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What are the best universities for pure maths?

I'm not interested in applied, just pure (and a little stats).

Would this list (in a rough order) be correct:

Oxford
Cambridge
Warwick
Imperial
Manchester
Bristol
Southampton
Nottingham
KCL
Edinburgh
(edited 2 years ago)

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Original post by AlgebraKing3
I'm not interested in applied, just pure (and a little stats).

Would this list (in a rough order) be correct:

Oxford
Cambridge
Warwick
Imperial
Manchester
Bristol
Southampton
Nottingham
KCL
Edinburgh

I would have to admit (painfully, since I'm an Oxonian) that Cambridge is probably thought higher of than Oxford when it comes to maths, and may well be a bit harder to get into. For example, I know that most of the British Olympiad team went to Trinity College, Cambridge in my year. (I still would prefer Oxford to Cambridge personally though.) Imperial is obviously also very good.
Original post by -Imperator-
I would have to admit (painfully, since I'm an Oxonian) that Cambridge is probably thought higher of than Oxford when it comes to maths, and may well be a bit harder to get into. For example, I know that most of the British Olympiad team went to Trinity College, Cambridge in my year. (I still would prefer Oxford to Cambridge personally though.) Imperial is obviously also very good.

What is your area of maths out of interest?
Original post by AlgebraKing3
What is your area of maths out of interest?

I'm coming to the end of my 4th year reading Computer Science & Philosophy. There is a lot of overlap between maths, theoretical computer science, and philosophy (particularly philosophical logic and the philosophy of mathematics). I'm primarily interested in formal languages, logic, the foundations of mathematics and probability theory. I'm allowed a huge amount of choice, including the option of taking some modules from mathematics courses. I've taken modules in set theory, category theory, logic and probability.
I unfortunately find that the further you go down the league tables, the more applied-focused the uni.
Original post by AlgebraKing3
I unfortunately find that the further you go down the league tables, the more applied-focused the uni.

That might be true, but even at the top, different universities are very different. For example, Oxford gives computer science a very theoretical treatment (which has frustrated some of my friends, since we rarely code on pc). This is actually the main reason Oxford was my first choice. Imperial College, on the other hand, offers a very practical course, and, being in London, Imperial students find it very easy to find employment after.
@CoolCavy please move this to the university maths forum
Reply 7
Original post by AlgebraKing3
I'm not interested in applied, just pure (and a little stats).

Would this list (in a rough order) be correct:

Oxford
Cambridge
Warwick
Imperial
Manchester
Bristol
Southampton
Nottingham
KCL
Edinburgh

Every mathematics course will require you to do at least some applied mathematics, so you have to be prepared to do some. If you only have A-level/Further Maths to go on, you may also be surprised at what counts as pure and applied at university. The larger the department, the greater the variety of options available (as a rule of thumb) which is something to look into. I'd say that Oxford's first year is somewhat more pure than Cambridge's but you'd be able to do a good range of pure mathematics during your degree from either, and from most universities on that list.
Original post by AlgebraKing3
I'm not interested in applied, just pure (and a little stats).

Maybe you already know this, but the pure maths you do in A level is applied maths in university. Pure maths at university is rather different. Try looking at lecture notes or books in Analysis, which is a pure maths module at university and it will give you a taste of pure maths at university

Also regardless of where you study, even if its high up in the league tables, you will be made to do (as should be the case !) a lot of university applied maths before you can truly specialise in pure maths.

Finally assuming you knew all this and you still just really want to do pure maths at university and not applied, then Oxford, Cambridge, Bristol, Warwick, Imperial all have very good maths courses and will give you enough pure maths modules to chose from, but as I said you still will be made to do some applied maths.
Original post by Rohan77642
Maybe you already know this, but the pure maths you do in A level is applied maths in university. Pure maths at university is rather different. Try looking at lecture notes or books in Analysis, which is a pure maths module at university and it will give you a taste of pure maths at university

Also regardless of where you study, even if its high up in the league tables, you will be made to do (as should be the case !) a lot of university applied maths before you can truly specialise in pure maths.

Finally assuming you knew all this and you still just really want to do pure maths at university and not applied, then Oxford, Cambridge, Bristol, Warwick, Imperial all have very good maths courses and will give you enough pure maths modules to chose from, but as I said you still will be made to do some applied maths.


