How's the Cambridge Tripos for undergrad Maths?

[IGU]

My kid is considering going to Cambridge to read maths. I've been reading everything I can find about the University, especially all the official stuff on the web. I've also looked at Tim Gowers's blog, comments from MIT people on their exchange program, and other stuff (including posts here). I've also corresponded with faculty. So at this point I think I know a fair amount.

What I'm missing is the perspective of students who have been through it recently. I have talked to old math guys who were students there many years ago (e.g. Conway), but that's just not the same. Is there anybody here who can give me a recent perspective on what things are like for students?

To the extent it matters, my kid is quite advanced and capable at mathematics, but that's pretty much all he's interested in. The most important reason to consider Cambridge rather than any school in the US is that he would study nothing but math as an undergrad. He's been home schooled in California, auditing university classes now and then. He's currently auditing this class at Stanford.

Some specific questions:
- Is Trinity the only college to consider for maths, or do others work well too?
- Is it rigid and traditional in its instruction?
- Are supervisions wonderful? awful?
- Is it a good place for extremely capable kids, or will they just get frustrated?
- Is it a good place for extremely advanced kids, or will they just get frustrated?
- How's the social life for math geeks?
- How flexible are they? Can students to do non-standard things like research?
- Is anything especially different for Americans?

 

[AlephZero]

Well, I wasn't there "recently", but to answer some of your points:

Is Trinity the only college to consider for maths, or do others work well too?

No, no, no. "College" is basically where you live. Lectures and exams are organized by the university not the colleges. Your college organizes your weekly supervisions (typically two sessions, each of 2 students with a supervisor), but since not all colleges have specialists in every branch of every subject (not even Trinity!) your supervisions may well be with somebody from a different college.

You might consider that Kings, Johns and Trinity are at the top of the to-do list for tourists. Unless you like being photographed by a coach load of Japanese tourists several times a week, you might prefer a smaller college a little way out from the center, like Pembroke, Peterhouse or Downing. Cambridge is pretty compact, and transport is not an issue if you can ride a bike. Or one of the modern colleges even further out, like Churchill. (Full disclosure of bias: I was at Pembroke)

Are supervisions wonderful? awful?

Yes, and yes (but not many were awful, in my day)

How's the social life for math geeks?

The same as for everybody else - very wide ranging. It's entirely up to you how much you participate in it (but it would be short-sighted to ignore all of it, IMO).

How flexible are they? Can students to do non-standard things like research?

Things may have changed since my day, but back then all you had to do to get a degree was (1) live in an "approved place of residence" in term time (i.e. actually in a college, or in student accommodation owned by a college) and not break too many college and university rules, (2) pass your exams, and (3) pay your college bills on time.

What else you did was entirely up to you. If you didn't want to go to any lectures at all in three years, nobody would force you. But skipping your weekly supervisions was not an option, so you had to keep up with the pace. (Math and science students usually did attend lectures, though some liberal arts students didn't, and spent most of their time in the library working on weekly essays for their supervisions).

Is anything especially different for Americans?

Hmm ... a home schooled geek from America might think they have been teleported into Hogwarts ... but so long as they don't also think "I'm from the USA" is some sort of magic spell, don't worry too much about that!

my kid is quite advanced and capable at mathematics

Check out the "Cambrdge STEP" entrance exams.
http://www.admissionstestingservice.org/our-services/subject-specific/step/about-step/

 

[pasmith]

My kid is considering going to Cambridge to read maths. I've been reading everything I can find about the University, especially all the official stuff on the web. I've also looked at Tim Gowers's blog, comments from MIT people on their exchange program, and other stuff (including posts here). I've also corresponded with faculty. So at this point I think I know a fair amount.

What I'm missing is the perspective of students who have been through it recently. I have talked to old math guys who were students there many years ago (e.g. Conway), but that's just not the same. Is there anybody here who can give me a recent perspective on what things are like for students?

To the extent it matters, my kid is quite advanced and capable at mathematics, but that's pretty much all he's interested in. The most important reason to consider Cambridge rather than any school in the US is that he would study nothing but math as an undergrad. He's been home schooled in California, auditing university classes now and then. He's currently auditing this class at Stanford.

That seems to be a mixture of 1st and 2nd year Tripos content.

