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Cambridge Maths Students and Applicants

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Original post by DJMayes

And there are no supervisions after third year, are there?

There are - the colleges pool together resources in the third year so that everyone can be supervised by someone with an appropriate level of knowledge in the respective subject.

That would be third year. You wrote (and I was questioning) after third year. I'm not aware of there being any supervisions for Part III. Are you?

Interesting example to choose, given that the famous anecdotes regarding Grothendieck are that he did not initially attract much attention for his mathematical ability, and it was this kind of supervision (when he did 14 questions when told to do one) which first attracted attention to him.

As grid pointed out, this particular story wasn't about any sort of undergraduate supervision.

Moreover though I will continue to argue that if a student is particularly able then they are the kind of people who will benefit from the likes of a supervision, where they can be pushed farther than question sheets and material designed for a larger group of people, and where they can be properly directed to more advanced material.

Absolutely agreed, so no need to argue. But that's only a benefit if they get that sort of supervision. How common is that? Have you ever had one like that? My impression is that the typical supervision involves going over the problem sheet, especially the problems gotten wrong and not done at all. Rarely is time spent on pushing farther into related (and obviously unexaminable) material.

Thus a massive amount of time is simply wasted with well-meaning teachers providing material that is of no benefit to their students.

This is categorically untrue, and supervisors can and will be proactive about aiming higher for a stronger student - they have taught enough students to be able to tell when one stands out and needs pushing farther.

I imagine that's true of some supervisors and some students. But there are certainly quite a few supervisors who haven't taught many students (everybody has to start sometime), and certainly some will have trouble teaching students more able than themselves (which must be common, given that the next generation of top mathematicians are probably Cambridge students today).

I thought you earlier agreed that the quality of supervisions is highly variable, which would mean that some aren't very good. Have you ever had a bad supervision? What have you done about it?

This is being facetious about wording.

Sorry, I'm not trying to be facetious. I'm just trying to be clear that Cambridge is not even attempting to teach maths above an undergraduate level in the first three years. If a student wishes to gain a deep understanding of any mathematical topic, he is on his own. Just like anybody working from home.

It is very easy to pick up bad habits, methods and techniques if you just work through mathematics on your own and supervisions are important for helping "trim the rough edges", so to speak. In addition it is very easy to think you've done a question when you actually haven't.

I think this is true for many students. I don't think it is true for the top mathematicians of tomorrow who are students today. In fact I think those who pick up bad habits when studying on their own are demonstrating that it is unlikely (but not impossible) that they will become top mathematicians.

For the best students, I think the "trim the rough edges" activity that's the most useful looks like "Yes, you solved that problem, but there's a better way that leads to a more general solution if you come at it from this other angle." And "Yes, and you can also use that technique to solve this seemingly unrelated problem -- it's even more powerful than it appears at first."

You appear to have quoted and agreed with yourself here...

I quoted my original assertion, since it seemed you had forgotten it and drifted. And I was trying to agree with some of what you wrote, but I guess I didn't make that clear enough. Oh, well. This is an imperfect medium and I'm not nearly as good at using it as I ought to be.

I would be very interested to hear your personal experience. What has been the difference for you between the very good and very bad (or not so good) supervisions? Is even a bad supervision better than none?

Original post by Hannzzaaa

This might be a dumb question but if you do take maths at Cambridge, what career options are open to you? Because I am in year ten and I don't know if languages or maths would be better job-wise. Also what do you have to do to get into Cambridge? What is STEP? Thanks.

STEP = The end of one's social life [for the vast majority]

Original post by IGU

...

That would be third year. You wrote (and I was questioning) after third year. I'm not aware of there being any supervisions for Part III. Are you?

Apologies, I misread this. Having looked at the handbook, there aren't 1/2 on one supervisions as earlier in the tripos but there are instead examples classes organised by the lecturer which seem to serve a similar function.

http://www.maths.cam.ac.uk/postgrad/mathiii/handbook.pdf

(Any part III students' input on this would be greatly appreciated)

Absolutely agreed, so no need to argue. But that's only a benefit if they get that sort of supervision. How common is that? Have you ever had one like that? My impression is that the typical supervision involves going over the problem sheet, especially the problems gotten wrong and not done at all. Rarely is time spent on pushing farther into related (and obviously unexaminable) material.

Yes; on multiple occasions. One of my Probability supervisions consisted of the supervisor finding the hardest topic related questions they could outside of the example sheets to give to my partner and I, another supervision that stands out to me is a Vectors & Matrices supervision where we were shown an analytic proof of Cayley-Hamilton. I do not think that a supervision that goes beyond the example sheet in some way is an uncommon occurrence, and bear in mind that I am nowhere near an exceptional student.

I imagine that's true of some supervisors and some students. But there are certainly quite a few supervisors who haven't taught many students (everybody has to start sometime), and certainly some will have trouble teaching students more able than themselves (which must be common, given that the next generation of top mathematicians are probably Cambridge students today).

I thought you earlier agreed that the quality of supervisions is highly variable, which would mean that some aren't very good. Have you ever had a bad supervision? What have you done about it?

