Team Math is a national Mathematics competition for 6th Year Secondary School Students run throughout schools in Ireland. The purpose of the competition is to stimulate an interest in mathematics.  Preliminary rounds of the competition are administered by the Irish Mathematics Teachers Association (IMTA). An invitation is issued to every second level school in Ireland inviting teams to enter the competition.  Following the preliminary round at thirteen centres around the country in January, fifteen teams qualified for the National Final.

The competition is based on a Table Quiz format. Students work in teams of four at a table solving eight rounds (and a tie-breaker, if required) of problems. At each round, teams are given two/four problems to be solved within a specified time limit. Problems are designed to be sufficiently difficult so that all the students must participate actively, no one/two students could solve all the problems within the time limit. Problems are based on the Higher Level Leaving Certificate Syllabus.

Dr Donal Hurley of UCC's School of Mathematical Sciences said Team Math Final is aimed at the very best Mathematics students throughout the country.  "Participants in the Final represent the very best cohort of Mathematics students nationally. The competition is a most enjoyable experience for all students who compete", he said.

At the preliminary round, students get the opportunity to meet other students. At the national Final, activities are organised during the day which enable students mingle with those from other centres. This social aspect of the competition ensures that students experience an enjoyable mathematical activity.

Teachers of award winning teams are presented with the same prize as their team members and all teachers of Finalist teams get an award. The IMTA prepare the  questions for the Final and oversee the grading of student solutions.

Organised by UCC's School of Mathematical Sciences, Team Math Final took place at UCC on Saturday, March 1st 2008 in the Multifunctional Hall, Áras na Mac Léinn with the competition running from 1.30-3pm and Presentation of Prizes at 3pm. Professor Patrick Fitzpatrick, Head, College of Science, Engineering & Food Science presented the prizes (see speech attached).

Picture:   Paidi Kelly, Rowland Bent, Teacher Geraldine Gilroy, Kieran Walsh and Thomas Bent of St. Joseph's CBS, Nenagh, Co Tipperary Winners of the National Final.
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Text of Speech by Professor Patrick Fitzpatrick at the Presentation of Prizes at Team Math Final

It is a great pleasure to welcome you to University College Cork and the College of Science, Engineering and Food Science.

You’ve all been through a very competitive process to get to this stage of the competition and no matter who gets the awards you are all winners. Congratulations on your success!

As well as being a fascinating subject in its own right mathematics provides the fundamental underpinning of all science. This is true now more than at any previous time in history. All of science needs applications of mathematics.

From the time of Newton in the 17th century through Euler, Lagrange, Laplace, Legendre in the 18th century and Fourier, Cauchy, and Hamilton in the 19th up to relativity theory and quantum mechanics in the work of Einstein and Schrödinger in the 20th centuries, mathematics and physics were the closest of collaborators. This was mainly in analysis and geometry but also in algebra where group theory plays a part as pioneered in the work of Lie, Cartan and Weyl.

During the 20th century mathematics took off on a journey of its own and discovered and rediscovered a whole range of different specialisations in analysis, number theory, algebra, and geometry. These were in “mathematics for its own sake”, “pure mathematics”, or what might be better called “abstract mathematics” where mathematicians find a wonderful world to explore, independent of any applications. One of the most outstanding discoveries was Andrew Wiles’s proof of the almost 400 year old conjecture known as Fermat’s Last Theorem, which we can now call Fermat-Wiles Theorem.

But history has a funny way of proving pure mathematicians wrong about the purity of their discipline. Or maybe it’s the way the human mind works that somehow the mathematics we come up with is just right for something – we may not know what at the time but later someone makes the connection.

To take some example from the fields of algebra, discrete mathematics, and number theory:

When the 18th century mathematician Leonhard Euler tried to figure out if the Sunday morning walkers in Königsberg could cross all seven bridges over the river and get back to where they started without retracing their steps he could hardly have anticipated that he was inventing the subject of graph theory which is so fundamental in the operation of the internet.

When, at the beginning of the 19th century Evariste Galois and Neils Henrik Abel invented what became known as Galois fields they would never have anticipated that they could be the key enabling technology behind the invention of the CD player and all other data storage devices up to the iPOD in your pocket.

When George Boole, working here in UCC in the 1850s and 60s, was trying to create a mathematical formulation of how people think logically, he could not have imagined his work being applied by engineers in the 1930s, who discovered how to implement Boolean algebra in electrical circuits and thus laid the foundations of computer science, and the whole of our high-technology, computer-driven society.