I studied mathematics at Trinity from 2000 to 2004, so some of this may be out of date. It's also largely Trinity-centric.

Some general points:

The Tripos is divided into courses, but it's not modular; there are four compulsory papers at the end of each Part, and each course in that Part has some number of questions on each paper. Part IA (1st year) offers essentially no choices whatsoever. In Part IB (2nd year) and especially in Part II (3rd year) there are more courses available than one can conveniently study or prepare for the exams, and a choice has to be made. Successful completion of Part II will get you a BA degree; Part III is essentially a combination of a taught MSc (if you obtained a Bachelor's degree elsewhere) and the fourth year of an MSci (if you obtained a Cambridge BA) and gets you an MMath.

You will be allocated accommodation by your college; this is likely to consist of a single room with a wash basin, bed (linen supplied) and desk. Kitchen, toilet and bathing facilities are communal. There will be bedders tasked with cleaning these areas, student rooms, and changing bed linen, although it is best to clean up after yourself. Laundry machines operated by coins or tokens will be available.

You will have no choice in the selection of first year accommodation, but in subsequent years one can choose. Priority in choosing second year accommodation is determined at random, the order being reversed for the third year.

Your college will assign Fellows to be your Tutor, who is responsible for pastoral care and is not necessarily a mathematician, and your Director of Studies, who is responsible for your academic work and will be a mathematician.

Some specific questions:
- Is Trinity the only college to consider for maths, or do others work well too?

As a Trinity man I am naturally obliged to recommend it. But of course it's not the only option for any subject.

The Tripos is the same whichever college admits you. If a college can't find a supervisor for a particular course from its own fellows or graduate students, it will find a supervisor from another college. This is not likely to be a problem for Part IA courses, but may arise for Part II.

In general terms one has a choice between the older colleges (which are convenient for the town centre but can be overrun with tourists) or the newer colleges (which are less convenient but not so overrun). I doubt there's much to be gained tactically in the admissions process by opting for a less well-known college as your first choice. The colleges on the Cam and to the west of the Cam will be the most convenient for the Centre for Mathematical Sciences (except Girton, which is not convenient for anything).

- Is it rigid and traditional in its instruction?

To an extent; this was certainly true of lectures, which consisted of a lecturer writing notes on a blackboard (or variant thereof) while the students copy it down on paper.

Supervisions will vary by supervisor.

- Are supervisions wonderful? awful?

It depends on the supervisor (and your supervision partner). You will get more out of them if you prepare adequately.

- Is it a good place for extremely capable kids, or will they just get frustrated?
- Is it a good place for extremely advanced kids, or will they just get frustrated?

Yes. Having read Gowers's Introduction to the Tripos you will know that "mathematics gets hard", but it's probably better for that to happen sooner rather than later.

There is little to no flexibility in the first year, but from the second term at least you can make a start on studying the second year courses (but you won't be examined on them until the end of your second year).

You can, subject to your other commitments, attend lectures on more advanced courses as you see fit (being a student of the university entitles you to attend any lecture offered by the university on any subject, although there are some exceptions), but your Director of Studies might not arrange supervisions for you if you attend a course too far in advance of its normal place in the Tripos, or if he or she thinks you are taking on too much too soon.

- How's the social life for math geeks?

There are college and university mathematics societies, and a wide range of other college and university clubs and societies. Every college has its bar (bear in mind that in the UK one can start purchasing alcohol at 18).

- How flexible are they? Can students to do non-standard things like research?

Terms are extremely intense. There will likely not be time for anything more than the Tripos. But students are free to attend departmental seminars if that fits in with lectures and supervisions.

Trinity does have prizes available for https://www.trin.cam.ac.uk/show.php?dowid=689 and the same may well be true of other colleges. There are summer research studentship schemes, although I have been unable to find any details online.

- Is anything especially different for Americans?

I cannot say.

 

[IGU]

A quick follow-up. Thanks to AlephZero and pasmith for their helpful replies. The kid has applied to Cambridge (Trinity College) to read maths and been invited to an interview. My biggest concern right now in figuring out if this would be the right thing for him is how flexible they are. If they (meaning his Director of Studies I think) agree he is ready, will he be able to get supervisions in Part II and III courses starting immediately? He'll need that if he sticks to pure maths.

