UKMT Leeds Summer School 2017

This year, I was fortunate enough to be selected as a Senior Student for the UKMT Leeds summer school. My role involved looking over the Juniors, giving them even more mathematics to think about to their hearts’ content.

The camp started with an icebreaker session upon arrival, building a bridge between two chairs. The effort of all the students proved fruitful, and the design was ultimately simple yet efficient! After the customary farewells to parents and a briefing, we went to dinner in our newly created groups of six, each led by a Senior student. Icebreaker activities followed, including some ‘puzzles’, some of which were pretty nasty! The night ended with a few group games including the likes of Splat and Mafia.

Monday marked the start of the proper schedule, with each following day roughly following a similar format. A lively breakfast with the Juniors, then some geometry in the morning. The masterclass was followed by ‘competitions’; some individual problem solving, followed by some groupwork then a relay. After lunch, the seniors began to prepare the Senior Surprise – the evening entertainment on Wednesday. Much discussion was had, until the theme of polyhedra seemed to prevail. Dinner was pleasant (especially the ice cream), then the Juniors had a talk about Conway’s soldiers. Games into the night, as before. 

Dinner

Dinner included some delicious ice cream. 

A rather hollow ‘football’ – with our intuitive way to supply pentagons. 

Tuesday began with a surprise – one of my team’s Juniors had to leave the camp, leaving us one short! In the competitions, we had a lot of fun doing more problems. Robin gave a wonderfully explained primitive root theorem talk, and at dinner, we were permitted to sit with people other than those in our teams. And so the seniors formed their own group, with some extended chatting. Not to mention the card games played before dinner… 

Card games for the 8 Seniors

The UKMT had provided some entertainment for Tuesday night, namely bowling! A short bus journey took us to Shipley Gobowling, and the seniors were allowed two lanes, four people each. It was fantastic fun, and we managed to fit in two games – high score for me was 108! Highest score was 122! Back at the gallery, we organised a concert schedule, and after that I played a bit of piano on the keyboard present. Appassionata, Fantaisie Impromptu, and more! It was tremendously enjoyable.

Bowling is a tough sport.

Wednesday was an eventful day for the seniors. For it was the day of the Senior Surprise! Breakfast followed by morning geometry and competitions, then a wonderful talk given by Oliver about Cayley’s Theorem about counting labelled trees. In the evening, all the seniors gathered to present the Senior Surprise concerning polyhedra. We gave three sessions, the first two of which were introductions, and the last was a proof of the six colour theorem. It was very enjoyable to present. 

Thursday morning was largely the same, and in the afternoon James gave a talk on Functional Equations. In the free session that followed, the seniors prepared their second surprise – a performance in the concert! The evening concert was a splendid array of talent, ranging from poetry to musical instruments. There was even a Dedekinds Hotter Cross Buns performance! I played La Campanella. The concert ended with a stunning Senior Surprise performance and the traditional Complex Numbers song. We were permitted to stay up for longer, and so games were played outside. 

Friday was the final day, and we enjoyed our final geometry masterclass. There were two more relays, and then everyone moved into the sports classroom for the final round – the mathematical pub quiz. Eight rounds later, and the points were totalled up for all activities throughout the week. And leading by over a hundred points were the Dedekinds (my team hehe)! Fantastic! 

Fish and Chips marked the final lunch of the camp, after which people started to disperse on their journeys. Photos were taken, and thanks to the staff were expressed.

Overall, the camp was a wonderful experience, especially as a Senior! Perhaps I may return in the future.

Joint UK-Hungary IMO Camp 2016

A report that I wrote for my school, from this amazing experience! Slightly modified from my official report but also with a bit of fun and extras added in 🙂

UK Hungary Maths Camp 2016 (link to pdf version)

Every year, the UKMT (United Kingdom Mathematics Trust) organises a joint UK-Hungary Maths Camp for the top 20 performers in the UK in the BMO1 (British Mathematical Olympiad Round 1), in order to train students for competitions such as the IMO (International Mathematics Olympiad). Having scored full marks in this competition, I was delighted to have been invited to the camp again this year. The camp took place over nine days in the Christmas holidays as usual, from the 27^th December 2015 to 4^th January 2016.

