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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.

In addition to competitive rates, a 10% discount is available to Institute members and publishers. Discounts may also be provided for multiple purchases. All adverts are in full colour and job vacancies qualify for discounted web adverts.

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Yes, dear Reader, this is an editorial, wrote David Broomhead in August 2002, and so began the tradition of editorials for Mathematics Today. Dave’s last editorial was in April 2011, and between these dates Dave helped recre­ate the magazine as a regularly enjoyable and informative read for members of the IMA. Dave brought the same enthusiasm and commitment to Mathematics Today as he brought to his collaborations and friendships, his students and his academic thoughts. He influenced science policy in the UK and beyond through his work for the Research Councils and his internationally renowned scientific contributions. A chemist by training, he became a Professor of Mathematics and his death last year at the age of 63 was tragically early.

IMA Public Lecture: Hawking and Green

Every year the UK’s pure mathematicians and applied mathematicians hold major conferences, the British Mathematical Colloquium (BMC) and the British Applied Mathematics Colloquium (BAMC) respectively, but once every five years these conferences come together in one super joint meeting. This year, on 30 March to 2 April 2015, it was the turn of Cambridge University to hold what was the fourth such joint meeting, and I had the good fortune (if that is the right phrase) to chair the Local Organising Committee. We were delighted that the meeting generated enormous interest, and involved more than 600 participants from the UK and overseas, giving in excess of 300 invited and contributed talks on a vast range of topics from all across the mathematical sciences.

How to Model Honeybee Colonies
E Thorrington

Mathematics is a way of travelling logically from A to B, where A is a set of precisely stated rules or axioms and B is a set of predictions logically arising from these rules. Mathematical modelling is the art of mapping the real world onto these sets A and B. These are the two basic components of applied mathematics. One part is an abstract, rigorous toolkit for investigating logical truth, the other part is an attempt to align that truth with a more messy reality.

Using Tropical Maths to Model Ribosome Dynamics

If two activities must be performed consecutively then the time required to complete both is the sum of the individual times, but if they may be performed concurrently then the time required is the maximum of the individual times. For instance, imagine you are designing a train timetable. What is the earliest time at which a train can depart a given station? Certainly, it cannot leave until after it has arrived (despite what departure boards are prone to suggest!), but what other factors should be considered? Suppose that there are passengers arriving at the station on connecting trains from three other towns. We would therefore like to schedule our train to depart after these three trains have arrived. We don’t need to worry about the order in which the three connecting trains arrive; we only care that the departure time of our train occurs after the maximum of the three arrival times. To give the passengers a chance to change platforms and board, we should also add on a fixed amount of time to this maximum. Of course, in reality, rail networks involve huge numbers of trains with more complicated systems of dependencies between them. This sort of timing-analysis will therefore yield large systems of non-linear equations involving sums and maxima.

Full contents page of the June 2015 printed issue
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Content from the May 2015 issue

There was a smart chap called Einstein,
Whose theories curved way out of line,
He claimed light is bent,
No one knew what he meant,
But now we all think he’s divine.

Yes, I know, don’t give up the day job! Anyway, pick a word from the first line of the limerick. Now count the number of letters it contains and progress that number of words. For example, ‘Einstein’ contains eight letters and maps onto ‘He’. Repeat this process to the end of the limerick and I guarantee ... [drum roll] … that you will end up on the word ‘divine’. This exercise seems to demonstrate the convergence of a Markov chain, though we can do better than that. Wherever you started, you selected the word ‘light’ en route and this is my theme for this issue of Mathematics Today. The United Nations has declared 2015 to be the International Year of Light and Light-based Technologies (IYL), and with very good reason. This year celebrates several anniversaries of events that changed our perceptions of light significantly.

An Interview with Alexandra Randolph

Alexandra Randolph née Neville CMath MIMA is a teacher at St Paul’s Girls’ School in London. Her PhD was on the reaction and diffusion of chemicals within tumours. When Alex became a chartered mathematician, Rick Crawford CMath MIMA caught up with her for this interview.

I’d be interested to know about your voluntary work for the UK Mathematics Trust.

I help mark the Maclaurin Olympiad paper, set questions for the Junior Mathematical Olympiad and Senior Team Challenge and help at teacher meetings. I’ve also helped out at their summer schools and given a lecture to 200 teachers about stretch and challenge in the classroom. It’s really good to work closely with such great mathematical material for the classroom, but also to meet mathematicians from a range of backgrounds.

Improving Access for State-School Students

E ThorringtonIn a Guardian article [1] in November 2014, Paul Mason described how students from private schools have an advantage over state-educated students when applying for courses at leading universities. We support his conclusion that there should be a system that offers clear and transparent information about the requirements for courses, so that all students, whatever their background or type of school or college, understand what is required to access prestigious undergraduate degree courses.

Urban Maths: Mind Your S’s and D’s

I still spend some time writing computer code, but not half as much as I used to do when I first began my career. Back in those days, which are longer ago than I would care to mention, I typed many more lines of code than I did lines of text. And the nature of the code I was writing, and the tools that I was using, meant that I typed string quite a lot.  Now, that wouldn’t necessarily be a problem, but that sequence of characters has become permanently lodged in the muscle memory of my fingers, so much so that when I try to write strong I often end up with string instead.

Full contents page of the April 2015 printed issue
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Content from the February 2015 issue


The opportunity of editing Mathematics Today was one that I seized gratefully. For the past thirty years, I have enjoyed receiving copies of this general interest mathematics publication (formerly IMA Bulletin), so I am delighted to have this chance of contributing to its ongoing success. It had already been published for twenty years before I subscribed and early issues are still well worth reading.

My predecessor, Professor Linton, maintained and improved the quality of Mathematics Today and I echo the vote of thanks that appeared in December’s issue. All members of the Editorial Board generously and voluntarily donate considerable time and effort, as do the many authors of feature articles, reviews and correspondence. Of course, much credit is due to the Editorial Officer, Rebecca Waters, and other professional IMA staff.

University Liaison: Industrial Placements

Happy New Year! I hope everyone had a good holiday and success if you had start of year exams. Good luck for those of you having interviews this term.

We are really fortunate to have for this issue, two pieces by Waleed Backler from University of Greenwich about his one year internship with the Department of Health and NHS England and his short PLACE (Patient-Led Assessments of the Care Environment) assignment at Leeds Teaching Hospitals.

Are You Paying Too Much for Your Car Insurance?

E ThorringtonInsurers are risk-takers, accepting premiums to cover unknown, but potentially very large, future insured events; insurers have to balance complex theoretical mathematics with commercial considerations; they must be profitable but yet offer commercially acceptable premiums. In particular, in the car insurance market insurers have to take into account the possibility of selling the customer other products, real time pricing (as a result of price comparison websites) and new EU-wide Solvency II rules for capital management.

Full contents page of the February 2015 printed issue
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