The following is offered as an example of a proof in which the important part is most easily written out in the form of a block flow diagram familiar to programmers of universal computers.

We shall be concerned with matrices of only a particular kind, namely antisymmetric matrices whose non-diagonal elements are all plus or minus unity. Call such matrices, p-matrices.

The American Mathematical Monthly in Vol. 68 (1961) page 380 gave a solution by Leon Bankoff of the following problem proposed by A. Oppenheim of the University of Malaya in Vol. 67 (1960) page 802.

Boolean class algebra is a special case of lattice theory and it is well known that the propositional calculus is Boolean. It is also well known that there are sixteen and only sixteen truth functionally distinct relationships between two elementary propositions in the pronositional calculus.

Some time ago Professor Prior circulated some typewritten notes due to Mr. C. A. Meredith on logical questions. These were written in the Polish notation and Professor Prior kindly translated those on equational logic into a symbolism more familiar to us. How much of the present paper was actually in those notes, it would now be impossible to say, but they introduced us to the subject and inspired this paper which, without them, would not have been written.

In an article entitled “Two Problems on Impulsive Motion” (M. G., XLIV, p. 95) the writer (J. O’Keeffe) complains of the lack of method in elementary books on problems such as the initial motion of two jointed bars under the action of an impulse. In our view, such problems are best treated, in an elementary course, by reducing the total momentum of the system to a single linear momentum and a momentum-couple. The necessary equations are then obtained by using the principle of equivalence of this system with that of the impulses. This treatment makes it clear why and in what form it is correct to take moments about the point at which the bars are hinged. Below we give the general treatment, and also the application to this particular problem.

There is a growing realization among mathematicians and logicians of the many-sided role played by the axiom of choice in various branches of mathematics. Many of them tend to accept the axiom of choice as a legitimate principle provided, of course, it is proved to be independent in a suitable axiom system. This tendency has been accelerated by Gödel’s proof of the compatibility of this axiom in a reasonably broad system of axioms [2]. Such a view seems to have been shared by Fraenkel and Bar-Hillel [1; pp. 44-80] in their excellent exposition of the function of the axiom of choice in the modern mathematics in general and the axiomatic set theory in particular.

I have in my possession a school exercise book written by John Stewart between January 1801 and 29th June 1802, while he was a pupil at Dundee Academy, later to become the present High School of Dundee. The book runs to 140 pages covering very much the same course as that outlined by T M. Flett in the Gazette of Feb., 1961. Rules are in the identical words repeated by Edward Winder 25 years later