The 1st Biennial Engineering Mathematics Conference of the Engineering Mathematics Group (EMG), a specialised group of the Australian and New Zealand Industrial and Applied Mathematics Division of the Australian Mathematical Society (ANZIAM), took place in the Townhouse Hotel, Melbourne, Australia on 11-13 July 1994. It was organised by Drs J. Steiner and A. Easton of the School of Mathematical Sciences, Swinburne University of Technology together with Mr L. Evans of Monash University. The EMG was formed on 16 June 1992, during a one-day symposium on Mathematics in Engineering at Swinburne University of Technology, a largely Australasian event, but one which proved very successful [1]. By contrast, the 1994 conference attracted considerable international attention, mainly from Europe, and over 130 delegates attended from 17 countries.
The Australian applied mathematics community, by organising such an event, is aiming at close interrelationships whilst encompassing a very catholic set of disciplines. This is eminently sensible for a large but relatively sparsely-populated region where emerging development underpins the need for engineering. A close liaison has been built with the European Society for Engineering Education (SEFI) via its Mathematics Working Group (SEFI-MWG). The latter has held seven seminars devoted to engineering mathematics education since 1984 and has also published a Core Curriculum in Mathematics for the European Engineer [2], hereafter called the SEFI CC, which, inter alia , advised tertiary institutions in Europe about the mathematical content of courses for engineering students. A letter of greeting from Professor L. Rade, Chairman of the SEFI-MWG, preceded the Conference abstracts which were made available to delegates.
As well as the EMG, ANZIAM and SEFI, the Conference was sponsored principally by The Institution of Engineers, Australia, by Swinburne University of Technology, by Monash University, by Victoria University of Technology and by the Royal Melbourne Institute of Technology (RMIT). There were a number of commercial sponsors.
The principal organiser, Dr Steiner, opened the Conference with a welcome address. He was followed by Mr I. Deveson, Chancellor of RMIT, who quickly got to grips with issues of controversy that have long been a part of the Australian academic and commercial scene. He said that throughout history, Australian communities of whatever form, eg engineering mathematics, have suffered from the tyranny of isolation as a microcosm of the country itself but have progressed forward aided by the need for technological development and the wealth of natural resources. Another benefit has been the impetus to keep together those interested in differing but related sub-disciplines who so easily might have drifted apart in a larger community such as Europe. This theme was echoed by Dr N. Barton, Chairman of ANZIAM, and Mr B. Lloyd, immediate Past President of the Institution of Engineers, Australia, both of whom emphasised the benefits of a sound education in developing a broadly-based but ad hoc inter-disciplinary approach to engineering.
The plenary sessions took place on the mornings of each of the three days with parallel sessions scheduled after lunch. Following the general introduction, Professor H. van Tilborg from Eindhoven University of Technology, Netherlands, opened the specialised keynote plenary addresses. He said that discrete mathematics is vital to both computer science and engineering though its importance really only made its proper mark in the 1980s. With cleverly illustrated examples in error-correcting codes, statistical experiments and cryptology he carefully explained how often finite and countable elements or components lie below the concepts of modern technology. Dr K. Horadam, RMIT, continued on a related discrete mathematical theme with linear feedback shift registers as an important source for data transmission, spectrum spreading and encryption.
So much discrete mathematics rests upon abstract algebra and its constituent subjects such as Galois fields and irreducible polynomials. When looking forward to the engineering mathematical requirements of the next century we should not forget that abstract algebra and number theory were purist subjects looking for a role back in the 1960s but they now lie at the centre of engineering mathematics.
It is sometimes humorously suggested that the response of the mathematician to a definite but particular engineering problem is to generalise it and then produce the solution required as one of a suite of sub-examples. Dr Horadam accepted this principle in relation to shift registers, but Dr I. Jones of the Industrial Computational Fluid Dynamics (CFD) Unit of AEA Harwell, UK, speaking the next day, suggested that the CFD used in solving non-linear partial differential equations was quite general enough. He did point out that in spite of reduced industrial activity, the world-wide demand for CFD continues to grow apace at about 20% per annum. On the related theme of mathematical modelling in heat treatments, Drs Jiansheng Pan, Mingjuan Ho and Xiao Chen of Shanghai Jiao Tong University, PR China, explained how they had developed a mathematical modelling-based computer on-line control technique which creates fits for real-time heat treatment processes such as quenching heating, gas carburising and gas nitriding.
