Gary Hall

A Graphical Model of a Class of Molecules

Summary It is shown that a class of planar conjugated hydrocarbon molecules can be modelled in terms of a simple graph and the related adjacency matrix. Various physical and chemical properties are related to properties of the graphs. The resonance energy is related to such simple invariants as the total number of CC links and the number of Kekule structures. Rules for enumerating these structures are described.

Model building—an Educational Philosophy for Applied Mathematics

Summary The present state of applied mathematics in British education is reviewed. The nature and scope of applied mathematics itself is then discussed. The building and development of mathematical models is suggested as the basis of an integrated philosophy of the subject. Some implications of a ‘model’ approach to school and university mathematics are developed. The article concludes with a brief description of the creative role of the applied mathematician.

Motivation among mathematics undergraduates

A list of 20 possible motives for doing a mathematics course was drawn up using the analysis of motivation given by Maslow. Responses from students reveal a generally low level of motivation and some significant changes between the anticipation in the sixth form and the reality of the university. The role of the teacher in improving motivation is discussed.

Applied Mathematics in the Secondary School

It is suggested that applied mathematics in the secondary school should be based on the practical investigation of everyday situations which lead to the setting up of various mathematical models. These situations should be selected so that problems of social and psychological importance are considered as well as dynamical and statistical problems. Activities of this kind in the areas of classical mechanics, networks, information theory and linear systems are outlined. These lead to models involving many different branches of mathematics. A syllabus embodying these suggestions is proposed.

Information and communication

This paper describes a course given during one term within the second year of a mathematics degree programme. Although it occupies only 25 hours it makes a distinctive contribution to the education of the students because it relies on their active cooperation and because it opens up a large number of real situations to their investigation. The course is concerned with information and its communication. Simple concepts are introduced not only from information theory but also from automata theory and pattern recognition. Lectures are supplemented by class experiments, organized and controlled by the students themselves, in which some of the phenomena are demonstrated. The course is assessed by a project which each student finds for himself. Since both the course and the project are examples of communication their presentation is also part of their content. This practical experience of a self‐referencing system is important to mathematicians. Not only is this theory mathematically simple, it is also simple i...

Critical configurations of cars on motorways

The arrival simultaneously at one point on a motorway of more cars than there are lanes will result in a collision. Situations leading to this are analysed using a simple model so that critical configurations can be identified and preventive action taken.

A plea for octal

It is argued that there are strong practical and pedagogical reasons why some of the traditional units of volume should be preserved. In particular, a working example of an octal system is shown to have many advantages in an otherwise decimal world.