IMA Talk: Maths – There’s an App For That

This is a guest post I wrote for the IMA BlogDr. Darren Dancey: “Maths – There’s an App For That!”

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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.

Limerick 2011

[This is an extended version of an article I wrote for MSOR Connections magazine – which you can read online]

During the final year of my combined honours degree in Mathematics and Computing at Manchester Metropolitan University (MMU) I received an invitation to a two-day Student Mathematical Modelling Workshop at the University of Limerick in the Republic of Ireland, hosted by the Mathematics Application Consortium for Science and Industry (MACSI). The workshop was followed by the 82nd European Study Group with Industry. The maths course at MMU is highly oriented around real world problem solving involving mathematical modelling, dynamical systems, numerical methods, ODEs & PDEs and contains a strong programming element, so this was something I thought would be good to attend.

My friend Chris and I applied for our places on the workshop and booked our flights. What better way to unwind after completing a maths degree than being put to the test! While packing our shared suitcase for the trip, we weighed the case and realised we were too heavy, so we repacked – some of it crammed in to our backpacks, some we left behind. Arriving at the luggage check-in desk, the suitcase was weighed and we were well under the limit. At this point we realised we had looked at the wrong units on the weighing scales. Typical mathematical modelling error – how apt. We reshuffled the contents of our cram-packed flight bags and put things back in to the suitcase, thinking idiots of ourselves.

Not really knowing how useful we’d be in helping solve problems, nor which type of problems we would like to tackle, we began by sizing up the problems set online while on the plane. I chose a problem on Equity Options & CDS Risk Management because it seemed an interesting situation to work with. The group consisted of both those who had studied financial mathematics and those who hadn’t, so there was a mix of abilities and understanding. The finance people got on with what they have done with similar problems, explaining themselves along the way, and others found useful things to bring to the group. I personally looked at the data we had been given, analysed the trends in the evolution of option prices over time and ran a Monte Carlo simulation in MATLAB to demonstrate the effectiveness of the strategy.

The second week was the study group so the lecture theatre was filled out with academics as well as the students who had stayed on. I chose to work on a problem in Electricity Prices and Demand Side Management, looking at estimating usage for a company called Crystal Energy in Ireland who offer electricity to companies at variable tariffs based on consumption. I worked with other members of my group on analysing the company’s data in MATLAB and Mathematica. We were able to produce useful information for the group, including isolating volatile periods in the day (e.g. between 12-2am) and in the year (e.g. mid-late December) by looking at the absolute difference (error) between corresponding timeslots and plotting contour maps. A report explaining our findings has been submitted for publication. As the study group fell after our final exams, it gave us a great insight in to the usefulness of what we had learned at university, indicated gaps in our knowledge and inspired us to attempt to solve problems that arise, small and simple or bigger and more complex problems alike. It gave us both the courage to realise that this is something we could do with our lives, applying our skills in such a real and meaningful way which could lead to significant results in personal, small or large scale industry problems.

A couple of times during the trip, I arranged Skype calls with Peter Rowlett, where he interviewed by about the study group and conference for his Math/Maths podcast, along with his American co-host Samuel Hansen. You can listen to these here: Episode 53, Episode 55

We had a fantastic time staying on the beautiful campus of the University of Limerick. We enjoyed the food, drink and surroundings, but most of all, the company – everyone there was really interesting, and it was great to share conversation with such an intelligent group of like-minded mathematicians. Although the daytime was spent working on maths problems, the trip was very social – we would move from a classroom or lecture theatre straight to the pub with the other students and staff and carry on discussions from the problems of the day, and our approaches to solving them. Also, during the second week, I received the results of our degrees – and I’d passed with second class honours.

We also took the weekend at the end of the trip to travel to Dublin, where we stayed with the family of one of the conference delegates we met. Dublin is a fantastic city, and we really enjoyed the weekend. We visited the campus of University College Dublin and its Maths Society‘s room. I was shocked to see their Maths Society was so well established that it had its own designated area of the Maths Department building! Last year I founded the Maths Society at MMU and we had nothing at all. We hung out in the Maths Society room for a while, looked at some books from their library and played on their N64! We also took a walk through the Maths Department’s own library, deep down in the basement of the building – where we walked through about five big rooms full of books – and when we reached the end, I picked up a magazine I saw on top of a box, turned it over to look at the back page, and spotted a review of a book written by my lecturer Stephen LynchDynamical Systems with Applications using MATLAB. Quite a coincidence!

Unfortunately I had some sad news on the night we left – a friend called to say one of my friends from the university canoe club, Dave Evans, had died in a climbing accident on Mont Blanc. This was devastating, and I found the news very difficult to take in. A hard thing to deal with – losing a friend so young. Dave was just 24 and had been out of university less than a year. RIP.