The probabilities of certain English football teams winning different playoffs are determined. In each case, a mathematical model is fitted to the observed data, assumptions are verified, and the calculations performed. (LS)

Starting from the concept of one-to-one correspondence, an introduction to the different types of infinities is presented. The usual problems concerning the infiniteness of the rational numbers, the real numbers, and the unit interval are given. Several other theorems follow. (LS)

Reprinted are "The Teaching of Euclid" by Bertrand Russell, an article on integrals by G. H. Hardy, "An Address on Relativity" by A. S. Eddington, "The Food of the Gods" by Prof. E. H. Neville, and "Simplicity and Truthfulness in Arithmetic" by W. Hope-Jones. (CT)

by a geometric method, a one-to-one correspondence is set up between the set of real numbers and the set of all points, except one, on a circle of unit diameter. Then some interesting results relating the corresponding points and real numbers are derived. (Author/CT)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

An attempt is made to detail the nature of mathematics as perceived by mathematicians. Mathematics is viewed here as both abstract and an experimental science. The typical working mathematician is described as proceeding through problems with an attitude of discovery and examples of such an approach are given. (MP)