MATHEMATICAL MODELS - Clongowes Wood College

Posted: 8th May 2013

MACSI is a project that is unique to Clongowes and is a fantastic opportunity for us to get involved in real world applications and see how problems in science and industry can be dealt with using physics and mathematics. The project on mathematical modelling was undertaken in conjunction with the Mathematics Applications Consortium for Science and Industry (MACSI) department of the University of Limerick (UL). It ran for the first time ever last year and we were the first school in Ireland to undertake such a project. After the success of last years project, this year MACSI returned to Clongowes and its Physics Department. In October Senior UL Research Fellow, Dr. Jean Charpin visited Clongowes to launch the first phase of the project and met for two hours with almost 40 students from Syntax and Poetry to begin the data collection phase of the work. The students in groups of five were asked to select one of four problems to work on. The problems were:

  1. If you were setting up a safari park how many lions and impala should you have?
  2. If you were to run a marathon, how long would it take?
  3. How can a room be maintained at a constant temperature?
  4. If you were to buy a car which one would suit best?

After each group chose their problem they set to work knowing that they would be under pressure to have their problems solved before they went down to Limerick to present their completed model and presentation of their project. Dr. Jean stressed to start off simple, but as we soon found out there was nothing simple about it! These were real world problems that didn’t appear to automatically lend themselves to mathematical analysis, and yet this is what we were expected to engage with.

So, after a month or so of gathering data on our problems, we were beginning to patch together a very basic formula on which our model would be based. It was a matter of taking the vast amount of information we had and taking what we felt was necessary and important for our models. This is where we began to run into difficulties, as the data seemed endless, and any formulas we came up with, simply didn’t make sense. In many cases we were on to something strong, maybe we weren’t quite sure what that was and in other cases we just didn’t know how to get there!

We got a massive boost in our progress however in December, when we were delighted to welcome Prof James Gleeson back to Clongowes for the second time. Prof Gleeson is one of the worlds foremost applied mathematicians and, notwithstanding the help we were getting each week from our Physics teacher Mr Stephen O’Hara and our applied maths teacher Mr Patrick Gorman we could not deny that the help of a world leading mathematician would be nice! And so along with Dr Jean Charpin they launched the second phase of the project, which involved the development of the actual mathematical models describing these systems. The two researchers worked with all of the groups and the day was inspirational for all involved. The Models now really started to take shape and, despite a few dodgy figures, we were nearly there. However, we still had to put the models to the test, create a poster on the model and prepare for the final presentation of our model in The University of Limerick. And so after a few late night sessions in the physics class and a few rehearsals of our presentation everything was in order and we were ready for the big day.

We arrived in UL and headed straight for the MACSI lecture room where we would be making our presentations. When we entered the room we were shocked at the turnout we had received. Not only had students come to view our projects but there were several professors in the audience as well so the pressure was on. The presentations ran smoothly and, while a few challenging questions from the students and professors were thrown our way, we found ourselves more than capable of answering them. Although not all our models had turned out exactly as planned, we learnt a lot from them and received a few tips on how we might improve them from Professor Gleeson. It was a great day out and a great way to finish off our year’s work. Who knows a few of us may even return to the world of Physics and Applied Maths in MACSI in the future.

The College and the students are deeply grateful to the MACSI group in UL and in particular to Dr Jean Charpin for his dedication to and enthusiasm for this project. Special thanks must go to Professor James Gleeson through whom this link has been established. Professor Gleeson is one of the world’s foremost applied mathematicians and we are deeply grateful for the time and effort he has invested in this project. But of course we must not forget Mr Stephen O’Hara without whom this project would not exist. He is the man responsible for establishing the links with UL and also put in hours of work with us helping us create our models along with the help of Mr Gorman. For their time, work and above all commitment to the project we are extremely grateful.

Peter Stapleton

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