I understand that he will, if he wants to graduate, have to go through three years sitting exams for Parts IA, IB, and II at the end of each year. This is inconvenient, slow, and expensive, but I think I can live with that. Three years of hanging out with undergrad math geeks might even be good for him.

The other main question I have is since he'll be far away from home it's likely he'll be spending lots of time at Cambridge between terms. Is there anything (official) for him to do or will he just be on his own? I'm guessing there might be research opportunities if he seeks them out, but perhaps not.

I'm still trying to come up with good alternatives to Cambridge but I don't know any so far. It would be good to have a back-up choice closer to home in case it doesn't work out. Are there any schools like Cambridge in the US?

 

[IGU]

Don't know if anybody's interested, but here's another update. I've included some answers I've found.

The kid has applied to Cambridge (Trinity College) to read maths and been invited to an interview.

He's now received a conditional offer. Meeting the condition should be straightforward.

For those unfamiliar with the process, in the UK you aren't usually just accepted to a course of study at a university, but rather the conditions on your acceptance are explicit. These usually include specific grades in relevant subjects. For maths at Cambridge they usually involve specific grades in the STEP tests.

... will he be able to get supervisions in Part II and III courses starting immediately? He'll need that if he sticks to pure maths.

If he can convince his Director of Studies that it's the right thing to do, then he can get supervisions in Part IB and Part II courses from the start. I've conversed with recent and current top maths students who tell me this is so. Part III courses do not have supervisions, but rather have larger problem sessions that are available.

But nothing changes the fact that the exams will happen in their proper year, and taking the courses early won't change that.

Is it a good place for extremely capable kids, or will they just get frustrated?
Is it a good place for extremely advanced kids, or will they just get frustrated?

People who meet these descriptions and have been through it assure me that it is the best place.

Is there anything (official) for him to do [between terms] or will he just be on his own?

I'm still not sure exactly how that goes. There are summer research projects for some undergrads.

Are there any schools like Cambridge in the US?

If there are I haven't heard of any.

 

[AlephZero]

Is there anything (official) for him to do [between terms] or will he just be on his own?

I'm still not sure exactly how that goes. There are summer research projects for some undergrads.

It's unlikely there will be anything "official" between terms except in summer, except reading to catch up on the term just ended, and reading ahead for the next one. The other two breaks are relatively short, and are interrupted by UK national holidays at Christmas/New Year and Easter.. Also, the colleges make good money from hiring their meeting rooms and accommodation to conferences etc (not necessarily "academic" conferences) out of term time, so the normal college "way of life" stops.

On the other hand, the summer "long vacation" is about 14 weeks, so there is plenty of time to do something (not necessarily in Cambridge) and also have a rest break. But unless things have changed since my day, what you do out of term time has no bearing on the undergraduate degree - but of course it may be very relevant to getting a future research position or a job in industry.

 

[IGU]

Another quick follow-up. STEP exam results are in and my kid will be going to the University of Cambridge, Trinity College, to read maths in October. It will be interesting to see how it turns out -- their approach is quite different from what he's been doing on his own.

 

[adi19956]

Another quick follow-up. STEP exam results are in and my kid will be going to the University of Cambridge, Trinity College, to read maths in October. It will be interesting to see how it turns out -- their approach is quite different from what he's been doing on his own.

That's great news! I was just reading this casually, but coincidentally I have a friend going to read maths at Trinity College this year.
What did he get in his STEP exams? And which ones did he do? I assume STEP II and III? Don't worry, I know the grading system.

I was interested in what you said about choosing Cambridge because their maths course only does maths. This is the standard for British unis and I was wondering what it's like in the States if it's not like that. Do you have to do something else concurrently?

 

[IGU]

That's great news! I was just reading this casually, but coincidentally I have a friend going to read maths at Trinity College this year.

Exciting!

What did he get in his STEP exams? And which ones did he do? I assume STEP II and III? Don't worry, I know the grading system.

Yes, STEP II and III, but he doesn't know his scores yet since there's some kind of registration process you have to go through to get them and he didn't get the right information from the test centre. However UCAS shows his offer turning unconditional so I'm guessing he met his conditions.

I was interested in what you said about choosing Cambridge because their maths course only does maths. This is the standard for British unis and I was wondering what it's like in the States if it's not like that. Do you have to do something else concurrently?

