best uni in world for pure maths

Reply 20

7

hungry_hog

Interesting question. I would say Cambridge has the best rep, particularly for part III.

Interestingly in the IMO the UK normally finishes pretty mid-table. So there are obviously lots of genius mathmos not at Cambridge (I think Romania are particularly strong as a smallish country). But obviously use of IMO as an indicator is dodgy (and other countries may focus more time on prep than us).

I think a few years back the whole USA team got perfect scores at IMO.

Since the IMO is a pre-university thing that doesn't make a whole lot of sense...
Also, the maths syllabus in the UK focuses much more heavily on calculus etc. than geometry/inequalities/whatever unlike some other countries.

Reply 21

s.e.r.e.n.e

12

Speleo

Since the IMO is a pre-university thing that doesn't make a whole lot of sense...
Also, the maths syllabus in the UK focuses much more heavily on calculus etc. than geometry/inequalities/whatever unlike some other countries.

True.

Reply 22

SouthernFreerider

OP

12

yeah im quite good at maths, not genius or anything, but by far better than most (not being arrogant).

yeah my plan (atm) is to apply to cambridge and 4 lesser uk unis, then apply to 6 or7 of the top unis abroad, then hoping to use the 4 lesser uk unis as a backup. lol. good to have aspirations eh

Reply 23

Popa Dom

2

Out of curiosity, for the first 3 years is cambridge actually that much better than oxford, or is it just the partIII and postgrad thats way better? Just I saw a cambridge first year analysis paper and it looked pretty much the same as ours.

Reply 24

Kolya

17

I have two reservations about the question:

- In what sense do you mean "best"? Best at research, or best at providing an undergraduate education, or best in the illustrious alumni that they have? I doubt that one university can be called the "best" in all of those categories. There might not be a "best" in any of the categories.

- A large majority of posters on this forum are students. Do you honestly think that the average Maths student is going to have much knowledge about mathematical institutions across the globe?

Maybe you could make the question more specific? :smile:

Reply 25

DFranklin

18

Popa Dom

Out of curiosity, for the first 3 years is cambridge actually that much better than oxford, or is it just the partIII and postgrad thats way better? Just I saw a cambridge first year analysis paper and it looked pretty much the same as ours.

I agree, there's not much difference. My feeling the Cambridge exams provide a little less in the way of "guidance" through the questions, but it's not a big difference. Incidentally, I did the IA tripos back in 88, and looking at the current papers, the analysis section has got a lot easier since then.

I am actually pretty cynical about the Cambridge maths system. I don't think there's much doubt that Cambridge has the strongest intake of students by a fair margin over any other university (I'd guess 90% of the IMO team go on to Cambridge, for example). And the majority of them will end up struggling to understand even half of the material on their course. Other universities may have somewhat easier courses, but they also get far more of their students to actually understand the topics.

Slight aside, but I've noticed a fair few people from Oxford asking questions on the Maths forum, and I don't think I've seen anyone from Cambridge do so. Any idea why?

Reply 26

KAISER_MOLE

7

Popa_Dom - I showed someone who is studying maths at Bristol the exams I sat this year and he said that the Vector Calc/Groups stuff was in advance of his course, but the analysis looked more or less the same. I think since analysis is tricky to get your head round initially they don't rush you into it. Honestly I wouldn't have thought Oxford would be much less in depth than Cambridge. Though Second year pure maths has a lot of analysis (Complex, analysis II, Further Analysis, Met and top spaces)

Reply 27

KAISER_MOLE

7

DFranklin

Slight aside, but I've noticed a fair few people from Oxford asking questions on the Maths forum, and I don't think I've seen anyone from Cambridge do so. Any idea why?

Am scared my DoS would find out and chastise me :p:

Reply 28

DFranklin

18

KAISER_MOLE

Popa_Dom - I showed someone who is studying maths at Bristol the exams I sat this year and he said that the Vector Calc/Groups stuff was in advance of his course, but the analysis looked more or less the same. I think since analysis is tricky to get your head round initially they don't rush you into it. Honestly I wouldn't have thought Oxford would be much less in depth than Cambridge. Though Second year pure maths has a lot of analysis (Complex, analysis II, Further Analysis, Met and top spaces)

OK, that explains a lot. Looking at the current IB papers, Analysis II seems pretty similar to when I did it, but when I did it, it was in part IA. So IA only has half of the content it had when I did it.

