Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.

In 1691 Michel Rolle (1652?1719) first published his famous result, now widely known as "Rolle's theorem", in an obscure book on geometry and algebra, named "Methode pour resoudre les egalites." Joseph Louis Lagrange (1736-1813) and Augustin-Louis Cauchy (1789-1857) derived their mean-value theorems easily using Rolle's theorem on suitably chosen…

Glycated haemoglobin (HbA1c) is regarded as the gold standard of glucose homeostasis assessment in diabetes. There has been much discussion in recent medical literature of experimental results concerning the relative contribution of fasting and post-prandial glucose levels to the value of HbA1c. A mathematical model of haemoglobin glycation is…

A study of first-year undergraduate students' interpretational difficulties with first-order ordinary differential equations (ODEs) in modelling contexts was conducted using a diagnostic quiz, exam questions and follow-up interviews. These investigations indicate that when thinking about such ODEs, many students muddle thinking about the function…

A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt-Poincare.

In applying the variational method, six different sets of trial wave functions are used to calculate the ground state and first excited state energies of the strongly bound potentials, i.e. V(x)=x[2m], where m = 4, 5 and 6. It is shown that accurate results can be obtained from thorough analysis of the asymptotic behaviour of the solutions.…

A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…

This note shows that for semiprime rings the anticommutativity implies commutativity.

The notion of equivalence relation is a fundamental concept in mathematics and yet mathematics students often are not given formal exposure to it until midway through their college careers. Not only do they need to become adept at working with equivalence relations but they should also understand the wide applicability of this notion. In this…

In this paper, an error in a well-known work which claims to prove Young's inequality is discovered and a concise proof of Young's inequality is given.

This paper deals with a brief historical introduction to fractional calculus with basic ideas, definitions and results of fractional order integration and differentiation of arbitrary order.

In this note, a modified Golomb algorithm for computing unit fraction expansions is presented. This algorithm has the advantage that the maximal denominators involved in the expansions will not exceed those computed by the original algorithm. In fact, the differences between the maximal denominators or the number of terms obtained by these two…

Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

The coordinates of an n-dimensional regular simplex are found. These coordinates are used to derive properties of the regular simplex that generalize their two- and three-dimensional counterparts.

This study investigates whether students' approach to studying their main honours degree subject differs from how they approach studying mathematics as a service subject. It builds upon work by Crawford, Nicholas, Gordon and Prosser that looked at mathematics students' approaches to studying mathematics and their conceptions of mathematics. Two…