Yeah, we do things differently here. You can read about it in a variety of places. Serious concentration on one or two things is generally for the last two years of undergraduate school and grad school.

 

[adi19956]

Exciting!

Yes, STEP II and III, but he doesn't know his scores yet since there's some kind of registration process you have to go through to get them and he didn't get the right information from the test centre. However UCAS shows his offer turning unconditional so I'm guessing he met his conditions.

Yeah, we do things differently here. You can read about it in a variety of places. Serious concentration on one or two things is generally for the last two years of undergraduate school and grad school.

Ah that must be frustrating that he didn't get his scores. Yes that's exactly what that means on UCAS and being Cambridge there is 0% chance they'll take someone who didn't meet their offer conditions so he definitely made or beat them.

I just looked it up and I find the US system... Odd. Sure we can do courses with different things if we want. I was thinking of physics and economics, and physics and French at one point, but mainly our degrees are single subject. Maybe this is why our degrees are generally shorter than US ones.

 

[IGU]

Ah that must be frustrating that he didn't get his scores.

Not for him. He doesn't care about exams. I'm the one who's curious whether he'll get the marks he expected (95-110/120 on STEP II and 110+/120 on STEP III). I'm also waiting to see how he does when he sits his first Tripos exams without revising (as I suspect he'll do); that will either be a sobering disaster or an unsurprising confirmation (to him) that he knows how he works better than other people do. It should be interesting either way.

Yes that's exactly what that means on UCAS and being Cambridge there is 0% chance they'll take someone who didn't meet their offer conditions so he definitely made or beat them.

I'm reliably informed that 20-25% of Cambridge maths admits each year did not meet their offer conditions. A little thought makes sense of this -- it gives Cambridge the flexibility to pick and choose amongst the borderline cases to admit those they most want to teach. They can also avoid gross injustices due to health, environmental, or A-Level teacher anomalies. Wiggle room in a very inexact process is probably a good thing.

I very much like that professors make the admission decisions at Cambridge. Over here it's generally professional admissions people who don't understand the first thing about the actual courses of study. I remember talking to a Caltech professor who told me the department had tried for two years to get an absolutely amazing math kid in as an undergraduate, but admissions said they couldn't. Just plain stupid.

 

[adi19956]

Not for him. He doesn't care about exams. I'm the one who's curious whether he'll get the marks he expected (95-110/120 on STEP II and 110+/120 on STEP III). I'm also waiting to see how he does when he sits his first Tripos exams without revising (as I suspect he'll do); that will either be a sobering disaster or an unsurprising confirmation (to him) that he knows how he works better than other people do. It should be interesting either way.

I take it for son is astoundingly intelligent then. I've never known such casualness about Cambridge. If that's what he was getting in STEP past papers that is absolutely insane. If anyone else were reading this I can't put into words just how difficult Cambridge makes these exams.

I'm reliably informed that 20-25% of Cambridge maths admits each year did not meet their offer conditions. A little thought makes sense of this -- it gives Cambridge the flexibility to pick and choose amongst the borderline cases to admit those they most want to teach. They can also avoid gross injustices due to health, environmental, or A-Level teacher anomalies. Wiggle room in a very inexact process is probably a good thing.

I'm really enjoying this, it's full of surprises. This must be because of STEP, there's no other course they'd do this for. I'm surprised they don't take pooled candidates, who did meet the requirements, instead.

I very much like that professors make the admission decisions at Cambridge. Over here it's generally professional admissions people who don't understand the first thing about the actual courses of study. I remember talking to a Caltech professor who told me the department had tried for two years to get an absolutely amazing math kid in as an undergraduate, but admissions said they couldn't. Just plain stupid.

I'd say there's a mix of that here. It's generally professional admissions people who manage the process, because it's a full time job, but professors who do interviews and as far as I'm aware make recommendations. I don't really know too much about Oxbridge applications though because I didn't apply.

 

[pasmith]

I'm really enjoying this, it's full of surprises. This must be because of STEP, there's no other course they'd do this for. I'm surprised they don't take pooled candidates, who did meet the requirements, instead.

