Oxford Maths Students and Applicants

Also, it might be interesting if Oxford took advantage of its modular papers to allow students to sit Part C exams when they're in Part B. Obviously this wouldn't be an everyday thing, but it might be nice if the option were there.

The 2013 examiner reports are out, and they make surprisingly interesting reading. Kudos to whoever in part B averaged 98 UMS, that's pretty impressive!

@gkmc: I really don't like Oxford's course: there is too much inflexibility. However, the collegiate system is the same, and I believe the undergrads at Cambridge aren't based in the Isaac Newton institute (which is their fancy building).

You can. The handbook says 'courses of M or H level' for part B, and 'M-level' for part C.

However, there is no official extra credit, so oddly enough it's not often taken up.

I get the impression that that language is only there because a few courses are cross-listed between parts B and C, and the regulations say "In Part B each candidate shall offer a total of eight units from the schedule of units for Part B". I wonder if they would permit a Part B student to take a course only intended for Part C students, or if anyone has ever tried that?

I wonder if the institute has any intentions to start uploading videos of lectures, seeing as the main three lecture halls all have recording equipment in the room at the back.

I doubt it...

Yeah I doubt it as well, although it would be pretty cool.

(Although now I've thought about it, it's very unlikely I'd ever look at them despite being someone who doesn't go to lectures very often)

Yeah I doubt it as well, although it would be pretty cool.

(Although now I've thought about it, it's very unlikely I'd ever look at them despite being someone who doesn't go to lectures very often)

It would be really good for analysis lectures where there are really useful overviews/where we're going remarks - though it doesn't make sense to travel for 50 minutes for a 1 hour lecture, so this would solve that. Also skipping/replaying things.would be useful. If only it would happen...

Yes, I agree - although it's a point I usually avoid making because I chose to live out and so it adds a good 30 minutes extra travelling time (there and back altogether) than if I were to just walk from college. Also, it doesn't really help when you generally only have two lectures a day and don't find half of them very helpful (so you're literally just going in for one lecture).

As soon as I saw that they bothered to install what looks like professional equipment in the two main lecture theatres I just assumed it was in the planning (I seriously hope they haven't done it just to upload du Sautoy's occasional lectures )

From what I've seen, I don't think Oxford and Cambridge are all that different (for the first three years). Out of curiosity, are there any examples where Cambridge is more flexible?

The examiners reports are indeed pretty interesting. The Part B externals make an interesting read. The external examiners essentially think that we give out too many 2:1s, that the people getting low 2:1s should probably be getting worse (e.g. 2:2), and that a main cause of this is too much bookwork on exams. Their points seem very sensible and well-argued and I'm inclined to agree with them.

I get the impression that that language is only there because a few courses are cross-listed between parts B and C, and the regulations say "In Part B each candidate shall offer a total of eight units from the schedule of units for Part B". I wonder if they would permit a Part B student to take a course only intended for Part C students, or if anyone has ever tried that?

I'll have to caveat by saying I went to Imperial, but the amount of STEP prep I have helped with means I have ended up knowing more about their (current) course than any other!

Off the top of my head:

1) Most importantly, and one you've already mentioned, is that students can offer as few or as many courses as suits them for exams

2) their third (Easter) term in the first year is dedicated to second year courses - you get to choose when to do them

3) no course in the second or third year is compulsory - you get to specialise in whatever you fancy. This obviously carries through to their exams too. What that means is that theoretically, there can be Cambridge students who don't cover any of the Oxford second year core (although a core is compulsory for a reason - I expect it's a minority)

Why aren't the external reports public? unfortunately I can't comment because I can't see them - unless I put in a FoI request...

If someone is exceptionally strong, I'd be disappointed if Oxford didn't try to do something to tailor their programme accordingly. It would have to be someone extraordinary though because Parts B and C are no walks in the park (even in comparison to other top universities)

Personally I'm not too fussed about the last two points; there are only a few core courses in Oxford's second year and they're all pretty fundamental.





I think they should be publicly available from this link: https://www.maths.ox.ac.uk/notices/exam-reports/external-examiner-reports/2013



I imagine there are some opportunities available for those who really go out and seek them. I do know a few people at or near the very top of their year and nothing special really happens to them. I've always idly wondered if we don't push our top students enough, and I think a large part of that might be lack of institutional support. Especially at parts B and C, when the department is just about entirely responsible for your education. I would cite the limit of 5 courses per term (for context, one does 8 courses for exam), the inability to sit extra papers, and the inability to sit papers from higher years as three examples of restrictions which I don't like (even though they are perfectly standard and reasonable, mind).

