Welcome to the Institute of Mathematics and its Applications (IMA) blog. The IMA is the UK's learned and professional society for mathematics and its applications. We promote mathematics research, education and careers, and the use of mathematics in business, industry and commerce. Among our activities we produce academic journals, organise conferences and engage with government.

In this blog we will publish mathematical articles and news to reflect the interests of our members who come from a multiplicity of different organisations including university academics, industrial mathematicians, financiers, school teachers, scientists, civil servants etc.

Friday, 9 December 2011

Lessons for mathematical modelling from the global financial crisis

Professor Lyn Thomas (Southampton University) made the long trip up Nottingham Trent University yesterday to give a talk to the IMA East Midlands Branch on 'Lessons for mathematical modelling from the global financial crisis'.

Lyn wanted to talk to us about the crisis, where the problems were, but, to satisfy the audiences' hunger for mathematics, bring out the issues with the models that were used!

An interesting background to consumer finance, for both the US and UK was given, with some big numbers like 1500 billions of debt in the 2000s, up from 400 billions in the 1980s. Though I didn't note down if this figure was dollars or pounds, but, on the scale of it, I don't think that matters too much as it is a lot of money no matter what!     

The historical aspect to the talk was really quite interesting, I'd suspect that the audience, like me, had some interest in finance, but may not have known about some of the specifics that were involved in the crisis, particularly in the US. If you cannot get to this talk elsewhere, then you may wish to find out more about Fannie Mae and Freddie Mac, two companies whom between them had more than 50% of the US mortgage market in 2000.

The timeline of events continued to meander up to the prime time (or should that be sub-prime time) of 2007-2009 where the crisis really hit. Specifics on what happened leading up to and which contributed to the issues seen during this period were explained - this included the modelling!

Lyn summarised with seven key points, the last being:
  • If the model disagrees with common sense think carefully about using it.
The idea of disagreeing with common sense treads the fine line between pushing the boundaries and being able to come up with something new, innovate and useful, or coming up with something that may even cause a global crisis!

The next East Midlands Branch talk is Complex Networks in Biology by Jonathan Crofts (Nottingham Trent University) on 26th January 2012 at the University of Leicester.

Thursday, 1 December 2011

Dr. Darren Dancey: "Maths – There’s an App For That!"

Ben Nuttall wrote this guest post about the recent talk to the IMA North West Branch "Maths – There’s an App For That!" by Dr. Darren Dancey, given at Manchester Metropolitan University on 15 November.


This North West regional talk was delivered by Manchester Metropolitan University’s Computer Science lecturer Darren Dancey, whose teaching specialisms include programming and artificial intelligence. Darren also runs an iPhone development course for industry programmers and his research involves Neural Networks, Genetic Algorithms and Decision Trees. Known among students and colleagues for his coffee drinking and vast array of shiny iProducts, we were all keen to hear what he had to tell us about what people were utilising the latest in handheld technology for, with regards to mathematics.

Darren’s presentation involved a visual display of his iPhone screen on to a widescreen television for live demonstrations of the apps he wanted to share with us. We were shown a number of different types of apps – simple addition games for kids, quiz fire maths questions for all ages, interactive number games, a range of calculator apps, all the way to more technical software like Wolfram Alpha and real-time Fractal generators.

The simple games demonstrated were discussed and the group generally thought their usefulness depended on whether they were actually teaching concepts or forcing memory, or whether they were merely games using numbers. It was suggested that for two main reasons, the use of a smartphone for purposes such as learning times tables or revising exam topics would be invaluable: children and teenagers love gadgets and anything on them is immediately more attractive; and a smartphone (unlike a parent) will never get bored of asking “What’s 7 times 8?”.

The iPhone comes with a standard calculator, and as Darren demonstrated, rotating the screen yields a set of additional functions – the sort of thing you get in a standard scientific calculator. However there are alternatives available in the app store – such as an RPN financial calculator, or a more modern interactive calculating space:  an app called Soulver, which allows text to be entered in human readable form, such as “£30 per night x 3 nights” and each line entered stores its calculated value in a side column, accessible for following calculations. See acqualia.com/soulver

The Wolfram Alpha app, Darren explained, is a product developed by the makers of technical computing software Mathematica, and was initially sold for £30 on the app store despite the web version being available through any phone’s web browser. The price dropped several times, now under £2.00. I recently purchased it for my Android phone at just £1.89. Wolfram Alpha is described as a computational knowledge engine. It works like a search engine – you just enter your query – but rather than showing search results potentially leading to an answer, it interprets your input and provides whatever it thinks you were looking for: the solution to a calculation (normal operators +-x/, derivatives, integrals); a conversion (currency, units), ask for information about a topic (ODEs, pi, Riemann Hypothesis) or discipline-specific definitions or calculations from the whole range of mathematics – discrete maths, dynamical systems, finance, topology. Darren demonstrated a good example of its power of interpretation with the query “earth population / surface area” which yielded the result “34.5 people per square mile” as well as a graph showing the growth of population and some unit conversions. The latest review on the app store is currently “Love this app. It's like having a geek in your pocket.” – Take a look at the online version (see examples) at wolframalpha.com

We were also shown a video entitled ‘Interactive Exploration of a Dynamical System’ in which Apple user interface designer Bret Victor demonstrates the effectiveness of using the interactivity of using a tablet (his iPad) to explore the nature of evolving systems such as the predator-prey model. Rather than looking at so-many-x and so-many-y a system is changing, we can use the tip of our finger to drag the initial values up and down and see the effects these changes have right in front of our eyes. A fantastic video well worth a watch at worrydream.com.


Ben Nuttall is a mathematician & web developer in Manchester. His blog is at BenNuttall.com.

The next IMA North West Branch talk is 'Metamathematics: Strange Loops and Incompleteness' by Dr Joel Haddley (University of Liverpool) on Tuesday 6th December 2011 at University of Central Lancashire, Preston.