True enough. My experience with bad supervisions are that they have largely been my fault as I have not engaged with them. I find that if I engage more in the supervisions then they get better, which is what I try to do. Probably my worst is Quantum Mechanics, because I dislike the course and have no plans to study it beyond the conclusion of the 2nd year lecture course either in lectures or alone, which means I don't engage with it as much as I should have and spend most of the supervisions giving little input.

Sorry, I'm not trying to be facetious. I'm just trying to be clear that Cambridge is not even attempting to teach maths above an undergraduate level in the first three years. If a student wishes to gain a deep understanding of any mathematical topic, he is on his own. Just like anybody working from home.

As a faculty, no. Supervisors can and will advise more advanced content - an example I have is of a friend who was given the Hairy Ball Theorem (algebraic topology) to work on, which is certainly more advanced than the typical stuff given to 1st year students.

I think this is true for many students. I don't think it is true for the top mathematicians of tomorrow who are students today. In fact I think those who pick up bad habits when studying on their own are demonstrating that it is unlikely (but not impossible) that they will become top mathematicians.

For the best students, I think the "trim the rough edges" activity that's the most useful looks like "Yes, you solved that problem, but there's a better way that leads to a more general solution if you come at it from this other angle." And "Yes, and you can also use that technique to solve this seemingly unrelated problem -- it's even more powerful than it appears at first."

Certainly these are some of the most useful. It is also true that top mathematicians will likely become top mathematicians regardless, there are plenty enough examples to demonstrate that. But for a student who is modestly good (which I would argue is the majority of Cambridge students, the exceptional are not that common) then the situation I described is more likely.

I quoted my original assertion, since it seemed you had forgotten it and drifted. And I was trying to agree with some of what you wrote, but I guess I didn't make that clear enough. Oh, well. This is an imperfect medium and I'm not nearly as good at using it as I ought to be.

I would be very interested to hear your personal experience. What has been the difference for you between the very good and very bad (or not so good) supervisions? Is even a bad supervision better than none?

Bad supervisions I described above; it is better than none as I do not think I have ever handed in a perfect sheet. For a good supervision, it is either with a supervisor who can make a topic I am struggling with crystal clear, or if I engage with the content in a deeper way. For example I used one of the questions on a sheet last year as a basis through which to derive the cubic formula, and this kind of engagement made the supervision much better as a whole.

Original post by IGU

We are talking about undergraduate classes here. When you're done with them you've just scratched the surface. A "perfect understanding" is many years of study away, if ever. For many it won't happen until they've taught the course.

Modulo quibbles over what constitutes a "perfect understanding" (I don't think one exists - nobody's understanding couldn't be deeper), I think the very top undergraduates make sure they achieve an understanding of undergraduate-level material that is much deeper than most undergraduates achieve or that most lecturers have.

(edited 9 years ago)

Original post by grid

'always learning things properly the first time'

Could you elaborate on this please?

Original post by IGU

...

I don't understand the point you're trying to make. Supervisions, just like any other educational method, are imperfect. But there is a lot of evidence to suggest that they are generally effective, for students over a wide range of ability.

You've also been given examples of supervisors who stretch and challenge students. I am struggling to think of activities that Cambridge can offer students beyond what they already do to motivate their best students. At the end of the day, learning maths requires deep concentration in a solitary environment for most people - if someone is able to breeze through the course material, I'm sure there is freedom for students to spend their time on what interests them.

If some of the world's most talented mathematicians can't inspire and guide their top students, I can't think of any environment where such students would do better than Cambridge.

Forgive me if I've misunderstood you, but I just don't get your issues with supervisions :confused:

:confused:

Original post by grid

Grothendieck wasn't a problem-solver. He was a theory-builder. I don't think he would have got on very well at Cambridge, where many faculty members, even in pure, assume that "thinking about hard problems is the way you learn (and do) maths".

My suspicion too is that he wouldn't have fit in well at Cambridge; that's why I chose him as an example. But since everybody's different, and top mathematicians are somewhat individualistic, what I'm wondering is what Cambridge does with such people. Do they adjust to meet their needs? Even a little? The supervisions present a clear opportunity to do so.

I remember reading Littlewood's opinion that his undergraduate years at Cambridge were pretty much a waste of time as all they did was revise hard exam questions. This was in the glory days of Tripos exams (before Hardy put that somewhat to rest), with specialized coaches enjoying great renown. He wrote that he didn't get to learn much in the way of mathematics except what he pursued on this own.

I'm hoping that Cambridge maths is much better these days. I'm hoping that a student or two will chime in with personal experience of how Cambridge accommodated their unusual needs.

An example might be: "I love algebraic geometry and it's not part of the undergraduate curriculum (at least not beyond pretty trivial stuff). In my second year, when I saw a Part III class was being taught, my DoS arranged for me to get a supervision in the class even though such a thing isn't normally provided."

