Are you a university maths student and want to share your passion with younger generations? Then why not take part in the second Further Maths Network - Rolls-Royce poster competition? Undergaduate and PGCE maths students from the UK are invited to submit posters conveying the essence of a mathematical topic they have covered at university. The poster should be aimed at school and college
students who are studying AS or A level mathematics. Entries from teams of students are welcome. The closing date is the 31st of March 2009, and two winners will receive a prize of £100 each. The winning designs will be printed as A1 posters and sent to schools and colleges registered with the Further Mathematics Network, and others with which FMN centres are in touch, for display in the
mathematics department, potentially reaching over 2000 schools and colleges.
Last year's winner, Michael Manfredi, was presented with his prize by Charlie Stripp of the Further Maths Network at the Rolls-Royce Learning and Career Development Centre in Derby (Michael's the one in the picture receiving the cheque!). You can see Michael's winning poster on cryptography on the Further Maths Network Website.
If you want to take part, then email your entry to Janice Richards, including your name(s) and full contact details, with the poster attached as an editable file. For more information, contact Richard Browne.
And if you prefer writing to designing posters, don't forget the Plus new writers award 2009. Anyone can enter, and there are special categories for university and school students. Winners will achieve everlasting fame through publication in Plus, and receive iPods and books. Closing date is the 31st of March 2009.
Gaffes, murder plots, and hockey mums — the US election circus is in full swing. Personality politics is partly a consequence of the first-past-the-post system — but what are the alternatives? Can any system guarantee to represent the will of the people? Do opinion polls manage to capture its voice? The following selection of Plus articles provides mathematical answers, insights and
With US election week upon us, we thought you might appreciate a look at alternatives to the first-past-the-post system used to elect the US President and Congress, as well as the UK government, and many others around the world.
For an even 'fairer' alternative to proportional representation, have a look at the Hare-Clark system of quota-preferential voting use in Tasmania. A good summary is at http://www.abc.net.au/elections/tas/2006/guide/hareclark.htm
Plus is proud to bring you a brand new regular feature: the Plus sports page. This will be regularly updated with stories exploring the maths in sports, from analysing scoring statistics to planning the perfect strategy.
We start off by looking at — what else? — football. Being the manager of a Premier League football club may seem like one of the most glamorous jobs in the world — with the fame comes fortune and the opportunity to travel (well, to Hull, Wigan and Portsmouth anyway). However, as far as job security goes, football managers live on the edge. Their terms can be terminated almost on a whim by
their club's owner, and they live and die by their team's results.
It would seem that there is no way to predict how long their tenures will be. However, a collection of researchers from the UK, Singapore and the US have found that there may be a strong mathematical trend underlying how long football managers stay in their jobs.
Really interesting results and an enjoyable article. I think an interesting sideline could be the relationship between the chairmans length of tenure and the managers. Clubs also have a reputation; take the Newcastle United fiasco recently. Did the researchers find a link between the prior success of the club under the previous manager, with the length of tenure of subsequent managers? i.e.,
when Alex Ferguson leaves Manchester United, will his successor last as long?
The History of Mathematics Special Interest Group of the Mathematical Association of America (HOMSIGMAA) has just launched a writing competition for undergraduates. The MAA invites students to write on any topic in mathematical history they choose, and winners will receive a year-long MAA student membership, as well as books from the MAA bookstore. Closing date is the 31st of March 2009. For
more information, visit the HOMSIGMAA website.
And if you're not a student, or want to write about something other than history, or simply want to be published in Plus, then don't forget our very own Plus New Writers Award 2009. Besides the fame and glory of appearing in Plus, you could win an iPod and selected books. Closing date 31st of March 2009!
It's hard to believe these days, but bankers do occasionally base their decisions on rational and robust bits of mathematics. A central player in this context is the Black-Scholes equation, which won its discoverers the Nobel Prize in Economics almost exactly 11 years ago, on the 14th of October 1997. The Black-Scholes equation is a partial differential equation which tells you how to price
options. An option is a way of reducing risk: it's a forward contract giving you the opportunity (but not necessarily the obligation) to buy a certain commodity or stock, for example fuel, at some specified time in the future for an agreed strike price. An option is an example of a so-called derivative, because it derives its value from the underlying variable (the price of the fuel).
Derivatives and options, as we all now know, can be traded in their own right, and have the potential to make people very rich, but also to break the bank (as happened literally with the Barings Bank in 1995). One important question if you're in the business of trading derivatives, is how much they should cost. Since options are all about the future, it may seem as if pricing them should
involve a certain amount clairvoyancy, but in fact the Black-Scholes equation does it all for you (for a type of option called a European call). All you need to know to use the equation are the current price of the stock and strike price of the option, the expiry time of the option, the interest rate and an estimate of the versatility of the stock.
In their original 1973 paper Black and Scholes built their model on the assumption that the stock price was a function of a Brownian motion. A Brownian motion is a random motion, as you would expect to see when you let a particle float in a liquid or gas. Mathematically, you can describe it as a stochastic process: at any given time, the stock price (or the particle) moves up or down (or, with
a particle, in any of the available directions) with equal probability. Using this model for stock price behaviour, Black and Scholes found that the problem of pricing an option becomes equivalent to that of solving the heat equation from physics.
The original Black-Scholes model made some simplifying assumptions, for example that shares don't pay dividends, but it is possible to work around many of these and obtain more sophisticated and comprehensive models. These have been at the heart of financial mathematics ever since. Unfortunately, Fischer Black died two years before the award of the Nobel Prize, so Myron S. Scholes and Robert
C. Merton (who's name isn't attached to the equation) ended up sharing it.
If all of this makes you wonder who should really be blamed for the current financial crisis, read the Plus article Is maths to blame?
For more in-depth information on derivatives, read the Plus article Rogue trading?