While I'm on the topic of completely minor and inconsequential gripes ( I love you really, Oxford) there's something that's always bothered me a little. The department as a whole and many lecturers individually encourage students to read from third-party sources, but from what I've seen few students do, preferring instead to just work from the course notes. Speculating here, a reason for that might be that other expositions of the material won't be that useful in light of exams. A third-party exposition is likely to go via a different route than the lecture notes, probably relying on different theory. However, for exams, you basically need to learn the theory exactly as presented in the lecture course, because I think few people would dare to cite theorems from outside the course on an exam. This leads to every paper having the same regurgitated proofs of bookwork, something complained about in examiners reports.

As a concrete example, suppose you're a fresher doing real analysis, and you're confused about the proof that a continuous function on a closed bounded interval is bounded and attains its bounds. The proof presented in prelims is by contradiction: construct a sequence (x_i) from [a, b] such that f(x_i) is unbounded, find a convergent subsequence (x_k), note that f(x_k) converges, and you've got your contradiction (since we assumed it was unbounded) (it's remarkable how much easier it is for me to construct this proof now compared to the difficulties I had as a fresher! One of those times when you look back and appreciate how far you've come). Anyway, I found this proof (and still do, to be honest) to be opaque and confusing. Suppose you go to a textbook looking for some more explanation and you find a discussion of compactness. After a while studying it, you say aha! It is all clear! f([a, b]) is compact and so closed and bounded! But then you sit and reflect: you can't really cite this on your problem sheets, and you certainly don't want to start talking about compactness on the exam, out of fear you will lose some or all marks for using theory from beyond the course. In fact, you realize, the time you spent struggling with a textbook was entirely wasted; this was useless to you (from your perspective)! You resolve not to do this again and just stick to the notes.

If I had to guess, that is what I would blame for our generation's ever-decreasing reliance on textbooks: the perception that they won't be helpful for the exam.

Personally I'm not too fussed about the last two points; there are only a few core courses in Oxford's second year and they're all pretty fundamental.

I think they should be publicly available from this link: https://www.maths.ox.ac.uk/notices/exam-reports/external-examiner-reports/2013

I imagine there are some opportunities available for those who really go out and seek them. I do know a few people at or near the very top of their year and nothing special really happens to them. I've always idly wondered if we don't push our top students enough, and I think a large part of that might be lack of institutional support. Especially at parts B and C, when the department is just about entirely responsible for your education. I would cite the limit of 5 courses per term (for context, one does 8 courses for exam), the inability to sit extra papers, and the inability to sit papers from higher years as three examples of restrictions which I don't like (even though they are perfectly standard and reasonable, mind).

While I'm on the topic of completely minor and inconsequential gripes ( I love you really, Oxford) there's something that's always bothered me a little. The department as a whole and many lecturers individually encourage students to read from third-party sources, but from what I've seen few students do, preferring instead to just work from the course notes. Speculating here, a reason for that might be that other expositions of the material won't be that useful in light of exams. A third-party exposition is likely to go via a different route than the lecture notes, probably relying on different theory. However, for exams, you basically need to learn the theory exactly as presented in the lecture course, because I think few people would dare to cite theorems from outside the course on an exam. This leads to every paper having the same regurgitated proofs of bookwork, something complained about in examiners reports.

As a concrete example, suppose you're a fresher doing real analysis, and you're confused about the proof that a continuous function on a closed bounded interval is bounded and attains its bounds. The proof presented in prelims is by contradiction: construct a sequence (x_i) from [a, b] such that f(x_i) is unbounded, find a convergent subsequence (x_k), note that f(x_k) converges, and you've got your contradiction (since we assumed it was unbounded) (it's remarkable how much easier it is for me to construct this proof now compared to the difficulties I had as a fresher! One of those times when you look back and appreciate how far you've come). Anyway, I found this proof (and still do, to be honest) to be opaque and confusing. Suppose you go to a textbook looking for some more explanation and you find a discussion of compactness. After a while studying it, you say aha! It is all clear! f([a, b]) is compact and so closed and bounded! But then you sit and reflect: you can't really cite this on your problem sheets, and you certainly don't want to start talking about compactness on the exam, out of fear you will lose some or all marks for using theory from beyond the course. In fact, you realize, the time you spent struggling with a textbook was entirely wasted; this was useless to you (from your perspective)! You resolve not to do this again and just stick to the notes.

If I had to guess, that is what I would blame for our generation's ever-decreasing reliance on textbooks: the perception that they won't be helpful for the exam.

x.