I'm mainly interested in topics such as abstract algebra, combinatorics and geometry.
Original post by AlgebraKing3
I'm mainly interested in topics such as abstract algebra, combinatorics and geometry.

Most universities (especially the 5 I mentioned) will have courses in Abstract Algebra and some Geometry. It mostly depends on which year you are introduced to the courses and in how much depth. But I think you will definitely have courses in your undergraduate where you are introduced to Group Theory, and Topology (although this might be basic point set Topology)

Combinatorics I don't think is a course that an undergraduate degree will have? Because it is quite specialised and difficult, but if you want to do combinatorics you can always apply to do a masters at a place which has combinatorics courses.

Again no matter where you go you will be made to do applied maths. But at places like Oxford, Cambridge, Warwick, Imperial I think you can drop a lot of the applied by the 2nd year. Not sure about the others.
Reply 11
Original post by Rohan77642

Combinatorics I don't think is a course that an undergraduate degree will have? Because it is quite specialised and difficult, but if you want to do combinatorics you can always apply to do a masters at a place which has combinatorics courses.

You can do combinatorics in the Oxbridge maths degrees, but not till the fourth year. Not sure about elsewhere.
Original post by RichE
You can do combinatorics in the Oxbridge maths degrees, but not till the fourth year. Not sure about elsewhere.


AFAIK Warwick, Bristol and Manchester have combinatorics in the second year
Reply 13
Original post by AlgebraKing3
AFAIK Warwick, Bristol and Manchester have combinatorics in the second year

A lot of this comes down to labels. Warwick’s first combinatorics course is covered in Oxford in year 1 and in later graph theory courses. A lot of it might just be termed discrete maths at another uni. Their second course in the third year is more specialised and I guess reflects Warwick’s specialism in this area.
Original post by Rohan77642
Maybe you already know this, but the pure maths you do in A level is applied maths in university. Pure maths at university is rather different. Try looking at lecture notes or books in Analysis, which is a pure maths module at university and it will give you a taste of pure maths at university

Also regardless of where you study, even if its high up in the league tables, you will be made to do (as should be the case !) a lot of university applied maths before you can truly specialise in pure maths.

Finally assuming you knew all this and you still just really want to do pure maths at university and not applied, then Oxford, Cambridge, Bristol, Warwick, Imperial all have very good maths courses and will give you enough pure maths modules to chose from, but as I said you still will be made to do some applied maths.

reading this with interests. similar situation. My son applied for Pure maths degree at Queen Mary and received an offer. He must get "A" for Maths. his passion and strength is Pure, he have other universities offers but they all are mathematics course.

Now i am not sure whether he would get A grade because his school is a below average school and not much constructive teaching however is able Mathematician and because of his needs he can only do Maths. he is studying Further Maths privately. I like to know would Queen's will offer him a place if he get "B" grade ,I know no one knows but I like to know how lenient they have been in past.

My son normally comes third of fourth highest in the class but never got an A grade and rarely someone get A in mocks. I would like to know would the school would award him A grade if he achieves this at the final exams in summer?. they have mentioned latest assessment will weigh more but i am confident he will do lot better in summer because of the content they covering.
you mentioned the Pure Maths is different at university, can you please explain that in bit more details, . the modules they teach seems good for my son because he is more able in Pure than applied, obviously everyone will have to to do some applied but what is your opinion on Queen's pure degree?
Original post by sweetcherry55
reading this with interests. similar situation. My son applied for Pure maths degree at Queen Mary and received an offer. He must get "A" for Maths. his passion and strength is Pure, he have other universities offers but they all are mathematics course.

Now i am not sure whether he would get A grade because his school is a below average school and not much constructive teaching however is able Mathematician and because of his needs he can only do Maths. he is studying Further Maths privately. I like to know would Queen's will offer him a place if he get "B" grade ,I know no one knows but I like to know how lenient they have been in past.

My son normally comes third of fourth highest in the class but never got an A grade and rarely someone get A in mocks. I would like to know would the school would award him A grade if he achieves this at the final exams in summer?. they have mentioned latest assessment will weigh more but i am confident he will do lot better in summer because of the content they covering.
you mentioned the Pure Maths is different at university, can you please explain that in bit more details, . the modules they teach seems good for my son because he is more able in Pure than applied, obviously everyone will have to to do some applied but what is your opinion on Queen's pure degree?


