# Jun 2011

## Thu, 30 Jun 2011

While waiting for yesterday’s exam to start I read through the unopened front cover the question “What is a prime?”, and no that wasn’t some crazy abstract concept but it was actually asking me to write down what a prime number is. This was swiftly followed by “prove that there are infinitely many primes”, possibly the most famous proof there is, that we got in our first week of first year, followed by “state the fundamental theorem of arithmetic”, again not really degree-level stuff. There were then a couple more prime number things to prove, both of which were fairly standard—very frustratingly I couldn’t prove that there are infinitely many primes of the form $$6k + 5$$ despite doing such a proof by myself before and liking it; I just couldn’t get it to come out in exam conditions, ah well.

This was yesterday’s paper which was fine, but today’s was disastrous for me. Hopefully with moderating/scaling I should get 50%, but this basically means that “I’ve definitely got 60% average this year” has gone to “hopefully I’ve got 60% average” which is rather unsettling. And today’s paper was supposed to be my best: the first year probability question I was expecting to answer was entirely impenetrable and so I wrote down a few number theory definitions and theorems and did most of a topology question, so that’s not very many marks really. Can’t believe I forgot what sequential compactness is!

It really is bad how Maths tutors are so incapable of writing questions. It seems that while results get scaled separately by subject, to take into account the fact that Math/Phils are famously good at Topology and Maths/Stats people beat everyone else on probability, they are not in fact, as I thought, scaled by question. On these options papers, there are questions for different courses and not only are these courses wildly different in actual difficulty but each question is set by a different person, that is the course lecturer for that year, so the chances of getting a consistent difficulty level even within a single year is pretty low. When you add to this that the lecturer’s conception of how hard a question is is so wildly different to how hard an undergraduate thinks it is (reflected in examiners’ reports), and you have a pretty stupid situation. When, like me, you only revise the minimum number of options, you meet disaster when the questions you want to answer are too hard to let you do very much at all.

An example of this is that fellow Math/Phil Sophie who had poured her time into the Fields option which I’d dropped a long time ago had a dreadful time yesterday, writing pretty much nothing, whereas today she owned it and came out very happy. We’ve both done similarish amounts of work and have similar levels of ability and interest so that shouldn’t be happening.

I’ve been reflecting on revision and how I’m going to do it better next year. It seems that actually learning everything is probably a good idea, rather than trying to strategise based on past papers, and you’d think that’d be doable next year when we have something like two and a half months of revision. The problem is that the first week of revision is worth less than the last two days, I suspect: proofs don’t stay in long enough. The best I can come up with is: make sure you have understood all the lecture notes as early as possible and have a good set of summary notes inc. sketch proofs, and then spend the middle period doing all the past papers, and then doing them again, and then at the end force bookwork into your head. But then there is too much bookwork. I can’t figure out how to make this work better.

Now it’s all over for the summer and despite the fact that there’s not been anyone around for the better part of a week already, I’ve been left sad now that the year is over. I have to leave Oxford, a place where we say, we’re going to do everything we can, we’re not going to take the easy way out, we’re not going to let up because once one thing finishes, be that academic, social, political or whatever, we’re going to hit the next one equally as hard. It’s exhausting but I fear nothing else will ever be enough. It’s an exhilarating intensity that actually does work, we do come out rather better thinkers. More importantly we’re all that we can be, realistically, on every level. I have to make as much as I can out of the final half of my degree, and out of my time in the unique position of being an Oxbridge undergrad; staying here for graduate study does not mean extending this which you only get three or four years at, and then that has to be it.

Edit 1/vii/2011: I’ve since confirmed that the question on Monday that wasn’t on the syllabus wasn’t, but they won’t do anything, which is fair enough because some people answered it. The question yesterday that was impossible to me was impossible because it was on stuff I’d never done before i.e. it was completely off the syllabus, not just an unexaminable proof. So carelessness on the part of the examiner has turned my best paper into my worst :\

The time of this post is inaccurate; forgot to fill it in at the time.

## Wed, 29 Jun 2011

Pumping the Phone | Now I KnowInteresting read:

I reinstalled Minecraft yesterday and hopped into my minecart system, only to learn that minecart boosters have been fixed. Boat elevators have been fixed too. A lot of the fun of Minecraft was exploiting cool, if buggy, Physics mechanics. I no longer have any interest in spending ages mining materials in order to build cool stuff if this element is removed, so I’ve decided that I’m going to play with mods that give you unlimited items and just try to build interesting things. I might even install a mod to replace boosters.

The upcoming creative mode is not quite what I want as I would still like monsters and the possibility of dying, but I’m not interested in spending hours strip mining just so that I can build things.

So normal Minecraft has become boring for me, but I’m still interested in sandboxing.

## Tue, 28 Jun 2011

You make a stupid mistake in every exam I suppose; today mine was forgetting that a matrix over a complex inner product space is Hermitian exactly when it induces a self-adjoint linear transformation, duh, but it wasn’t as bad as a fellow Balliol Math/Phil who answered three Algebra questions when a maximum of two from each section of the paper count; he came out really happy with how well he’d answered those questions too. The exam was a good end to core for me as there was a great Rings question, lots of Algebra bookwork (== proofs from memory) but there wasn’t any classic Analysis bookwork. We reckon this is because the questions were set by our college tutor who is hardcore.

It’s quite something that I’ve now finished what has been the mainstay of my degree for the past two years: Analysis and Linear Algebra. I’m sad to be leaving Analysis behind because I like the proofs, and it was just starting to get interesting with things like Contour Integration (again, Cauchy’s Residue Theorem, wth), but third year analysis is apparently pretty tough so I’m avoiding it. I’m not at all sad to be leaving Linear Algebra. You define something fairly simple, that doesn’t do anything exciting and for which most of your intuitions are correct, and then you laboriously churn out all those consequences. Sure it’s easy marks to prove something is linearly independent or that something is a linear map (did one of those today and the other yesterday) but it’s so dull to study.

Instead I have Abstract Algebra open before me. I know so little of this, interestingly I seem to know so much less than my friend just finishing his first year at Cambridge. Presumably he’s done less Analysis and Linear Algebra than me, I don’t know; it feels like I’m almost starting afresh, though, because of how much I am now leaving behind, only to be used for the occasional example.

No more flippin’ matrices!

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