Cambridge's course is great, but some aspects of it seem fairly odd to me. Like how you can choose to take fewer options than the standard 192 lectures, while other people take more - so you end up with a significant difference in workload between students, which doesn't seem like the best idea to me (although I have no doubt it works).

One thing that is quite striking about second year at Cambridge is that it's quite heavily applied and has a lot more physics (probably not too surprising that Oxford have started an MMathPhys programme - someone at Oxford probably saw how much physics you could do on a maths degree at Cambridge )

Another thing about second year at Cambridge is while, as far as I can see, nothing is absolutely mandatory there seems to be a couple of options which are probably heavily recommended (such as the Linear Algebra course - which includes some material covered in first year Algebra at Oxford (bilinear forms, for example), same for Analysis II (uniform convergence/continuity)) and I find it hard to believe you could go to Cambridge and not study complex analysis (also, the pure mathematician in me can't help but think there's no need to offer Quantum, Electromagnetism and Fluid Dynamics all in the same year). Although I do appreciate some people really just prefer the applied and want to get rid of pure as much as possible. Something you could do a much better job of at Cambridge than you could on Oxford's course.

I can't work out whether this is just me being biased as an Oxford student, but looking at the first three years of both courses, I actually prefer Oxford's course. The pure aspects seem to progress at Oxford in a much more natural progression in the first two years than it does at Cambridge - but again, that's probably just because it's what I'm used to.

Cambridge's course is great, but some aspects of it seem fairly odd to me. Like how you can choose to take fewer options than the standard 192 lectures, while other people take more - so you end up with a significant difference in workload between students, which doesn't seem like the best idea to me (although I have no doubt it works).

One thing that is quite striking about second year at Cambridge is that it's quite heavily applied and has a lot more physics (probably not too surprising that Oxford have started an MMathPhys programme - someone at Oxford probably saw how much physics you could do on a maths degree at Cambridge )

Another thing about second year at Cambridge is while, as far as I can see, nothing is absolutely mandatory there seems to be a couple of options which are probably heavily recommended (such as the Linear Algebra course - which includes some material covered in first year Algebra at Oxford (bilinear forms, for example), same for Analysis II (uniform convergence/continuity)) and I find it hard to believe you could go to Cambridge and not study complex analysis (also, the pure mathematician in me can't help but think there's no need to offer Quantum, Electromagnetism and Fluid Dynamics all in the same year). Although I do appreciate some people really just prefer the applied and want to get rid of pure as much as possible. Something you could do a much better job of at Cambridge than you could on Oxford's course.

I can't work out whether this is just me being biased as an Oxford student, but looking at the first three years of both courses, I actually prefer Oxford's course. The pure aspects seem to progress at Oxford in a much more natural progression in the first two years than it does at Cambridge - but again, that's probably just because it's what I'm used to.

I'm surprised by the comments. I think that for comparability purposes with other universities. 85% firsts or 2:1s is entirely appropriate; Oxford should have a strong intake. What surprises me is Dr Thomas's view that an Oxford 2:1 is worth 'a little less' than an Imperial 2:1. My experience at Imperial is that a low 2:1 was fairly easy to achieve with a minimum amount of problem solving, and is not a particularly high standard. For Oxford to fall into the same trap is a bit shocking. Your lectures must be more in depth than Imperials, or he have misjudged the difficulties of the papers (which I entirely possible - academics aren't great at assessing the difficulty of something they're an expert in).

Based on those comments, rather than change the proportion of 2:1s achieved, I would try to focus on the weakest 25% and try to improve their standards. Clearly this is easier said than done. It would be unfortunate if in one of the worlds best universities you have doubts over the reliability of a 2:1 student.

Finally, the temptation to compare with humanities subjects awarding silly classes (things like 85% 2:1s, 5% firsts are not unheard of) should be resisted. Employers and other users of degree grades would do well to take a more nuanced view of a degree.

The question is do the top students want additional challenge? If not, then the current support is entirely reasonable. If a great student said "hey, I'd like more maths please!" I'm sure their tutor would find something to keep them occupied.

In principle, any correct proof should gain all of the marks. Things get tricky if you employ more sophisticated machinery which makes a question really straightforward. For example, in Part A presumably you will see contour integration. This makes some nasty integrals rather easy - and if the intended method was not to use complex analysis, the question becomes a heck of a lot harder.

Analysis is always a minefield because once you encounter metric and topological spaces, the first year way of handling epsilonics just seems archaic.