letters to Part III

As if keeping up with the lectures were insufficient challenge, Michaelmas term is also the time when Part III’s have to think hard about if and where they are going to go for further studies. During the time I had responsibilities for Part III, this issue was a major headache.   I hope there are more resources, and better publicised now.   Deal with the if first. The year is young but the first few weeks may well have brought previously held answers to the “if” question into doubt. In the face of uncertainty, one must still apply now. How to deal with this: there are several options. For most, the usual plan is go ahead and apply as if new doubts had not arisen, but apply to a broad range of places. For those who don’t feel the pressure of passing years, delaying applications until you have the results of Part III may be a reasonable strategy.   There are creative ways of spending an interim year. Putting the “if” aside, the problem of “where” can be a daunting ...

September, 1973. Mathematics Institute, University of Warwick “You don’t need to start taking notes just yet.”   Well, that was reassuring, I suppose.   I had never taken notes in a maths class before.   There were books where things, proofs definitions and the like, were written down, right?   You just listen, and think about what you are being told, understand it, and then there’s no need to remember it is there? Why write anything down? How can you forget what you understand? Something understood doesn’t need to be remembered, not as such. “A representation is a homomorphism from a group into a group of invertible matrices.”   Cool.   Yes. Got that. A few handwavy remarks. “Now you may take notes.   We will begin with a review of semi-simple Artinian rings.” Ice settled in my stomach. Fear paralysed my arm. I had never before been lost in a maths class*, and here I didn’t even know the words. Well, ok, I knew what a ring was, review and beg...

Did I mention that no Part III student has too much time? The corollary to that is that short cuts to learning are to be taken at every opportunity, particularly for those students coming from outside Cambridge, who may find there are critical gaps in their background knowledge. If you need to know something, ask.   Someone is bound to know it.   Ask first.   Yes, read it up later, but it will be much easier reading if you know the story line first. It’s pretty obvious, that if A needs to learn something in a hurry, A should ask for help.   But why should B help? I claim that B should, in her own interests. Batchelor’s law on the transfer of understanding says the following.   Let U(A)_0, U(B)_0 be the initial levels of understanding of students A and B respectively, and suppose that U(A)_0<U(B)_0. A and B then meet and discuss, after which their respective levels of understanding are U(A)_1, \ U(B)_1. Batchelor’s law states that   (U(B)_1 -...

Hi.   I’m Marj. For nearly ten years I had the pleasure of standing in front of Part III students on day one and introducing myself, and then talking at them regularly through the year. It was a responsibility that I relinquished with regret. I watched jealously and tried with greatest difficulty to keep silent as others took on the job. I am now retired.   Retiring is a very liberating experience; I no longer feel at all constrained to silence, so I will write. I felt uniquely qualified to advise Part III’s by virtue of having failed corresponding exams (MSc, Warwick, 1974) - a life experience shared by too few of my colleagues. Most of them got where they are now by being very good at sitting in lectures and passing exams. I felt there should be someone standing in front of them who has an in-depth, visceral understanding of what Part III might be like for those who come here with less than ideal preparation, who sit in lectures, and wonder whether the lecturer is indee...