The set of whole numbers less than and coprime to n, with the operation of multiplication modulo n, forms an Abelian group (try to prove it for yourselves). We'll write Mn for this group, and call all such groups modulo groups or M-groups. M-groups are easy to compute. It is also particularly easy to calculate quotient groups of M-groups, making them a good source of examples and practice for the beginner. There are also some very hard, possibly unsolved, problems in classifying M-groups. In attacking such problems there is an interaction between number theoretical and group theoretical arguments which makes this a rich topic, for projects or personal pleasure.

Among the ways in which a teacher can kindle a pupil's interest in mathematics is by invoking spirits from the subjects past: spirits of men full of imagination and determination; enterprising individuals brimming over with new ideas; pioneers who not only changed their particular discipline, but who in some cases even altered our perception of the world. The Scots have a heritage of which to be proud in science and mathematics. This article discusses four pioneers in statistics.

In 1355 the Italian professor of law Bartolus of Saxoferrato (1313-1357) wrote a treatise on the division of alluvial deposit. The problem he discussed is the following (figure 1). Some landowners, Bartolus calls them Gaius, Lucius, and Ticius, have neighbouring properties beside the bank of a river. The river deposits silt so that new land is formed at the riverside. How is this new fertile soil to be divided up ?

Except for the circle, for which the true anomaly v is proportional to the time t, the position of a body in orbit about a central body at a given time is simplest to derive for a parabola. The classical determination of the time of flight on a parabolic trajectory is through the integration of the dynamic equations of motion. (See Appendix.)

As a student in the Department of Textile Industries of the University of Leeds—then the Yorkshire College—I was taught to emulate the successes of my forefathers in the spinning of yarns and in the weaving of fabrics,—and also to perpetuate some of their errors. Empirical work, without any discrimination or “imaginative insight,” was the fundamental basis of practically all instruction.

In Matters for Debate, David Singmaster (DS) discusses some topics relating to the use and misuse of decimal points: the use of a full stop in writing times of the day, confusion between the decimal point and a dot used for multiplication, and writing amounts of money.

Francis Bacon held every man a debtor to his profession, and there are few of us who would not discharge this obligation if we could. I feel particularly indebted because I have been fortunate, over a long period, in having been able to attend Association and Branch meetings, where I have met many of the best informed, most active and aesthetically inspiring teachers of mathematics of all ages and at all levels. When, in addition, the Association honoured me by making me its President, I knew that I was, in more senses than one, permanently overdrawn. I know that this distinction would never have come to me had it not been for the accidents of time and place that made me Honorary Treasurer for several years. I am an assistant master, and, since 1954, a House Master, so that I could describe myself, in a light-hearted way, as a full-time research worker in the educational field. My researches are not entirely mathematical, but close contact with boys of 13 to 18 has been an interesting and instructive experience.