Original post by shamika

I don't understand the point you're trying to make.... Forgive me if I've misunderstood you, but I just don't get your issues with supervisions

I think supervisions ought to be great. It's clear to me that they are a major advantage of being at Cambridge as opposed to being at home with web access to to lecture notes and problem sheets. I'm trying to understand how often and how well they fulfill their potential, especially in the case of students who need something outside the usual bounds.

Hearing personal experiences of how they were great and what action was needed (if any) to make them great is very helpful to me. I want to give good advice, and telling somebody that Cambridge is a good place for him is a big deal. Right now I'm very reluctant to direct towards Cambridge (for example) a quiet, unassuming kid who is very advanced mathematically. I'm not at all sure that she won't be bored the first year with classes in material she already knows, and sit quietly in supervisions that don't teach her anything; she won't say anything, and generally just study on her own much as she has to in school now.

So I'm very curious as to how students get what they want and need, especially when they aren't good advocates for themselves. If it just magically happens, even for students who are very unusual, that would be wonderful. But so far I'm not seeing anybody claim that level of magic. If it's important to take action to get what you need, I'd love to understand better what sort of action people have found has worked for them.

Original post by IGU

...

I don't think there's ever any point in taking classes in stuff you already know. This is assuming you know it properly, which requires really working hard at it the first time, which is what everyone should do when they learn something difficult that's worth learning. It's kind of weird when you hear people who seem (because they are regarded as being charismatically) hot at maths and at teaching maths express the backward opinion that it's good for someone to 'learn' the same thing twice. Kind of treading water with some 'hard problems' thrown in to pass the time. Cambridge may yield another John von Neumann but is unlikely to yield another Alexander Grothendieck or even Isaac Newton. Consider the fact that at Cambridge there are some students who've done the same Part III course two or even three times.

The Cambridge attitude is that students who've done well in the IMO tend to be genetically super-'talented', and those who haven't, with a few exceptions, tend not to be. Those few exceptions - well, whether they go further than they're 'supposed to' at Cambridge still comes down to what they learn on their own, as in Littlewood's day. Some have twigged that it's best not even to tell their DOSses what they're doing (but in that case, don't expect supervisions). Many DoSses aren't much interested; those who are highly rated usually channel the received opinion that 'hard problems are where it's at'.

But with enough drive, you can do anything! :smile:

:smile:

(edited 9 years ago)

Hi guys, I just got a standard rejection letter following my application for maths at clare :frown:

:frown:

needless to say I'm gutted. My grades upon application were A* in a level maths, A in AS physics and B in AS spanish. For my gcses I got 7 A*s and 3 As. This year I'm doing A level further maths and A2 physics. I thought these would be good enough to get me an interview? I got fairly low ums in the Maths which I imagine is the main reason for my rejection. I feel like my personal statement was strong so that won't have been a problem. Does the average student offered an interview have more than this? I know Cambridge is the cream of the crop but I'm very disappointed not to have been given an interview, and i think if my apparent naivety could be explained to me it would help me...? :smile:

:smile:

thanks guys

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(edited 9 years ago)

username1162972

Original post by Foxab

Hi guys, I just got a standard rejection letter following my application for maths at clare :frown:

:frown:

needless to say I'm gutted. My grades upon application were A* in a level maths, A in AS physics and B in as

Posted from TSR Mobile

what ums in maths a level?? and physics?

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Hey, I've edited that post if you wanna look (accidentally hit submit). Maths ums was ~535, physics ~245 both ± like 5 :tongue:

:tongue:

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username1162972

Original post by Foxab

Hey, I've edited that post if you wanna look (accidentally hit submit). Maths ums was ~535, physics ~245 both ± like 5 :tongue:

:tongue:

Posted from TSR Mobile

yep definately maths ums. i think i seen the quintiles for maths and fm ums and the lowest quartile was 95 and highest was 100.

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Ah that's a shame, thanks for your help mate :smile:

:smile:

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username1162972

Original post by Foxab

Ah that's a shame, thanks for your help mate :smile:

:smile:

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what was your second choice? imperial or warwick??

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Original post by physicsmaths

what was your second choice? imperial or warwick??

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Imperial, waiting for feedback. I've got a standard a*a*a offer from Warwick that they sent everyone :tongue:

:tongue:

username1162972

Original post by Foxab

Imperial, waiting for feedback. I've got a standard a*a*a offer from Warwick that they sent everyone :tongue:

:tongue:

yh same waiting for imerial aswell. how do you think you did on the mat

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Original post by physicsmaths

yh same waiting for imerial aswell. how do you think you did on the mat

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I didn't get to do the MAT due to family stuff so I'm just gonna do STEP. They prefer MAT but steps fine if you cant do it

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username1162972

Original post by Foxab

I didn't get to do the MAT due to family stuff so I'm just gonna do STEP. They prefer MAT but steps fine if you cant do it

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I would tell them that if I was you cause they would assume you were gna do it due to applying before 15th October. It wouldn't look good to them, so I would tell them that you had circumstances

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Original post by physicsmaths

yep definately maths ums. i think i seen the quintiles for maths and fm ums and the lowest quartile was 95 and highest was 100.

Posted from TSR Mobile

How can you have seen them when they haven't been released?

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