College this evening reflected the pitifulness of our situation. It’s the last weeknight of term, so everyone has finished their work and there is a bop on to celebrate this fact—the last bop many the third year will be at and they will be there in force, and of course we’re to miss it. The denizens of the library have been whittled down to a handful of freshers with exams next week, one fourth year with a final exam tomorrow morning and of course the second year mathematicians, doggedly quotienting rings and solving partial differential equations or whatever it is the applied mathematicians do. We’ve essentially spent four weeks feeling like our knowledge of the material is dropping or, at best, staying roughly the same with the minor addition of a few memorised proofs, and watching people finish their exams. Yes, people from all four year groups have been finishing around us, and yet we’re still slogging away at it. And of course all our friends at other universities finished for the summer weeks ago. Oxford second year Maths.

Of course we do actually know rather a lot more than we did a few weeks ago, and there are a few who have really knuckled down and are managing to take things more seriously than the rest of us—but it never feels like that when revising and that’s what makes it so unpleasant. For my part if you average out the days I haven’t made six hours, I’ve basically done four weeks of six hours a day with one day off per week, so I’ve done a perfectly respectable amount of revision. But I feel like I could have done more—say, eight—and I know that that if I could have manged those extra productive hours that my mark would have risen, putting a first a little more in reach. Today is a good example. This week we’re all dejected and worn out, and by 3:30pm I’d only done one hour of revision (11:15–12:15) and of course I get up at 7, so this is quite a lot of wasted hours (although some used usefully in getting vac reading from a library). I then worked in All Souls 3:30–6:30 and then went to Hall and then worked in Balliol 7:20–9:20 so a did a total of six hours, but I could have done so much more! One between midday and 3:30 and, say, 10:15–12:15 would have been so easy. Then on the other hand maybe the hours I did do would have been less useful had this been the case; I don’t know.

My six hours today were on the Rings course and I reckon that my work today is more hours than I’ve spent on this course in the entire rest of the year, since I paid almost no attention to the lectures (despite, of course, attending every one…). Why didn’t I do more before; this is really cool. The first isomorphism theorem which was examinable in first year actually makes sense in this context, and I get how if you quotient a ring R by a maximal ideal I then x, y ∈ R are in the same coset iff x − y ∈ I because this means that their ‘difference’ is small enough to be in the ideal so when you divide they’ve got the same remainder, gargh, I had this in the library earlier but I think it’s gone again; the analogy with division of integers was very clear to me for a moment back there. If I’d actually done this compulsory course—i.e. listened in the lectures and done the work set, which I didn’t really—I think I’d be laughing.

Second year algebra at Oxford, both linear and abstract, is pretty weird. It’s not actually that hard—linear algebra never is, and the abstract courses don’t go far enough in how much content they have to be too problematic—but we’re all rubbish at it, so presumably something is wrong with the teaching or the course structure or whatever. Examiners’ reports reflect this, and the fact they keep re-arranging the course every few years shows it’s a problem they’re trying (yet failing) to solve. There is also the problem that there are some really oddball examiners about who set stupidly hard questions every few years. We had one on a past paper which our tutor said was part of/leading up/in the style of the proof of the classification of simple Lie groups or something terrifically advanced. Chatting about the Gram–Schmidt process and dual spaces is mostly just crunching out definitions, yet we’re quite a lot worse at doing questions in it compared to, say, the Complex Analysis course, which is really quite deep. The integral of a holomorphic function round a closed contour containing singularities is 2π**i times the sum of the residues of the function at those singularities; wow, why the heck is this the case. And Liouville’s Theorem is pretty baffling too.

I was pleased to learn this evening that the prodigy in our year at Balliol, who was either first or second in first year exams across the whole university—and don’t forget this is Oxford so we have some Very Clever People—and mastered a eight hour lecture course in fields this week in two hours to avoid doing a question in probability, is doing all the options that I’ve chosen to do. Third year Maths teaching is in inter-collegiate classes so while it just so happens that one of my courses is being lectured in by my college tutor (hence we’re all doing it), which will mean we can get a little help in-college, it’s going to be detached and more like a real university where we actually have to do the work. Despite failing so hard at algebra, somehow I am doing lots of algebra next year:

• B1a Logic—have to do this as a Math/Phil, it’s a third year Maths course remarkably similar to our first year logic course taught by philosophers, so no problems expected here aside from getting conventions mixed up.
• B1b Set Theory—again have to do this as Math/Phil, this should be pretty fun, lots of induction and curly brackets and axioms.
• B9a Galois Theory—this is the one our tutor lectures. Apparently very elegant, and not too hard.
• B3.1a Topology and Groups—I like topological arguments, I don’t really know much about groups but apparently this is alright too.

