Mathematics Today
Mathematics Today is the membership publication of the Institute of Mathematics and its Applications.
Issued six times a year, this general interest mathematics publication provides articles, reports, reviews and news for mathematicians.
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Content from the current issue 
Editorial 
Celebrai! Rio de Janeiro is where the parties will be during August and September, as the Summer Olympic and Paralympic Games converge on this beautiful Brazilian city, which paradoxically will be celebrating winter. The statistics are stunning: more than 10,000 elite athletes from 206 nations will compete for 306 sets of Olympic medals in 39 sports, which will offer an amazing variety of challenges for competitors and much excitement for those of us lounging on sofas. These sports include two new events, rugby sevens and golf. Similarly impressive, more than 4,000 athletes from 56 nations will compete for Paralympic medals in 23 sports. These sports also include two new events, canoeing and triathlon: a thrilling prospect indeed. 
Hitchin wins Shaw Prize 
This year’s Shaw Prize in Mathematics was awarded to Professor Nigel Hitchin FRS (Savilian Professor of Geometry, University of Oxford) ‘for his far reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance.’ Indeed, Hitchin’s profound and imaginative work has had tremendous impact in many different areas of Mathematics, including algebraic geometry, differential geometry, complex analysis, topology, integrable systems, mathematical and theoretical physics. 
Mathematics and Financial Markets 
The David Crighton Lecture 2016, was delivered by Frank Kelly on Thursday 12 May 2016 at the Royal Society. The following is a brief outline of the lecture. A substantial proportion of mathematics graduates, at both first degree and doctoral level, enter the financial services sector (Table 1). This is hardly surprising given the apparent importance of the sector to the economy (Figure 1), and the role of mathematical modelling in the valuation of instruments and the assessment of risk. What is striking is that, with some notable exceptions, few mathematicians have been actively engaged in the design of financial markets. This is undoubtedly a serious challenge with parallels from other largescale complex networks: to design a distributed system, linking selfinterested and intelligent agents, so that the outcome is effective and efficient. 
Maths in a Twist 
It seems such a simple thing. Take a strip of paper, bend it around, and join the ends. You end up with a familiar and not very interesting object – a simple cylinder. It’s no surprise that when we cut the cylinder in half we end up with two, somewhat narrower, cylinders. This is easy to do, and easy to visualise. But this article is going to be an introduction to topology. In topology we discard the concept of distance and angle. We are allowed to smoosh things about, stretching, squashing, and generally deforming things. No tearing, cutting, and glueing allowed, unless we put things back afterwards. For these reasons topology has sometimes been called ‘rubber sheet geometry’. Topology does talk about shapes, but it turns out that that description is attractive, catchy, and wrong. We will see why later. 
Full contents page of the August 2016 printed issue to receive Mathematics Today subscribe or join the IMA! 
Content from the June issue 
Editorial 
The question facing voters on 23 June is ‘Should the [UK] remain a member of the [EU] or leave the [EU]?’ with corresponding answers ‘Remain ...’ and ‘Leave ...’. This format is well designed: clear, concise and impartial. In contrast, regional referendums on Welsh devolution (2011) and Scottish independence (2014) had draft questions ‘Do you agree ...’, which would have led voters towards apparently favoured positions had they not been changed before implementation. However, their simple answers of ‘Yes’ and ‘No’ could still have introduced bias as affirmation is generally deemed more pleasing than negation. These were also the options for nationwide referendums on the European Community (1975) and alternative voting (2011). The current referendum avoids these problems and has fair campaign rules, though extensive feedback arising from media reports, opinion polls and social networks will surely influence the outcome. 
The IMA Lighthill Lecture at BAMC 
Delivering the 2016 IMA Lighthill Lecture was not only a great honour, but also an opportunity to reflect on the influence of Sir Michael James Lighthill (19241998). Of course, he is well known to this audience as the founder of the IMA and Lucasian professor at Cambridge. He is remembered worldwide as a pioneer in theoretical fluid mechanics, especially in aeroacoustics and swimming, which was also his passion in real life. Personally, I first came across the work of Lighthill, when I was trying to calculate the inducedcharge electroosmotic flow around a polarisable particle and its resulting electrophoretic motion. Half a century later, his seminal paper on the ‘squirming’ motion of microorganisms provided a useful mathematical framework that could also be applied in this context. Lighthill’s emphasis on broken symmetries in swimming also foreshadowed recent developments in inducedcharge electrophoresis. 
A Tennis Assignment Algorithm 
For some years, I have played social tennis at a local club and have recently organised midweek men’s doubles matches for those who are retired, work parttime or have flexible working arrangements. This used to consist of asking each member of the group about their availability in the coming week, and how much they would like to play, and from their responses, putting together a set of fours using just pen and paper. However as the numbers increased, I started to think about how I could make the process easier and more efficient by writing some code and treating it as an optimisation problem. This article describes how I tackled the problem. The initial purpose of the algorithm was to automate what I had done manually, by finding a feasible assignment of players to groups across the week and to maximise the number of groups formed. As it is clear that generally there are many possible solutions, the next step was to remove any bias or favouritism in the choice of the groups, by generating all possible feasible and equallyoptimal assignments and choosing randomly from them. 
