sequel to Euclid, Supplementary Chapter, Section I. etc.). But many of the properties connected with these points can be obtained in a more direct manner, and this suggests some interesting investigations involving nothing but the ordinary processes of Geometry and Trigonometry.

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:

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.