It seems IB has a fair bit of when we used to do in IA (Analysis II, Electrodynamics, Relativity, some of the methods stuff), but it also seems to have pretty much everything we did in IB. Which feels like IB would be a fairly horrific workload. Of course, analysing an entire syllabus on the basis of 5 minutes skimming the end of year exam might be a little foolhardy on my part...

Reply 29

Popa Dom

2

Lusus Naturae

I have two reservations about the question:

- In what sense do you mean "best"? Best at research, or best at providing an undergraduate education, or best in the illustrious alumni that they have? I doubt that one university can be called the "best" in all of those categories. There might not be a "best" in any of the categories.

- A large majority of posters on this forum are students. Do you honestly think that the average Maths student is going to have much knowledge about mathematical institutions across the globe?

Maybe you could make the question more specific? :smile:

I just meant in terms of how much material is covered and how hard the exam questions were, sorry I wasnt very clear.

Cheers for the responses guys, yeah I suppose we are kinda led through the questions quite a bit, always "prove this" then use it to solve something. And I've just had a look through the other exams from last year's first year, and its mostly pretty much the same, especially on the applied side, though you seem to have done number theory which we havent done yet, and your groups looks a bit more advanced (orbit stabilizer theorem??). Nice to see you also have the messy looking geometry questons! Cant say I'm gonna complain though, had enough on my plate trying to remember the rest of it..

Reply 30

Kolya

17

Popa Dom

I just meant in terms of how much material is covered and how hard the exam questions were, sorry I wasnt very clear.

I think I was the initial cause of confusion. I was referring to the question, "What is the best uni in the world for pure maths", not to your question! Apologies. :smile:

Reply 31

RichE

15

Popa Dom

Cheers for the responses guys, yeah I suppose we are kinda led through the questions quite a bit, always "prove this" then use it to solve something. And I've just had a look through the other exams from last year's first year, and its mostly pretty much the same, especially on the applied side, though you seem to have done number theory which we havent done yet, and your groups looks a bit more advanced (orbit stabilizer theorem??). Nice to see you also have the messy looking geometry questons! Cant say I'm gonna complain though, had enough on my plate trying to remember the rest of it..

If you compare any two roughly comparable courses you'll find some things done in one course ahead of the other and vice versa - there isn't an inherent way to present maths. IIRC Cambridge don't meet Fourier series till 2nd year nor boundary conditions PDEs, don't meet field extensions till the third year (second year Oxford), have no stats in the first year but do meet Cartesian tensors in the first year (third year relativity in oxford if at all), meet a little on group actions and meet number theory in the first year rather than 2nd.

Reply 32

sonar

If you have outrageous qualifications, an American university may be better, as you can take whatever you wish. Harvard's 55 and UChicago's Honors Analysis are definitely stringent.

That said, for many students in undergraduate mathematics, Harvard, MIT, Princeton, Stanford, and UChicago will all do them well.

When I applied, an old instructor highly recommended that I take the place at Oxford, "Not because Oxford would necessarily be far better than Harvard, etc,*but because it would be just as good ...."

Reply 33

JeremyC

8

DFranklin

(I'd guess 90% of the IMO team go on to Cambridge, for example).

Quite a good guess :smile:

- according to this website, of the people who competed in the IMO (including reserves) who are old enough to be at university 89.8% went to Cambridge (56% of whom went to Trinity - I suspect that percentage is higher nowadays).

As for workload, none of the IB courses are compulsory (although I suspect most DoS' will expect their students to go to most of the courses). How did you cope with IA when it had twice as much material? :eek:

Reply 34

DFranklin

18

fatuous_philomath

Quite a good guess :smile:

- according to this website, of the people who competed in the IMO (including reserves) who are old enough to be at university 89.8% went to Cambridge (56% of whom went to Trinity - I suspect that percentage is higher nowadays).

Given it was a figure pulled out of the air, that is a good guess, isn't it? :biggrin:

As far as the number of IMO people ending up at Trinity, to be honest, I'm not sure how "healthy" the links between Trinity and the IMO really are. From the outside it looked pretty cliquey at times.