Full contents page of the June 2016 printed issue to receive Mathematics Today subscribe or join the IMA! 
Content from the April issue 
Editorial 
One of the most enjoyable aspects of being a mathematician in academia is encountering diverse and exciting challenges. One such incident occurred recently when a refrigeration engineer brought two tubes into my office and plonked them on my desk. ‘Can you model intrinsic weight gain and predict time to saturation?’ she asked. As so often happens, my mouth uttered ‘Yes’ with little input from my team and despite my ignorance. These right annular cylinders were 127 mm long and sealed at both ends, with external diameter 124 mm and bore 70 mm, as illustrated opposite. One of them rattled ominously, though my visitor explained that they were sections of pipe lagging and that the noise was caused by a desiccant. Cold liquid refrigerants pass through the pipes, with the adverse effect of causing costly condensation damage. The engineer had executed the following well designed experiment, which was repeated many times for tubes of various materials and dimensions, in order to address this problem. 
Raising the Profile of Black Mathematicians 
According to Professor Rosina Mamokgethi SetatiPhakeng, the first Black South African female to get a PhD in Mathematical Education: Being the first is not something to be proud about, it is a calling to ensure you are not the last. My name is Dr Nira Chamberlain and I became the first Black Mathematician to be referenced in Who’s Who, which is a leading source of biographical data on more than 33,000 influential and distinguished people from around the world. Published annually since 1849, I am only one of approximately 30 mathematicians referenced in the 2015 edition of this book. Inclusion has therefore come to carry a considerable level of prestige. 
Small Worlds by Design 
Connecting all the members of a large group involves many exchanges; think of it as clinking glasses at a social gathering. Allowing secondhand exchanges/clinks where the group splits into subgroups who clink glasses, and then representatives from each subgroup clink with each other – secondhand clinking – can decrease the number of clinks. This paper finds the optimal number of subgroups necessary to minimise the total number of clinks. It also looks at what is optimal if there is third and higher level clinking. Examples are given of such problems arising in parallel computer systems, social media, communication systems, and sports tournaments. 
Historical Notes: A Mathematical Inscription from Ancient Pergamon 
During the latter part of the 18th century, the wonderfully named polymath Comte MarieGabrielFlorentAuguste de ChoiseulGouffier, French ambassador to the Ottoman Empire based in Constantinople, embarked on an extensive series of travels around the Aegean and Asia Minor. Writing up his journeys and observations in the similarly wonderfully named Voyage Pittoresque de la Grèce, he copied the details of a particular inscription, written in Greek, found at Pergamon and dating from the 2nd century CE during the Roman Antonine period. This inscription is the only ancient one, known to me, that contains any mathematics. Sadly the stone itself would now appear to be lost. 
Full contents page of the April 2016 printed issue to receive Mathematics Today subscribe or join the IMA! 
Content from the February issue 
Editorial 
Let me start by congratulating Professor Chris Linton on his recent appointment as IMA President and wishing him well during his term in office: the IMA will undoubtedly prosper under his leadership. His predecessor, Professor Dame Celia Hoyles, was an excellent president who achieved much over the past two years. Among her many contributions, Celia was guest editor with Professor Richard Noss for December’s special issue of Mathematics Today on the theme of education, surely one of our most important professions. I hope that you enjoyed reading the wide selection of entertaining articles by international authors, which clearly demonstrate the fluidity of mathematics and the adaptability of teaching to incorporate new technology as a means of enthusing and inspiring our students. For those interested, IMA Councillor and former Honorary Secretary, Professor Nigel Steele, and his colleague Matthew Bulmer (NCTL) will present a talk on Training Mathematics Teachers at the Mathematics 2016 conference in London on 17 March. 
The 2015 ECM Autumn Conference at Bath 
On Saturday 14 November, more than 80 mathematicians in the early stages of their career gathered together at the University of Bath to hear and talk about promising areas of mathematics, and the challenges that young mathematicians face in those fields. The day was a big success despite the unfortunate weather, and it gave ample opportunities to everyone who attended to network with their peers from different universities and organisations. 
How to Make the Perfect Pancake 
We explore the cooking of pancakes using a combination of kitchen experiments and mathematical theory. The properties of a pancake are characterised in terms of a dimensionless geometrical measure of aspect ratio (I_{1}) and the baker's ratio that describes the mass ratio of water or milk to flour (I_{2}). The patterns on the top and bottom of pancakes are analysed in a kitchen study and explained in terms of how the vapourised liquid in the batter escapes. We determine the properties of a perfect pancake. Pancakes are a starchbased comestible created by pouring batter onto a hot solid surface and cooking until solid [1]. They come in a lot of different shapes from the large, thin, circular French crêpes to small, thick, circular drop scones from Scotland or ballshaped æbleskiver found across Scandinavia. 
The Participation of Girls in Further Mathematics 
Further Mathematics (FM) is a qualification designed to broaden and deepen a student’s mathematical knowledge, and can be taken to either AS level or Alevel alongside AS or Alevel Mathematics courses. It is valuable for a number of reasons, including:

Full contents page of the February 2016 printed issue to receive Mathematics Today subscribe or join the IMA! 