Prof J. Perry of the Swinburne University Energy Systems Engineering Centre concluded the second day plenary session in thermodynamical and fluid-dynamical numerical models by providing examples of modelling complex flow fields using finite difference codes. The examples explored the availability and accuracy of physical modelling data for validating numerical solutions, recognition of Coanda effects, modelling combustion in multi-burner furnaces, variable geometry effects, etc.
On the final day more general issues came to the fore with prominence being given to the international input. Dr N. Barton of ANZIAM, who had spoken on the first day, examined some industrial case studies at the interface between engineering and mathematics. This is a frequently recurring theme at international conferences devoted to engineering education and the Australian experience reflects the experience elsewhere. He said that particular attention was drawn to commercial advantage, the contribution to research, education and the role of the computer. Engineers often complain that mathematical modelling follows engineering pragmatism and the need to produce affordable solutions, but once in place the modelling can, with versatile and adaptable computer software, actually improve upon existing processes and get products to the market more speedily. Real industrial case studies very often pose exceptionally challenging research problems and these in turn can be broken down into new course material and student projects.
Professor P. R\'ozsa, Technical University Budapest, Hungary, addressed the specialised needs of engineers in linear systems analysis by discussing block matrices and their applications. The partitioning of matrices often proves highly useful in getting theoretical results or in reducing the computational work for systems with a high degree of freedom. One example where substantial computer time can be saved is with the transient voltage distributions in altering ladder networks which can be determined by a system of linear ordinary differential equations with a periodic tridiagonal coefficient matrix. Theoretical results enable problems to be solved quickly in explicit form.
Dr G. Kurz, Fachhochschule f\"ur Technik (FHT) Esslingen, Germany, discussed student entry test scores, investigations and experiences at FHT Esslingen when compared to the benchmarks laid down by the SEFI CC. If anything, the mathematical education of engineers was rather under-represented at plenary level in this conference compared to similar events elsewhere, but the Esslingen experience seems to reflect those being felt in other countries about the declining mathematical fitness of engineering students. The results of a recent test given to freshman students showed a lower mean than anticipated by college staff, a very wide spread of marks, significant differences between different potential engineering sub-specialisations, and significant differences between different admission criteria. There is now a pre-degree programme in `Elementary Mathematics' at FHT Esslingen for weaker students. Such a programme for freshman engineers exists in an increasing number of universities in several countries.
The afternoon parallel sessions took place in three groups. The range of topics covered very many aspects of engineering mathematics in 62 papers. These provided a rich diversity that would be difficult to find in any engineering mathematics related conference in Europe or North America. A sizeable minority, 12 of the papers, were devoted to education, curriculum and related issues. These redressed the balance of the plenary sessions vis--a--vis education and in the next section we will look at education as a separate issue.
The contributors to the parallel sessions came from many Australian universities with some international input. Nonetheless a sizeable minority of the Australian contributors are first generation in that country, so in effect the international input was high and of excellent quality. It is not practicable to list all the contributions or even cover the themes as these overlapped considerably. However two or three papers at least concentrated on aspects of the following major topic areas: Communication Systems, Gas Dynamics, Structural Dynamics, Waves in Solids, Optimisation, Industrial Mathematical Modelling, Computer Algebra, Applied Integral Equations.