On the 27^th December, our group of 23 (including the three leaders Dominic, Kasia and Gabriel) gathered at Terminal 3. An aura of excitement was already developing. The journey, comprising of a flight and coach ride, was relatively painless and after six hours we finally arrived in a scenic town named Tata where we would be staying for the next week or so. There we met the twenty Hungarian students, some of whom I had already met last year, and then we had some dinner which was remarkably delicious. After that, we played the ‘interesting’ game ‘Cards Against Humanity‘ (thankfully we only played that once!).

On the next day the proper schedule of the camp commenced. At 8:00am we sat down in exam conditions to do three maths problems in two and a half hours; what the Hungarians called ‘Individual Problem Solving’ (IPS). Following a 30 minute break we enjoyed an interesting geometry lecture given by András Hraskó. He talked about a heart shaped graph known as a cardioid, and how this could be used to prove Morley’s Theorem (an amazing result concerning angle trisectors). The lecture took place either side of lunch and a short walk. After some relaxation (often table tennis in my case!) we formed groups of UK and Hungarian students to do some problem solving together; in fact the problems were the Hungarian students’ favourites from the Hungarian Maths Olympiad. After dinner, having gone through the IPS we had some more free time until 10:30pm (lights out).

The next two days were largely the same, except for a few things. On the 29^th, the lecture was given by the Hungarian IMO Leader who went into complex numbers in geometry and also some number theory too. After dinner a mathematical relay took place, where we tried to do 21 problems in the shortest time possible. This proved to be extremely enjoyable and fortunately, no-one was trampled in the stampede of people checking their answers! On the 30^th we learnt about some theorems in number theory from a professor of a university in Budapest, and also had a bonus lecture from Dominic about minima after dinner. During our free time a lot of card games were played, especially the notorious ‘Mao’. But everyone knew that we had to sleep early that night, in preparation for the important test the next day.

New Year’s Eve was probably the most demanding of the days but also the most satisfying. At 8:00am we were treated with a four and a half hour exam (the ‘Tata Test’) instead of an IPS. This took us until lunchtime, and perhaps fortunately after that, no more maths was scheduled for the day! After lunch we had some free time and at 3:00pm we had an early light dinner. Then at 5:00pm we travelled to Budapest.

The beautiful city was already brilliantly illuminated in the dark upon our arrival, and its spectacular grandeur could only be wonderfully enhanced by the fact that it was the last day of the year. We went for a stimulating sightseeing walk around the city until we arrived at a theatre where we watched a Hungarian history interpretative dance performance (instead of an opera like last year, perhaps due to the fact that there was no intelligible speech for us!). This lasted approximately to 11:00pm in the evening, and consequently we only just managed to return to the camp at 5 minutes to midnight! Rushing up to the lecture room we celebrated the New Year with a sumptuous dinner accompanied by (optional) alcohol. Celebrations continued late into the night until everyone was exhausted, after which we finally slept.

New Year’s Day was much less arduous; of course there was to be no IPS in the morning and in fact the day started at 11:00am with a short talk on combinatorics given by the famous Chandal (with his ocarina). Incredibly it started to snow during the lecture and as a result the ground was covered with a thick layer of snow. The perfect setting for a colossal snowball fight! At 3:00pm we walked to the town centre to watch a concert and when that had finished, we started walking back. The dramatic battle began! (It all started when someone started throwing piles of snow into others’ faces.) Hours passed until we finally returned to the hotel where we ate some cake after dinner, and after this we had a supportive question-answer session.

2^nd January marked the last complete day of the camp for the Hungarian students. The schedule was roughly the same as the first day, in which we did our final IPS. In the evening we all participated in a (non-maths) quiz organised by our three UK leaders which was an excellent way to spend the Hungarian students’ final evening at the camp. In the morning of the 3^rd January we had a short lecture about set theory given by Zoltán, one of the Hungarian leaders in last year’s camp. After some Hungarian problem solving, a short walk and lunch, it was time to say goodbye to the Hungarian students who left promptly afterwards. But the camp was definitely not over for us.

At 1:15pm we did one more four and a half hour exam (for some sort of selection) and after that, the mathematics at the camp was basically finished. Whilst the scripts were being marked we all had some much needed free time (including some table tennis and card games), and after we received our marks, our conversations continued late into the night.

On the 4^th January, having packed our luggage we set off to the airport and boarded the plane back towards the UK. Saying our farewells we parted from London Heathrow and this marked the proper end of the exhilarating camp for this year.