THE INSTITUTE OF MATHEMATICS
AND ITS APPLICATIONS

Second IMA Younger Members' Conference

23 April 2005 - De Morgan House, London

On Saturday 23rd April 2005, an enthusiastic group of IMA younger members and their guests gathered in the Hardy Room in De Morgan House at 57 Russell Square in London for the second Younger Members' 1-Day Conference. The organising committee, chaired by Amanda Padbury, CMath MIMA, had put together an exciting programme for the day. We began with a simple buffet lunch from noon onwards as the delegates arrived followed by a warm welcome from Amanda at 1 pm.

The organising committee had secured the services of Professor Marcus du Sautoy to give the first presentation which was based closely on his popular 'touring presentation' entitled "Music of the Primes" from his book of the same title. Professor du Sautoy began with a general introduction to the nature of prime numbers and their historical importance to mathematicians.

He outlined the use of very large prime numbers in modern data encryption systems for secure communication of private data (e.g. credit and debit card numbers) over the public internet. On a lighter note, he reminded us that prime numbers are often thought to be 'lucky' numbers. An example of this being David Beckham's insistence on wearing the number 23 on his football shirt. Professor du Sautoy then described the 'quest' by mathematicians such as Gauss and more recently how a paper now universally known as the Riemann Hypothesis, published in 1859 (see http://mathworld.wolfram.com/RiemannHypothesis.html) has cast more light on the nature of prime numbers and their distribution. To date, apparently, no one has been able to derive a formula to predict the next prime in the series from any given prime nor has the Riemann Hypothesis been disproved. A prize of One Million Dollars was offered in 2000 by the Clay Institute to any one who could prove the Riemann Hypothesis. Professor Du Sautoy then demonstrated how consideration of Fourier Series that form an integral part of Riemann's Zeta Function, are also at the heart of the unique sound of different musical instruments. He demonstrated, by playing first a violin and then a clarinet and finally a trumpet, that Fourier Analysis shows how even and odd harmonics combine to determine the unique tonal quality of each instrument.

Following on from this very colourful one hour 'multimedia' presentation, it fell upon three Mathematicians to each give a 10 minute overview of how mathematics is used in their particular field of work.

Matthew Muirhead, AMIMA, began the session by describing how when he was studying for his Maths PhD, he had been looking for a solution to the Helmholtz Equation in the form of a partial differential equation. He then described how he subsequently joined Qinetiq at Farnborough and began to do research on the application of his PhD thesis work to the study of how the human perception of noise from jet aircraft engines at ground level varies with changes in wing configuration, whilst in another part of the same department they were now studying the propagation of sound from helicopters, developing various noise reduction schemes for these. Matthew rounded off his presentation by reminding us of what Albert Einstein said about the nature of research. "If we knew what we were doing - we would not need to do research".

The second presentation was given by David Lee, another Qinetiq mathematician, who had been working on Guidance and Imaging Solutions for intelligent guidance systems. As an analogy of his work, David cited the application of chaos theory to the simulation and analysis of the path taken by 'an ant' as it moves around an infinite grid of alternately black and white cells. David is a very keen and rigorous research mathematician and decided to return to Exeter to study for a Masters in 'Autonomous Systems' (Artificial Intelligence) studying how an agent behaves when confronted by various external physical obstacles with a range of different attributes. He summarised this work enthusiastically by saying it was really all about giving 'the agent' a specific objective and then setting the agent up to go about gathering information and then using it to make decisions about what to do next in pursuance of achieving the objective.

Jackie Offord, AMIMA who works for DSTL gave the third very enthusiastic presentation covering an outline of her career in mathematics to date, she stated that her employer really values professional expertise and is positively supporting her working towards achieving Chartered Mathematician status. Jackie said that for her, every day at work was different and stimulating, working in Operational Research and applying scientific methods to help business managers to make strategic business decisions, she outlined three approaches commonly used namely: (1) Linear Programming, which she exemplified as doing a cost benefit analysis of the most effective mixture of ingredients required to 'optimise the flavour' of the cake; (2) Network Analysis and Graph Theory, which might involve taking social network analysis and human psychology and expressing certain key attributes mathematically. Jackie gave as an example the study of how much more effective it might be to drop leaflets in a war zone rather than bombs to exert influence on a potentially hostile population and the modelling of how the rate and nature of leaflet recovery might 'spread the word'. Her third example was the use of Statistical Analysis to determine what are the key measures to determine the success of a break away organisation and the likely success of any 'counter break away' campaign.

From 2.45 pm until 3.45 pm, the second invited speaker, Dr Andrew Francis of Andrew Francis & Associates, Oil and Gas Transport Consultant Engineers, gave us all a thorough grounding in the nature and hazards associated with the deployment, monitoring, safety inspection and maintenance of high pressure pipe lines that are designed to run across country - usually in geographically remote areas - as used by the 'off shore' oil and gas industries. Dr Francis described the use of inspection robots - sent down the pipes periodically - to inspect for any signs of weakness or fracture in the one metre diameter, mild steel welded sections of pipe - buried just 1 metre below ground. He mentioned working with standard pressures of 75 bar (75 times atmospheric pressure) and went on to describe the consequences of accidental damage to such a line with dramatic effect:- (400 metre diameter 'fire balls' and flying mild steel 'shrapnel'). Needless to say the mathematics of probability and a very detailed knowledge and control, via certified procurement and installation programmes, of the tensile strengths of the steel used, all come in to play in full measure when these pipe lines are built. More mathematics is used to extrapolate safety limits and probable lifetimes of each and every section of pipe line. Hence the title of Dr Francis talk was not surprisingly "Safety in Numbers".

Following a coffee break Nira Chamberlain, CMath MIMA gave the final presentation of the day from 4 pm until 5 pm. Nira began his presentation with reference to the logistics of submarine rescue, using colourful graphical presentations and computer simulations of a large submarine crew, trapped in a crippled vessel being rescued by a limited number of emergency rescue vessels each capable of holding less than 10% of the total submarine crew at a time. His simulation included all aspects of the exercise including, necessarily, the utilisation of a limited number of decompression chambers on the surface.

Nira followed this by a demonstration of the logistics of keeping batteries of ship mounted anti-missile artillery 'in continuous service' during a typical military 'engagement' scenario involving the need to 'shoot down' all hostile incoming air-to-sea missiles travelling at up to Mach 2.8 using highly specialised high speed canon which throw up a blanket of artillery with up to 70 rounds of 35 mm shells per second and a high probability of any one placement 'jamming' at some time during the 'engagement'. The simulation presented included allowances for all facets of the logistics including the provision of spare parts and shells, via the supply chain from supply ships to the fleet in action, using both helicopters and sea going alternatives, with high resilience and to satisfy the ultimate requirement of providing 100% availability of the 'blanket' of artillery shells to protect the fleet from the incoming missiles.

To round up the day's events, Amanda Padbury invited questions from the floor and a stimulating debate ensued on a number of key discussion areas. These have now been captured in the Youth Proposition Document prepared by Amanda and her 'Action' team and the IMA is in the process of looking at ways of addressing the many and varied needs of younger members and younger mathematicians in the wider community.

The meeting closed after some final remarks by the chair with reference to the next 1-day YMC event in the Autumn of 2005 at Lady Margaret Hall, Oxford University. It is the intention of the IMA to hold two 1-day conference events every year, with the invaluable help of the growing organising committees, for the benefit of Younger Mathematicians and to encourage the growth of public awareness of the vital role played by Mathematicians in modern society.

Malcolm Davies
Deputy Executive Director