Showing papers in "The Mathematical Gazette in 1988"

A first course in coding theory, by Raymond Hill. Pp 251. £12·50. 1986. ISBN 0-19-853803-0 (Oxford University Press)

Abstract: Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

Applied mathematics—a contemporary approach , by J. David Logan. Pp 572. £42·50. 1987. ISBN 0-471-85083-7 (Wiley)

Abstract: DIMENSIONAL ANALYSIS AND SCALING: Dimensional Analysis The Buckingham Pi Theorem Scaling PERTURBATION METHODS: Regular Perturbation Singular Perturbation Boundary Layer Analysis Two Applications CALCULUS OF VARIATIONS: Variational Problems Necessary Conditions for Extrema The Simplest Problem Generalizations Hamiltonian Theory Isoperimetric Problems EQUATIONS OF APPLIED MATHEMATICS: Partial Differential Equations The Diffusion Equation Classical Techniques Integral Equations WAVE PHENOMENA IN CONTINUOUS SYSTEMS: Wave Propagation Mathematical Models of Continua The Wave Equation Gasdynamics Fluid Motions in R3 STABILITY AND BIFURCATION: Intuitive Ideas One Dimensional Problems Two Dimensional Problems Hydrodynamic Stability SIMILARITY METHODS Invariant Variational Problems Invariant Partial Differential Equations The General Similarity Method DIFFERENCE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: Finite Difference Methods The Diffusion Equation The Laplace Equation Hyperbolic Equations Index.

Problem solving in primary schools, edited by Robert Fisher. Pp 261. £6·95. 1987. ISBN 0-631-15374-8 (Blackwell)

Abstract: Problem-solving involves thinking and doing - acting for a purpose. It is a way through which children can learn, practise and demonstrate essential skills and knowledge, and it can give purpose to a whole range of curriculum activities. Exploring developments in the teaching of problem-solving across the primary-school curriculum, from writing and art to mathematics and the use of computers, this book contains a collection of thoughts and experiences which provide starting points for investigations. It also offers practical guidance on translating ideas into experience in the classroom.

No way: the nature of the impossible , edited by Philip J. Davis and David Park. Pp 322. £17·95. 1987. ISBN 0-7167-1813-8 (Freeman)

Abstract: Essays explore the concept of the impossible in mountaineering, biology, medicine, chemistry, computer science, technology, physics, mathematics, law, politics, economics, education, music, and philosophy.

A singular impact

Abstract: While I worked at Teeside Polytechnic I had some difficulty in arriving in the morning by 9.00. Not being an early bird my desire was to pull into the carpark at 8.58, but this I did not seem able to achieve. If I left home at 8.15 the journey was smooth and trouble-free, and I was at my parking place by 8.50. Whereas if I left a moment later there were a couple more cars at the estate exit, each succeeding roundabout and set of traffic lights was busier, and eventually I drove into the car-park at 9.05—not only five minutes late, but also quite likely finding the spaces all full and having to resort to street parking. It seemed that no matter how I varied my start time the arrival interval of 8.50 to 9.05 was somehow inaccessible to me. Of course some people did arrive in this interval—if I did the sensible thing and left early I enviously watched them arrive at the time I would have wished. But they did not start from where I started. So I was drawn to the belief that the relationship between start and arrival time was a genuine discontinuous function, and not simply a continuous function with a rather steep critical section. Maybe the catastrophe theorists could analyse this further (but to call my misfortune a catastrophe would be a bit strong).

What they don’t teach you about integration at school

Abstract: As a mathematician involved in teaching students whose abilities range from barely numerate to MSc level, I am frequently concerned by the lack of basic understanding exhibited by pupils regarding the subject of integration. Invariably the most practical way of introducing the subject of integration is by thinking of it as “anti-differentiation”, so that the problem is to pick a function which “when differentiated will give what you first thought of”. This of course may be allied to the idea of the area under a curve to give the student a conceptual feel for the subject. Usually when simple rules for the integration of powers, trigonometric functions, exponentials, logarithms and so on have been mastered, the next step is to introduce the standard methods for proceeding.

Equilateral triangles and the golden ratio

Abstract: This article could be subtitled ‘Thoughts on contemplating a model of five tetrahedra inscribed in a dodecahedron’; it is an attempt to communicate the pleasure that ensues when logical reasoning is combined with a visual delight in geometrical figures.

A computer verification of a pretty mathematical result

Abstract: A very appropriate use of a computer in a mathematics class is to provide investigation vehicles for formulating conjectures to be verified theoretically. In other words, first we notice something and then we try to prove it. In this paper we shall reverse the process, first arguing the plausibility of a very fascinating result and then obtaining confirmation by looking at some computer generated data. The argument is based on the work of the eighteenth century mathematical giant, Leonhard Euler (1707-1783).