From its formation to the present time, one of the major concerns of the Committee has been the identification of a common core of mathematical knowledge that pupils with one or two A-levels in mathematics could, and should, be expected to possess. The ‘Core Syllabus in Pure Mathematics’ (published by the Association in 1968 with the support of the Schools Council) was one outcome of that concern. The first report is currently being revised, along with a companion report on Applied Mathematics (and Mathematics Applied).

The transfer from pen and paper methods to hand calculator methods which has been made by many teachers still uses visible denary digits. We are now beginning the transfer to a computer and I feel that the Mathematical Association’s admirable new report does not place enough emphasis on the possibilities of computer system errors which are invisible to the user. The teacher looking at numerical error must not put untested faith in its abilities, and must not expect it always to behave in a regular denary fashion, as will be shown in the tests below. He must also be warned that the computer reference manual rarely has the reliability of a text-book.

Finite projective planes are a lively field of research, particularly in America and Germany. SMP Further Mathematics gives them some attention, and recently two American text-books which would serve as suitable introductions to the subject at the beginning undergraduate level have been published [Albert and Sandler, Introduction to Finite Projective Planes, Holt, Binehart and Winston (1968); and Blattner, Projective Plane Geometry, Holden-Day (1968)].

Junior School children seem to be able to get the feel of the Klein group by using aptly-prepared paper sheets and wooden blocks. Perhaps, surprisingly, they can also handle such logical implications (when suitably embodied in devices) as:

A→B, ∼B→∼A, B→A, and ∼A→∼B

Here “→” means “implies” and “∼” means “not.”

For many practical purposes, Lagrange’s undetermined multipliers can be used for the solution of problems where some function has to be maximised subject to a constraint.

The technique described here arose from a consideration of one such case, where there was a choice of several types of investment, and, within each type, a different scale or level. With a limited total budget, it was necessary to decide how much to spend on each alternative.

Some students on first meeting the axioms of a vector space are puzzled by the inclusion of the scalar unit law: 1v = v for all vectors v. It is the purpose of this note to discuss the consequences of omitting this law from the list of axioms.

In his recent article [1] F. J. Budden produced a binary operation on the set R0 of non-zero real numbers that was associative but not commutative, namely