Teach Yourself New Mathematics

Abstract

THE MATHEMATICAL GAZETTE referring to the method of elimination.) Does he allow his pupils to invert matrices of order 3 x 3 or larger? What would he advise them to do about (say) 10 linear equations in 10 unknowns? And what if the coefficient-matrix turns out to be singular? A look at any good book on Numerical Methods will show that, contrary to his remark (6), it is precisely the method of elimination which does generalise and is used for large sets of linear equations, even though the work may be set out in matrix form and a machine made to do the chores. Incidentally, with regard to remark (a), it may well be a purpose of O-level to " shed light on the concepts of linear equations and mappings, both of which are unifying structures (sic) in mathematics ", but surely this is not an end in itself. In the same issue (p. 399) I was equally intrigued by the last sentence in the opening paragraph of Note 3287. Elimination and " completing the square " are both elementary processes with many applications. Yet my freshmen degree students do not really know them, and many teachers attending modernisation courses do not seem to be aware of the potentialities. I am all for " Modern Maths. " (within reason), but if an O-level (or A-level?) pupil is thereby going to be deprived of such useful tools as these, my sympathies must incline towards the " enfeeblement of mathematical skills " outlook. I am still amused by a letter from a former student of mine who, during teaching practice, took Form 3d which could tell him about isomorphic infinite groups but which did not know how to calculate the area of a triangle. Finally, returning to the subject of matrices, I feel that more textbooks should make clear (as does, for example, Maxwell, " Algebraic Structure and Matrices ", p. 158) that an exclusive diet of 2 x 2 matrices can be quite misleading owing to their abnormal simplicity. For example, 2 x 2 skew-symmetric matrices commute and their product is a diagonal matrix, b u t. .. ? Yours faithfully,