Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

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…

In this paper, the author introduces a simple problem relating to a pair of ladders. A mathematical model of the problem produces an equation which can be solved in a number of ways using mathematics appropriate to "A" level students or first year undergraduates. The author concludes that the ladder problem can be used in class to develop and…

A model for car following on a closed loop is defined. The stability of the solutions of the model is investigated by considering the evolution of the roots of the corresponding characteristic equation in the complex plane. The solution provides a motivation for investigating the behaviour of the roots of a simple class of algebraic equation.…

Two simple mathematical models for how individual vehicles follow each other along a stretch of road are discussed. The resulting difference equations can be used as applications of techniques taught at A-level and first year undergraduate level, and as an introduction to the behaviour of the logistic map.

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

A simple model for how traffic moves around a closed loop of road is introduced. The consequent analysis of the model can be used as an application of techniques taught at first year undergraduate level, and as a motivator to encourage students to think critically about model formulation and interpretation.