Pooled candidates who received an offer from another college will be going to that college if they satisfy the offer. Pooled candidates who don't receive an offer from any college are in the same position as those rejected outright: they don't have an offer, so they won't be considered for admission in August, as the Trinity Admissions FAQ makes plain:

If I don't receive an offer in January, can I still be considered in August?

No. We always make more offers than we have places and no candidate will be accepted in August unless he or she is already holding the offer of a place at Cambridge. Candidates who do not meet the requirements laid down in their offer may still be admitted once all the examination results have been received and we know how many places are available. Trinity does not enter the UCAS clearing system.

Note that this applies to all subjects, not just mathematics.

I'd say there's a mix of that here. It's generally professional admissions people who manage the process, because it's a full time job, but professors who do interviews and as far as I'm aware make recommendations. I don't really know too much about Oxbridge applications though because I didn't apply.

College admissions tutors tend to be academics first and foremost although supported by administrative staff in College and by the University Admissions Office.

 

[IGU]

I take it for son is astoundingly intelligent then.

Intelligent in some ways and not so intelligent in others. But very, very good at math.

I've never known such casualness about Cambridge.

Well, we're American. We weren't brought up with a magical reverence for Oxbridge. Here we tend to regard Harvard, Yale, and Princeton that way. Me, I kind of think that every place is second rate compared to Caltech, but that's because I went there and I don't know the others personally.

If that's what he was getting in STEP past papers that is absolutely insane.

Well he didn't revise at all so there were no STEP past papers; his estimates were from after having sat the exams. I got his grades today. Actually he missed his offer -- he got a 1 (94) in STEP II (missing an S by 1 mark) and an S (112) in STEP III (the fourth highest paper according to the distribution they published). But they took him anyway, so now he's one of that 20-25% who are accepted despite missing their offers.

This must be because of STEP, there's no other course they'd do this for.

If you look at their statistics, you'll see they are generous in giving out offers for maths, but that way more maths applicants don't make their offers. They mostly let STEP sort them out.

If anyone else were reading this I can't put into words just how difficult Cambridge makes these exams.

They're just exams, and they don't cover any university level material. But they are designed to make sure you can actually use the material rather than just regurgitate it. So in that sense they're very hard for students who have never had to do that before. His experience is not like that at all.

 

[cgk]

Well... obviously it worked, but am I the only one who finds this level of parental care curious?

After finishing secondary school I would never even have considered the possibility of letting my parents have a say in what, where, and how I study. After all, it is not their life, and even though the continuing infantilization of society might seems to suggest otherwise, a 16-18 year old is perfectly capable of casting her own decisions if given the chance. Particularly so if its a youth who can casually get into Cambridge (and Trinity College no less).

Independence is a major part of studying. And at the latest once a person finishes secondary education, I think it would be best for everyone involved if they were regarded as adults in their own right.

 

[IGU]

Well... obviously it worked, but am I the only one who finds this level of parental care curious?

After finishing secondary school I would never even have considered the possibility of letting my parents have a say in what, where, and how I study. After all, it is not their life, and even though the continuing infantilization of society might seems to suggest otherwise, a 16-18 year old is perfectly capable of casting her own decisions if given the chance. Particularly so if its a youth who can casually get into Cambridge (and Trinity College no less).

Independence is a major part of studying. And at the latest once a person finishes secondary education, I think it would be best for everyone involved if they were regarded as adults in their own right.

Mathematics strong. Planning weak. "So this time next year you should probably be at a university somewhere learning what you want to learn with other students. What would you like to do?" "I don't know." Repeat endlessly with variations. If I hadn't made some choices for him then five years from now he'd probably still be sitting in his room reading math books. Works for him, not for me.

The main things I hope he gets out of Cambridge are: friends of like mind; a willingness to plan and make decisions for himself; some career guidance; some new interests; figuring out what he loves; other improved self understanding. I'm pretty sure he would learn more mathematics at home, and probably learn it better without the distractions of university life. But my goal for him, like most parents, is that he end up as a reasonably happy person doing things he loves with people he loves. That's especially difficult when you are very different from the people around you.

And it's obvious that it worked only if you think getting into Cambridge was the goal. It wasn't. Cambridge is a means to an end, and it may prove useful or terrible or anywhere in between. He'll find out. Personally, I hate making decisions for other people. But sometimes, as a parent, it's necessary.