IMA:Mathematics 2007

As part of its fortieth anniversary celebrations the IMA held a one-day conference in Manchester in 2004. At the Council Strategy Weekend in 2006 it was suggested that we should arrange an annual ‘overarching’ conference, reflecting the range of IMA activities. This suggestion was endorsed by the responses from the Membership Survey, which was conducted shortly afterwards. The result was the ‘Mathematics 2007’ meeting held at de Morgan House in London on the 26 April 2007.

The aim of the conference was to bring together people with an interest in mathematics and its applications to consider current issues in the subject. Conference topics covered mathematics education at school and at higher levels, research areas in mathematics, and industrial applications of mathematics. The presentations would address the impact of the work rather than merely emphasising its technical nature. In the event seventy delegates registered for the conference, the maximum allowed by the lecture room capacity.

The day began with a welcome by the IMA President Peter Grindrod. He explained the background to the conference and said that the programme was designed to showcase the variety of activities engaged in by the IMA and its members. Peter expressed the hope that the talks would enthuse the audience; he was not to be disappointed. The three presentations before lunch were given by the IMA’s three Vice-Presidents.

Although he prefers to bat as number three, Alistair Fitt, from the University of Southampton, opened the presenters’ innings with a talk on his research interests. His research portfolio is diverse, ranging from flow problems, through mathematical modelling of the human eye to mathematical aspects of betting. Disappointingly perhaps for those members of the audience who were financially less well off he centred his talk on the first area.

Alistair’s presentation was entitled The Mathematics of Optical Fibre Manufacture. He was concerned with ‘holey fibres’ - fibres which contain an array of air holes that run along their length. The geometry of the final fibre can be modified significantly by controlling the parameters used in the drawing process, namely the temperature of the furnace, the feed speed of the preform, and the draw speed. His model was for a fibre with a single central hole – a capillary. He described a method for modelling the fabrication of small-scale hollow glass capillaries based on an asymptotic analysis of the Navier-Stokes equations; this yields a simple closed-form solution for this problem. Alistair’s typically entertaining talk got the meeting off to a lively start.

Huw Williams, from Jaguar Cars, was the first speaker from industry and his presentation was entitled Measuring the Inertia Tensor. He was firmly of the opinion that all practising engineers need a range of mathematical skills. His case for knowledge of the inertia tensor was supported by examples of its applicability in the dynamic properties of vehicles, CAE modelling and in the manufacturing of sports equipment. In the last example he cited the polar moment of inertia of golf clubs, which were restricted by the sport’s governing body.

He explained how the moments of inertia and products of inertia were measured experimentally, the former by the use of a rotating table and the latter by spinning it at different orientations. He looked at the assumptions being made and at the consequences of them not being true. Huw then showed how he used the Lagrangian approach to develop the model and then discussed the robustness of the measurements.

After the first refreshment break Edward Stansfield, from Thales Research & Technology, gave a presentation on Industrial Mathematics. Ed is a true enthusiast for mathematics; his interest in mathematics stems from an early curiosity about how machines work. He chose electrical engineering for his career, and he later studied mathematics in greater depth in order to strengthen his skills in problem analysis with a view to providing innovative solutions to the problems he encountered.

Inter alia, he chose four recent illustrations of the diverse applications of his work. The first was on speech coding, which had been developed originally for military use and had now found its way into the technology behind mobile telephones. The second was in the field of locating emitters; in both these applications he had used least squares methods to minimise errors. The third example was concerned with smart containers, whereby it is possible to track the progress and integrity of a container in transit. Finally, in keeping with his theme of ‘fun mathematics’ he gave the example of solving a problem by lateral thinking; this involved a somewhat frenetic bird flying repeatedly to and fro, at record-breaking speed, between two trains approaching each other on a single track

A buffet lunch break gave the delegates an opportunity to mingle and hold discussions, and the opportunity was taken enthusiastically.

The first afternoon presentation was given by Robin Wilson from the Open University on the topic of Public Engagement. In an opening reminiscent of Professor Joad, Robin asked who constituted the ‘public’ and what we meant by ‘engagement’. He found general agreement from his audience with his sentiment that the role of mathematics today was widely misunderstood and certainly not appreciated for its valuable contribution to our everyday lives. He looked at various categories of ‘the public’ and bemoaned the fact that too many people equated mathematics with arithmetic.

As might have been expected he was disappointed by the lack of media interest in the 300^th anniversary, eleven days earlier, of Euler’s birth. He went on to review some examples of attempts to bring aspects of mathematics to a wider audience by books, by the Royal Institution and other public lectures and looked wistfully back at the 1950’s TV programmes given by Dr Bronowski. He was concerned that there were no brownie points in universities for those mathematics staff involved in public engagement. All too often the attitude was ‘anyone can do it’, and clearly that is untrue.

Next to speak was Celia Hoyles, the Chief Adviser for Mathematics at the DfES, on Engaging with Mathematics. She said that the Government was committed to increasing pupil and student engagement with mathematics and had supported a number of initiatives. She cited post-16 provision, the Further Mathematics Network, The National Centre for Excellence in the Teaching of Mathematics, curriculum reform of GCSE mathematics, the more maths grads project and Teaching Diplomas for non-specialists.

Celia discussed the general perception that school mathematics was a relatively difficult subject and was disliked by many pupils. There appeared to be high expectations for the top set only. Many pupils did not know what mathematics is and did not know why they were studying it. Mathematics is now a compulsory element in compiling school league tables and there was a hope that the tide could be turned, despite all the known attendant difficulties. Finally, Celia noted that the IMA was ideally placed to make available ‘real’ examples of the application of mathematics.

Following the final refreshment break, Nigel Peake, from the University of Cambridge, spoke about the Mathematics of Aircraft Noise Aircraft designers today needed to create less noisy and more green aeroplanes Sound obeys linear laws and the air particles transmitting sound typically have a velocity of 0.1 ms^-1 compared to the velocity of sound in air of 330 ms^-1. He quoted the statistic that the acoustic energy produced by one jet is equivalent to the entire population shouting. Sound energy was proportional to the eighth power of the Mach number and this clearly became a worry for aircraft traveling at higher speeds. Much work was concerned with predicting how much noise an aircraft would generate and how it would be dissipated.

The last contribution was a joint presentation by Duncan Lawson and Michael Grove representing the HE Academy Maths, Stats & OR Network and the ‘more maths graduates’ project. Duncan reviewed the state of pre-university qualifications and voiced concerns about the new ‘specialist diplomas’. The possible diminution of mechanics provision at Advanced level was a worry for university engineering departments. He said that mathematics was a vulnerable subject at university level, and he also discussed the QAA benchmarks, the Bologna Declaration and the Professional Standards framework.

Michael reviewed the work of the MSOR network and mentioned various support provision such as the CETL, mathcentre and an extension to mechanics topics, mathtutor and the HELM project. He explained the role of the Network and concluded with a sound clip of Tom Lehrer.

Following closing remarks by Peter Grindrod the remaining delegates enjoyed a drinks reception and wended their way home in more or less straight lines with plenty to think about from the day’s presentations.

The feedback received was generally very favourable. The online booking system was particularly welcomed but some felt that the venue was somewhat too cramped for the numbers attending. There was support for this kind of conference to be an annual event and some delegates suggested Birmingham as a possible location, whilst others thought that London was the best venue. Perhaps a talk on mathematics in the finance sector could be included.

Thanks go to David and his colleagues at IMA headquarters for organising what was a very successful event.

Leslie Mustoe CMath FIMA