let's talk about our maths exams, 1st year Cambridge people

Hello

My motivation to work varies too much. I'm not in the mood at all today.

My chances on each paper:
1 - V+M is easier than it seems, the lecture notes are far too in depth for the exam questions that appear to be set. As much as I like Analysis, the questions tend to be pretty hard. I've learnt all the standard proofs, and I'll see what I can do from there.
2 - I'll probably do best in this paper. I've spent a couple of days revising probability and I've realised I can actually do quite a large amount of it. Differential Equations is relatively straightforward. I think I'll be able to attempt 5 section II questions on this one.
4 - I'm not very good at D+R, and N+S is pretty variable. I'll struggle on this paper unless I'm lucky with the questions that come up.
3 - VC is my favourite course, Groups is my least favourite course. This makes me very glad that there are no compulsory questions.

Good luck to everyone

also, DE 2010 was an absolute nightmare, so chances are it will probably be a little easier this year.

I did all three probability questions except the volcano one, and I think I did two of them well, and the other I just struggled to find the mean with that binomial coefficient in it. Did you get 64/9 for the pea/mattress/prince question, and 51 (which, intuitively, seems unreasonably high) for the mean time to absorption?

64/9 - yes. Not sure which part you're talking about for the 51. I got the general formula $Q_k$ := (E(time) at position k) = $10k - \frac{k^2}{2}$, which is 0 at either end of the table (as it should be) and 50 at the centre, giving 25.5 in part d). (This comes from the difference equation $Q_k = \frac{Q_{k-1} + Q_{k+1}}{2} + 1$).

How come 2007 paper 3 (Groups & Vector Calculus), q7, asks for a proof of Green's theorem? Isn't that too long to do in a Section II question?

Are we supposed to reconstruct the long proof given in lectures, or do something clever using the first part of the question, about conservative vector fields?

Can you use Stokes' theorem to deduce it? I don't know the proof, but it seems a bit strange to have a short application bit in the first part then start the second with some tough bookwork.

It's a puzzler - using Stokes's theorem to deduce it only takes a few lines, and then the whole question would take maybe 2/3 of a page, whereas proving it by the method used in lectures would take 2 whole pages by itself. I've no idea what they actually wanted! In the lectures, Stokes's theorem was proved using Green's theorem!

There doesn't seem to be a quick way of proving Green's theorem using the result of the first part either.