It's just a more limited course I believe. QMUL is worse than quite a few non-RG unis so I'd avoid it.
Original post by AlgebraKing3
It's just a more limited course I believe. QMUL is worse than quite a few non-RG unis so I'd avoid it.

could you please tell me why you think QMUL is worse? do you know anyone did maths there or your personal experience? I know they are not top like imperial or UCL. we are not aiming for those but a reasonably good university and something what my son really enjoy and can do well.
Generally the top UK universities for pure maths correspond to the top unis here for maths in general. In no particular order the top 4 are more or less indisputably Cambridge, Oxford, Warwick and Imperial. Bristol is probably the next best, then Edinburgh and UCL. I think everything else is a bit more distantly behind those, although Edinburgh skews a but more to applied maths than UCL is my impression.

Note depending on the area of pure maths you want to study one may be better than the others. Warwick and Oxford seem to offer a lot more algebraic geometry and related areas, while Cambridge and Imperial seem to have a bit more offerings for number theory (although Oxford does have Andrew Wiles...no idea if he teaches, or if he does if he teaches well, however!). Oxford or Bristol are probably the best for foundations/logic and set theory as they have parallel strengths on the philosophy side of those areas from what I understand, and both have joint courses in maths and philosophy too. Oxford and Imperial seem to have the most topology, while Imperial seems to have the most geometry options, although UCL has a couple options in that regard too (possibly more tied to their GR work though? Not sure). Of course I'm not a mathematician so I can't comment on the actual strength of their research in their areas, and bear in mind just because a particular module/paper is offered doesn't mean it will be well taught! Also be aware that most of the differences in offerings indicated above are for the much more specialised third and fourth year options. The first two years there may be some differences in the exact order or sometimes depth some topics go into, but they'll all cover broadly the same material (because there is a fair bit of maths any mathematician needs to know to work in any field of maths).

However each of the top 4 offer their own maths masters programmes which overlaps a lot with their undergrad 3rd/4th year options, and I gather it's not uncommon for grads of one of the four to do oostgrad work at the others. So even if you don't get to take a particular course in final year(s) at one, you could still just as well do a master's and/or PhD at another that specialised more in the area of interest - and as indicated all will cover the material any mathematician (both pure and applied) "should" know. So you can't really go wrong going to any of those top four, or Bristol or UCL either. You can probably cover most if not all of the same material at Edinburgh, Southampton, or KCL as well. I think QMUL is a bit weaker though. Not so familiar with Manchester or Nottingham as far as maths goes though.
(edited 2 years ago)
Original post by sweetcherry55
could you please tell me why you think QMUL is worse? do you know anyone did maths there or your personal experience? I know they are not top like imperial or UCL. we are not aiming for those but a reasonably good university and something what my son really enjoy and can do well.


Look at the modules they offer and their research.
Original post by sweetcherry55

you mentioned the Pure Maths is different at university, can you please explain that in bit more details, . the modules they teach seems good for my son because he is more able in Pure than applied, obviously everyone will have to to do some applied but what is your opinion on Queen's pure degree?

I'm afraid I can't answer most of your questions, but I can answer this one. University pure mathematics is generally more abstract and rigourous.

Abstract in the sense that mathematicians like to study generalised objects and structures. To use an example, there is an algebraic structure called a vector space in which it is possible to add elements (called vectors) and multiply them by "scalars". Students are already familiar with vectors from A Level in the form of ordered tuples of numbers, but other examples of vector spaces arise (e.g sometimes the set of solutions to certain differential equations form a vector space) and a general understanding of the properties of vector spaces allows one to better understand the specific example.

Rigour means that pure mathematicians care about proof; we do not just want to know the answer to a question, we want to be able to prove that it is true using a logical argument which convinces ourselves and others. Although students are introduced to proof at lower levels, it is typically a sideshow to calculation. This changes at uni, where proof takes centre stage. So whilst an A Level student might, for example, enjoy evaluating integrals (which is labelled as pure mathematics in A Level), an undergraduate pure mathematician might be more interested in defining what exactly it means to integrate a function and developing concrete theorems about integration. In contrast, it is common for applied mathematicians to spend more time actually evaluating integrals!
(edited 2 years ago)

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