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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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Mathematics Today reaches a worldwide readership of over 4,400 professional mathematicians six times a year. It carries advertising for mathematics books, software, job vacancies, financial services and a whole range of products of interest to our readers.

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Content from the current issue


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 (1924-1998). 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 induced-charge electro-osmotic flow around a polarisable particle and its resulting electrophoretic motion. Half a century later, his seminal paper on the ‘squirming’ motion of micro-organisms 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 induced-charge 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 part-time 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 equally-optimal assignments and choosing randomly from them.

Full contents page of the June 2016 printed issue
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Content from the April issue


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 Setati-Phakeng, 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 second-hand exchanges/clinks where the group splits into subgroups who clink glasses, and then representatives from each subgroup clink with each other – second-hand 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 Marie-Gabriel-Florent-Auguste de Choiseul-Gouffier, 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
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Content from the February issue


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 (I1) and the baker's ratio that describes the mass ratio of water or milk to flour (I2). 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 starch-based 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 ball-shaped 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 A-level alongside AS or A-level Mathematics courses. It is valuable for a number of reasons, including:
  • the increased time spent engaging with mathematics and developing greater fluency;
  • the study of important topics in pure mathematics not covered at A-level, such as complex numbers and matrices, that are essential for anyone going on to study maths, physics or engineering;
  • the opportunity to study a broader range of applications of mathematics;
  • the development of increased confidence and resilience in tackling demanding mathematical problems.

Full contents page of the February 2016 printed issue
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Supplementary Downloads

  • Kalman Filter Tutorial (June & August 2016)
  • Domineering (August 2015)
  • Symbolic Solvers (October 2012)
  • Quadrature Programme (December 2010)