The implementation of the SEFI CC is an important issue in engineering mathematics education in Europe. This was highlighted by Dr Kurz and Dr M. Barry, RNEC Manadon, who detailed the contents, recommendations and international reaction to the Core Curriculum in the parallel sessions on the first day. The Institute of Mathematics and its Applications (IMA) sponsored conference, Mathematical Education of Engineers , held in March 1994 at Loughborough University of Technology (LUT), UK, had already systematically examined the practicalities of the curriculum for the UK engineering student, but many speakers at Melbourne commented that the declining mathematical ability of new entrant students was a much wider problem. Changing social attitudes, moves away from hard science and a restructuring of priorities in mathematical education are all detracting from student competence in the basic classical mathematics, particularly in algebra and geometry, that forms and always has formed the tool-kit of engineering mathematics. The response has been to monitor, motivate and even design special courses for new entrant students. Many speakers discussed their ventures in this area. Dr D. Bull, Monash University, Australia, described how a structured revision and remedial programme had been in place at Monash since 1990. Dr M. Fuller, University of Central Queensland, Australia, and Dr D. Jackson, Swinburne University of Technology, both gave details of first year student programmes in mathematics which are specifically designed to put that subject in a workshop environment and to stimulate interaction between students and communication in all respects.
Computer technology is believed by many to have transformed learning as well as the operational environment of the engineer and computer algebra especially is credited with the removal of drudgery and the capacity to check mathematical investigation and developments. Dr M. Pemberton, University of Queensland, noted a steady twenty-year decline in the mathematical fitness of new entry students as indicated by their performance in a benchmark entry test. However computer algebra packages such as MAPLE and MATLAB and even Computer Aided Learning were being used to improve the position. Further support for the use of computers in education came from Dr N. Sukthankar, Papua New Guinea University of Technology. For many of his students English is a second language but the only language of scientific discourse. When forced with learning both English and mathematics, computer supported feedback is a powerful spur to learning.
Not all, however, are convinced that computers are unreservedly beneficial in engineering education and Dr L. Mustoe, LUT, referred to the `poisoned chalice' of computers in the engineering mathematics curriculum. He argued that misdirected computer use and readily available picture images had deprived today's students of the need to read, persevere and to validate the commonsense of the most basic mathematics. Educators too, he claimed, are at fault in believing that the existence of increasingly sophisticated software has progressively obviated the requirement for sound mathematics teaching and have persuaded themselves that time spent in learning how to use software could be taken from that allocated to mathematics. Interestingly enough the SEFI CC has warned strongly against such a trend but the debate over the prior mathematical knowledge as well as the curriculum of the student engineer is set to run and run.
Professor R. Wasen of Applied Research Methodology, Rimforsa, Sweden, brought the Conference to an end in a plenary session. In discussing conceptual engineering, i.e. where theory and practice meet, he argued that at the end of the 1970s science appeared as a tremendous resource with a wealth of knowledge and ideas of what could be done with materials. This view had not changed in essence and computer tools like computer algebra have become perfectly usable to the modern engineer having learnt how to use the packages. The benefits of mathematical research do not translate so easily and a kind of meta-language is needed so that engineers can think about and discuss their findings in relevant terms. The need for programmes of continuing engineering education are thus paramount and this is one area that SEFI is trying to address.
AEMC 94 did much to bring together practical engineers, applied mathematicians and teachers of engineers of all kinds. Because Australasia is so isolated, many engineers and scientists of very different disciplines feel the need to stitch together and find a common purpose. To have such a diversity at a conference is a rare experience for the international delegates who are usually able to move in circles of similar fold, but in so doing precious opportunities and potential research openings may be lost. The organisers, Dr Steiner, Dr Easton and Mr Evans have made considerable progress in bringing the EMG of ANZIAM into international dialogue. They deserve to be thanked and congratulated for their efforts in putting together such a successful meeting. For their part, the First Biennial EMG Award, 1994 was presented to Prof Lennart Rade, Chairman of the SEFI Mathematics Working Group, whose inspiration led to the formation of the EMG. It is hoped to organise a special conference in 1995 devoted to engineering mathematics education and AEMC 96 is already being planned for 1996.
Department of Computing, Mathematics and Control Engineering
Royal Naval Engineering College
Manadon, Plymouth PL5 3AQ, England
Department of Mathematical Sciences
Loughborough University of Technology
Loughborough, Leics LE11 3TU, England