When I first went to university (Cambridge) I didn't have much of an idea what was supposed to happen there. No one in my family had been to university before, and my parents had even less idea about such institutions than I did - except that my mother thought I might meet and marry a princess. In that respect, though, I was a complete failure!
Luckily I had a couple of outstanding maths teachers who had both been to good universities, and they encouraged me to apply to their respective institutions - Manchester and Cambridge. For the former, I was accepted on the basis of my A-level results (four at grade A, plus one grade 1 Scholarship level - there wasn't an A* in those days), but for the latter I was turned down (which nowadays might even be regarded as quite scandalous, but at the time such daft ideas didn't occur to anyone) - to get in, I had to sit Cambridge's own entrance exams, which I duly did, and passed comfortably.
During my three years at Cambridge, the student experience was amazing and truly life-changing, but not just for the conventional reasons to do with contact hours and the like. Of course, we did have lectures, six days a week in fact (though in my first year, classes were over by 11am each morning!); and we had regular tutorials with at most one other student, sometimes taken by senior academics, sometimes by young graduate students. Back then I had no idea what a privilege it was to have tutorials in such a small group. And it was quite sobering, sometimes, to find that the tutors couldn't always answer our questions, mostly based on problem sheets handed out in lectures. The presumption was that if we did enough work and thought about the problems for long enough, we would figure out the answers for ourselves; and mostly we did. There was no spoon feeding, but academic staff were there to help, and sometimes took the trouble to answer questions in huge detail.
I was never required to submit any problem sets (or essays) for marking, and all assessment was based on exams at the end of each year. That suited me fine, though I know many students these days find a mix of exams and continuous assessment more manageable.
It seemed to me that any student who survived the three years without being thrown out, and who turned up for the final exams, was likely to get some sort of degree. The idea seemed to be that merely soaking up the atmosphere of Cambridge for three years was enough! For instance I knew one maths student, supposedly a Polish minor count, who rarely did any work as far as anyone could tell; in the final exams, he claimed to have written one very long essay - continuing over all four papers - and he graduated with a third. In those days - before grade inflation, and when there were few graduates - even a third from Cambridge was a worthwhile degree, so he did OK.
But aside from the basic degree work, what made Cambridge special was two things. First, in order to find out about lecture times you had to buy a copy of the Cambridge Reporter that had information on all lectures in the university. As matriculated students, we were allowed to attend anything that took our fancy, so I sometimes went to lectures in architecture, philosophy, history, and a little economics - the subject in which I ended up spending most of my working life. It was great to have such an opportunity.
Second, there was an enormous range of student societies on anything you can imagine - political, cultural, social, etc. For me, starting out as a very shy individual, these also gave lots of opportunities to meet people other than mathematicians, through quite a range of activities. One thing I never did, though I met lots of folk who were very enthusiastic, was to engage in any sport. I'm not against exercise, but I've never much liked competitive sport. In my final year, the rooms I had in college turned out to have been home to the Science Fiction Society, and their books were still there. So the year started with three weeks of reading solid sci-fi. Then one day the books were taken away and I settled down to work.
Overall, a really big lesson from all this is that university is what you make of it. It offers fantastic options to anyone who looks around to see what is on offer, usually much more than the basic degree course one signs up for. No one has to take part in anything other than their degree programme, but it seems a shame to miss out on everything else universities can offer. They're amazing places, and about much more than the conventional views about gaining an education in a specific discipline suggest!
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