And when the English mathematician and number theorist G.H. Hardy said in the 1940s I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world" he could never have known that half a century later his beloved number theory would form the basis for all our encryption systems and therefore make possible all the millions of the secure financial transactions that are done between computers throughout the world every day.

In the second half of the 20th century, there was a wonderful reconnection between mathematics and physics, as physics discovered new elementary particles and new quantum processes that required the most advanced mathematics, such as in differential geometry, and string theory to explain. Five winners of the Fields Medal, considered the "Nobel Prize" of mathematics are mathematician-physicists of the late 20th century Connes, Vaughan Jones, Kontsevich, Novikov, and Witten. This is still work in progress and some of the most significant new mathematics is being discovered in connection with physics. In another direction the physics of materials led to the invention of nanotechnology which again requires advanced mathematics in its development.

Meanwhile, the mathematics of computation and computers – the mathematics of discrete processes as opposed to the mathematics of continuous processes – also came to the fore in the latter part of the 20th century as computers began to enter the world (and it is worth mentioning that the internet is only 20 years old – it was invented just before you were born). 

Computers and the ability to do massively parallel computation and to solve computationally complex problems provided further momentum to mathematics and the computer became an essential tool for the working mathematician.

As I said earlier, we take it for granted that we can move information, images, music, and so on from one place to another, record information all sorts of disks and media like iPODs. We take it for granted that banks and other businesses can move financial information around the world keeping it secure and reliable. This cannot be done without advanced mathematics of complexity theory and formal languages as well as coding and cryptography.

Other new applications have arrived – for example in the work of Black, and Scholes and Merton who were awarded the Nobel Prize in Economics, for their work in developing the equations of mathematical finance. It is now the case that almost everyone who goes to work in the most complex areas of the financial services industry is first and foremost a mathematician.
 
The biggest and perhaps the most fascinating new area of application of mathematics is in biology: if we want to model biological processes or to analyse the massive quantities of information that is provided in the genetic code, we must have computation and we must have mathematics.

In fact, biology is where the mathematics of continuous processes and the mathematics of the discrete structures come together, where for example we need the tools of analysis to model blood flow in the kidney, while at the same time we need graph theory and algebra to investigate the DNA code.   In the 21st century biology will become more and more accessible to mathematical modelling and the pressure to solve problems in biology will put more and more pressure on mathematics to come up with solutions.
 
To emphasise the universal applicability of mathematics in the sciences I’ll quote from Nobel Laureate in Physics, Steven Weinberg, who says “I am not a mathematician, but I regard mathematics as the core of any research programme in the physical sciences.”

Joel Moses, who is a computer scientist and President of MIT says “I for one cannot imagine operating a school of engineering or science in the absence of a strong and research-oriented mathematics department.”

Professor Sir Michael Atiyah, Fields Medallist, Director of the Newton Institute at Cambridge, and past president of the Royal Society says “Increasingly, the complex problems that scientists now face require more sophisticated mathematical understanding. The advent of more powerful computers has in no way decreased the fundamental relevance of mathematics. I can illustrate the scope of mathematical interaction with other fields just by listing just a few of the interdisciplinary programmes that we have run at the Newton Institute in the past few years: computer vision, epidemics, geometry and physics, cryptology, financial mathematics and meteorology.”  
 
Your presence here today means that you are junior members of the community of mathematicians. You are here because you love mathematics and because you’re good at it. There is a whole world of exciting mathematics to be explored; there is a world of applications of mathematics in the sciences and engineering.

When we think of the “grand challenges” for science and engineering in the 21st century we think of biomedical science, disease modelling and prevention, global warming, climate change, protection of the environment and its ecosystems, invention of renewable and sustainable energy sources, and so on. Every one of these challenges, and many others, will need mathematics for its solution. They will only be solved by teams involving mathematicians, whether working in industry, in government agencies, or in universities and research laboratories.

You are budding mathematicians, you have demonstrated that by being here today. I encourage you to continue to pursue your interest in mathematics confident in the knowledge that mathematics will be sustained into the future, that there are many future careers that involve mathematics. I encourage you to grow from budding teenage mathematicians into fully fledged adult mathematicians.

Thank you.

ENDS 

657MMcS

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