I’m actually pretty limited because the second year options I chose, which are sort of like primer courses for third year with some exams in them too, were a stupid combination and so I’m going to have to do a fair amount of algebra over the summer to get myself ready for these. That’s okay though because I’m liking it as I, er, learn it from scratch four days before the exam; the main source of pain will be the continual thought of “if only I’d actually done this in second year.” I realised today just how much Maths I am allowed to forget after these exams. I don’t need any linear algebra, any analysis at all, not even any calculus aside from stuff with polynomials which’ll probably be used to generate examples. I just need abstract algebra, and the ability to mess around with symbols in B1 which we were trained well in in first year. Third year is gonna be gooooood.

I’ve also picked my philosophy options all the way until the end of my degree now which has a note of finality to it; up until now, the rest of the degree—and I have exactly half of it remaining after tomorrow, technically the last day of my second year—seemed fairly indeterminate and distant and not to be worried about, but suddenly by a process of elimination from the massive list of ‘papers’ (philosophy) and ‘units’ (maths) I’ve mapped it all out. I’ve got:

• Philosophy of Maths—unsurprisingly I have to do this as a Math/Phil. Looking forward to it as I enjoyed the taster we did in first year. However learnt today that tutor I was expecting to get will be on sabbatical next year :(
• History of Philosophy from Descartes to Kant—already done this this year, will be putting a lot of work into it over the summer so that I’m on top of it since maths took priority during this year. Excellent paper.
• Ethics—this is really worthwhile but I almost did it solely because I feel a philosophy degree really ought to have some ethics in it. Have done half of this and the other half will be next Hilary; stupid joint honours timetabling.
• Plato’s Republic—this is my wildcard paper; it doesn’t fit with the other things I’m doing except Ethics, some say it’s a bit easier as a paper, and it’s Ancient Philosophy so since I don’t have any Greek I can’t take it any further. But I really want to take the opportunity I have here to study the most influential text of Western thought with an expert.

And in fourth year (no Maths):

• Philosophy of Kant—probably the hardest paper you can do here. Kant is hard hard hard but so important. I want to continue the story told in the History paper above, and see if I can figure out why we get the analytic/continental split with such different interpretations of what Kant is really trying to say.
• Philosophy of Logic and Language—this is a traditional Math/Phil option, and most who do it do it when I did Ethics. I think it’s important stuff so I’ve put my more classic papers in third year and the modern analytic-tinged things like this into fourth year, where I can make more of them. I’m more interested in the Philosophy of Language than of Logic, but of course they are intertwined. I want to know just how much we actually should be worrying about language and how much we should heed those who tell us to deal in ideas instead of words.
• Either Knowledge and Reality or Philosophy of Mind. I had to choose either the History paper or K&R at the beginning of second year; K&R along with Ethics is one of the two “base” papers, if you like, that the rest build upon. So it would be unusual to do it as a fourth year paper and unusual to do it along with the History paper but we could take things a lot further. On the other hand Philosophy of Mind is another core topic of modern philosophy, and could take this sort of stuff further like K&R could as I understand it. Can decide this later though.

Timetabling this is going to be a pain. There are two terms to do all the third year stuff in. Michaelmas is going to be Logic, Galois Theory, Topology and Groups and Philosophy of Maths, so that’s three problem sheets and an essay a week. This is going to be a ridiculous amount of work. I’m aware of this so I can work harder from the very beginning to try to stay on top of things but I am worried about falling behind on particular courses since there is going to be just so much. I am tempted to just do most of the logic problem sheets over the summer, but am not sure this is such a great idea. Hilary will then be the other half of Ethics, the Republic and Set Theory. Hilary will be a beautiful term; it is frustrating that I can’t move Logic into it too.

Lots of stuff about third year there and about revision; hope it wasn’t too dull for those outside of the Oxford bubble.