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Participants were divided into five subject-based groups – humanities, languages, mathematics, medicine and social sciences. Sav was part of the mathematics group. Here is his diary.

Monday:

"I arrived at the Harvey Court site on West Road, after about two and a half hours on various trains and buses. My room was quite comfortable and I settled in quickly before going down to meet everyone.

"Dr Andrew Bell (Admissions Tutor at Gonville and Caius) gave us a quick introduction to the Summer School and before long we were having lunch. Everyone was very welcoming, especially the student helpers, and I was already struggling to remember everyone's names.

"I was amazed at the informality of our first subject session - our lecturer, Dr Ed Brambley was very approachable, and was quite happy to have conversations and open discussions about things, instead of talking directly at us.

" ̽»¨Ö±²¥welcome reception soon after helped to reaffirm the fact that members of faculties are as friendly and casual as the students themselves.

"Dinner in hall at Gonville and Caius’s Old Courts provided us with another excellent chance to get to know each other. ̽»¨Ö±²¥food is wonderful, and current students told us that this was a typical meal in hall. I could certainly get used to that kind of food every day!

"Not long after dinner, we all went punting on the Cam. This was a very relaxing and casual chance to get to know more people, while we drifted past the many grand buildings by river. I had a go at punting myself, and thankfully, I didn't embarrass myself by falling in.

Tuesday:

"After a good hearty breakfast, we walked to the Centre for Mathematical Sciences (CMS) for our next subject session. I think I speak for all the mathematicians who visited Cambridge when I say that the CMS is spectacular. We didn't expect to see such modern buildings, complete with a grass roof and well stocked cafeteria. In fact, over the next two days most of us chose to spend a lot of our free time playing cards in the CMS itself, because it was so comfortable.

"Our first real lecture, from Dr Richard Gibbens, gave us a true introduction to university-level mathematics. We were introduced to concepts in probability that we'd covered at school before, but with a lot more rigour and formality than we were used to.

"We had the first of our many coffee breaks soon afterwards, before returning to try our hand at some harder probability questions set by Dr Gibbens. Some of these were similar to questions we were given at school, but most were designed to let us think for ourselves and try different approaches.

"We had another great lunch in Harvey Court before we returned to the CMS for a lecture on Number Theory with Dr Vladimir Dokchitser. This started off with some very basic maths, and most of us were quite bemused, before Dr Dokchitser suddenly tied everything together and introduced us to higher level concepts such as Gaussian primes, building on these elementary ideas. It was particularly fun trying to prove part of Fermat's Last Theorem using these simple ideas in the last part of our session.

"Dinner was fairly rushed, but we enjoyed it nevertheless. ̽»¨Ö±²¥highlight for many was a delicious sticky toffee pudding. After dinner, we went to St John's College Gardens, for a performance of As You Like It by the Cambridge Shakespeare Company. Many of us were fairly sceptical about this evening event, but in the end almost all of us thought it was a very enjoyable play.
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Wednesday:

"Today was a day predominantly for the computer scientists in our group. We were introduced to many applications of computer science in our opening lecture, ̽»¨Ö±²¥Secret Life of a Mobile Phone.

"After lunch, we had a second lecture with Dr Gibbens, this time on Predicting M25 Journey Times. I thought this was a particularly unique lecture as it was given by someone who is a leading researcher in this branch of mathematical modeling.

"This was followed by a lecture from Dr Brambley on ̽»¨Ö±²¥Mathematics of Wave. During this lecture many of us felt quite uneasy, as the material we were covering was only barely comprehensible. But when we finished, Dr Brambley revealed we'd eventually touched on third year material, and we weren't expected to follow everything with ease!

"With sighs of relief on everyone's face, we were led to the grass roof on top of the CMS. No-one expected to see such a relaxing area on top of the building. Apparently people also try to sled down the hills on the roof in the winter, which is something I definitely want to see!

"Dinner in hall (our last one for this trip!) was brilliant as usual. For the mathematicians and a few lucky others, this was followed by a trip to the Computer Lab, where Prof Peter Robinson gave us a fantastic talk on Mind-Reading Machines. We were introduced to a few of the research projects that some Computer Science students were working on, and soon, we were allowed to try some of this technology ourselves. I thought the machine that read our emotions was shockingly accurate, although walking around in a virtual space trying to knock invisible blocks down had its own charm.

"Our final night together was one I'm sure many will never forget. Human pyramids and frantic card games were just a few of the highlights!

Thursday:

"For our final subject session,ÌýDr Ivan Smith explained the structure of the mathematics course at Cambridge, and offered us advice on how to deal with interviews and STEP papers, among other things. This was also a chance for us to ask any questions we had about the week so far, Mathematics, or life at Cambridge. I found it very reassuring to hear that the admissions process was nowhere near as intimidating as I'd feared.

"Soon after this, we had a final set of group photographs, before a debrief session from Dr Bell before our last lunch together. From here, we all went our separate ways. Some went straight home, and others stayed around town to look at other Cambridge colleges and go shopping. ̽»¨Ö±²¥journey back to London for me, with several other students returning home, was a great chance to make plans for future reunions with everyone else.

Closing Thoughts:

"I'd visited Cambridge before, but never in this capacity. Getting to know students, and getting a feel for academic and social life in Cambridge was an incredibly useful and enjoyable experience for me. I've made some great friends on this summer school, and taken some great memories. Not to mention the fantastic food and the brilliant lectures.
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"An important part of the mathematics course for me was the fairly open-ended nature of some questions we were given. These meant we were not always looking for just one way to solve any given problem, but to see if we could find other routes and solutions, and why these work.

"Being able to talk to researchers about their particular areas of interest was also fascinating. Dr Bell and the team of student helpers really made this summer school enjoyable, as well as useful. They were quite happy to sit and mingle with us, instead of just "looking after us", which I felt made a very big difference to us all.

"As we were leaving, it was not uncommon to hear shouts of "See you here in 2009!" which shows just how much we all enjoyed our stay. Hopefully, we WILL all see each other in a year's time."

Sav applied for a place on the Gonville and Caius Summer School at the suggestion of his head of year at St Olave’s Grammar School. He will get the results of his AS levels next month and plans to apply to Cambridge to study mathematics.

̽»¨Ö±²¥course tutors mentioned above are all Fellows of Gonville and Caius College:
Dr Andrew Bell, Admissions Tutor
Dr Ed Brambley, Research Fellow in Applied Mathematics
Dr Vladimi
r Dokchitser, Research Fellow in Mathematics
Dr Richard Gibbens, Senior Lecturer in the Computer Laboratory
Prof. Peter Robinson, Professor of Computer Technology
Dr Ivan Smith, Reader in Pure Mathematics

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