As for workload, none of the IB courses are compulsory (although I suspect most DoS' will expect their students to go to most of the courses). How did you cope with IA when it had twice as much material? :eek:

We didn't have Algebra and Geometry (although we had a full groups course); we didn't have Numbers and Sets either. Some of that is just a rearrangement - you do some stuff earlier than I did and some stuff later. But being honest, I think there's a fair bit (about 1/3 of each course) of Algebra/Geometry or Numbers/Sets that we were either expected to "just know", or at the least were expected to just pick up in the course of other lectures. (Most people had at least some exposure to group theory in Further Maths back then).

The other thing is that we had Electrodynamics (and something else I can't remember - it might have been the last half of Probability) in exam term of IA, and very few people put any time into them. So in reality, if you wanted to do courses requiring Electrodynamics, you probably ended up putting in a fair bit of supplemental work after the exams.

Overall, I think we did a bit more work than you do now, but I'm not sure it was that much of a difference.

The IB courses weren't compulsory for us either, but most people dropped no more than one or two courses. Your IB workload definitely looks a fair bit tougher than ours if you are still only expected to drop a couple of courses at most.

[Disclaimer: this is largely based on 20 year old memories. I do actually have a lot of my IB notes around in the attic, but I don't care enough to compare and contrast...]

Reply 35

s.e.r.e.n.e

12

The Orientalist

You've watched "A beautiful mind" too many times...

I don't even know the movie "A beautiful mind". I went to check it out on Wikipedia... I know what you are talking now! :p:

Reply 36

DFranklin

18

DFranklin

It seems IB has a fair bit of when we used to do in IA (Analysis II, Electrodynamics, Relativity, some of the methods stuff), but it also seems to have pretty much everything we did in IB. Which feels like IB would be a fairly horrific workload. Of course, analysing an entire syllabus on the basis of 5 minutes skimming the end of year exam might be a little foolhardy on my part...

Responding to my own post, but had reason to look at the actual syllabuses today. You may recall me saying that in my day very few people would actually answer any questions based on stuff lectured in the actual exam term. It seems the examiners noticed this, and so there are now some courses that are lectured in IA but examined in IB. Which would explain why the IA exam looks like it has a lot less content and it all gets "caught up" in IB.

[So obviously I was right to look at the exams and think "this looks really unbalanced" - there was a reason...]

Reply 37

CarneLevare

4

How viable would it be to go from, say, Maths&phil at Oxford to the part III at Cambridge? Would much catching up would be neccessary?

Reply 38

RichE

15

HPSH

How viable would it be to go from, say, Maths&phil at Oxford to the part III at Cambridge? Would much catching up would be neccessary?

It would be viable - it's viable for MMath students, and Math+Phil students reach just as high a level of maths, just in a smaller range of subjects, usually on the pure side and those would be the courses you'd necessarily be restricted to taking in Part III.

Whether it would be advisable is another matter - the fourth year of the Math+Phil course brings you to a position where you could start an DPhil/PhD, so why not just do that if you wish to study further. However if you just want to study for one further year some areas of pure maths are only represented in a limited way in Part III, in particular in logic, set theory, model theory which are typical areas of Maths & Phil students and you might well be better off looking elsewhere.

Reply 39

JeremyC

8

DFranklin

Responding to my own post, but had reason to look at the actual syllabuses today. You may recall me saying that in my day very few people would actually answer any questions based on stuff lectured in the actual exam term. It seems the examiners noticed this, and so there are now some courses that are lectured in IA but examined in IB. Which would explain why the IA exam looks like it has a lot less content and it all gets "caught up" in IB.

[So obviously I was right to look at the exams and think "this looks really unbalanced" - there was a reason...]

Ahh yes, the optional exam term courses (which can, with the exception of CATAM, be taken in the second year instead of the first year) would probably explain the discrepancy.

They did seem to be relatively underattended though, especially the Monday/Wednesday/Friday combination of Metric and Topological Spaces, Optimization and Numerical Analysis - after Met and Top which many colleges seem to think is important (resulting in a large attendance - very few of whom actually understood the material) people were leaving in droves, such that there were only around 30 people left for Numerical Analysis. A real shame, since the lecturer for Numerical Analysis, Professor Iserles, is (in my opinion; others would disagree) definitely the best lecturer I've had so far - he's so incredibly enthusiastic about the course. For those of you coming up to Cambridge in October I'd advise you to go to his lectures come exam term, if he's still doing that course (the lecturers rotate round every three years, I believe) - he's awesome. :biggrin:

Fascinating stuff DFranklin - it's interesting to know how the Tripos has evolved over the years. :smile:

best uni in world for pure maths

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