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During the past week, I attended an Easter school set by Cambridge university for maths applicants from not-so well off backgrounds (like my own, apparently), ostensibly in order to help them with preparation for STEP exams this summer, but (in my case at least) mainly to have fun doing maths and talking to current undergraduate students there. It took place in Churchill college, as well as the Centre for Mathematical Sciences nearby (a strange, parabolic building complex dug into the ground). About a hundred other applicants were there, from various different colleges within Cambridge, and it was great fun. Each day consisted of three lectures, with "question solving sessions" sandwiched in-between, where we went into rooms with our mentor groups and discussed mathematics - sometimes directly from the lecture, but other times weird and advanced pure mathematics - redefining, or rigorously proving results which seem totally obvious to a naive person like myself - such as the fact that if you have a continuous function running from ^`(x_0,y_0)`^ to ^`(x_1,y_1)`^ where ^`y_0y_1<0`^, then the graph of the function will cross the ^`x`^ axis at a point between ^`x_0`^ and ^`x_1`^. (This may not be obvious from my convoluted description, but if you were to picture it in your head or draw a graph, it should seem obvious. But to a mathematician, apparently it requires rigorous proof all the same!). Or conversely, disproving results which may seem true to the uninitiated but nevertheless are not, or are only true given certain axioms which have no real foundations.

As a taste of university life, it was of course quite short, but nonetheless enjoyable, and now I'm more determined than ever to pass my offer by gaining at least two firsts at STEP II and III. This doesn't seem quite as unachievable as it did about six months ago, as long as I work hard and don't become complacent. We had a mini-test in which I managed to get two questions out fully (sans a special, irrelevant case of ^`k=0`^ in a differential equation) within three quarters of an hour. It seems like the Tripos is very difficult, but equivalently rewarding.