What Are the Best Alternatives to Cambridge for Studying Mathematics?

[roger]

If Cambridge don't accept me, which universities would be second or third best for mathematics at undergraduate level?
Oxford or Bristol for example?

and why does it actually matter?

thanks
roger

 

[fasterthanjoao]

It really depends on what you're looking for from your degree. Why did you apply to Cambridge? Theres the obvious distinction factor some Universities bring, but that doesn't necessarily mean that their course will be best for you. League tables of Universities are, I suppose, a help if you're looking for a non-biased objective - still though, those observations take nothing on your personal interest in the course content.

If you're asking why does it matter, it might be best to sit back and think about what you actually want from your degree, see what places offer that then compare their content.

In saying that, the University you apply to matters for tonnes of reasons other than personal interest - better recognised institutions generally have more funding, so a better staff-student ratio, better facilities etc.

 

[cristo]

and why does it actually matter?

It depends what matters to you. If you go to any of the top ten universities then you'll get a good degree! It matters more, IMHO, that you enjoy your time at university. There are different "styles" of universities i.e. campus or city; there are some in large cities, and some in smaller cities. Go and visit a few universities and the cities that the universities are in-- that's how I decided where to go. One university campus just stood out more than the rest, and I've enjoyed my time here!

 

[mathwonk]

Unless you are a future star, and even if you are one, it matters very little what undergraduate svhool you go to for maths.

LET ME GIVE AN EXAMPLE. Have you ever heard of Reed College in Oregon? Maybe not. I just looked at theor math dept webpage and found thius guy:

Jerry Shurman. He got his PhD at Princeton, under Shimura. yet he teaches primarily undergrads at Reed.

He has writtena book updating Felix Klein's work on the icosahedron and solkving quintic equations.

There is hardly any likelihood at all that in 4 years you can learn all he has to teach you, and that does not count the other faculty members there.

Hyperventilating over what undergrad school you get into is onkly slightly differtent from people who try to find the kindergarten that will insure the highest likelihood of entrance into Harvard.

gom somewhere decent, do well. Then see what comes. It is niot where you get into, but WHAT YOU DO THERE that matters. (caps intended.)

bless you, young foolish person.

 

[roger]

Unless you are a future star, and even if you are one, it matters very little what undergraduate svhool you go to for maths.

LET ME GIVE AN EXAMPLE. Have you ever heard of Reed College in Oregon? Maybe not. I just looked at theor math dept webpage and found thius guy:

Jerry Shurman. He got his PhD at Princeton, under Shimura. yet he teaches primarily undergrads at Reed.

He has writtena book updating Felix Klein's work on the icosahedron and solkving quintic equations.

There is hardly any likelihood at all that in 4 years you can learn all he has to teach you, and that does not count the other faculty members there.

Hyperventilating over what undergrad school you get into is onkly slightly differtent from people who try to find the kindergarten that will insure the highest likelihood of entrance into Harvard.

gom somewhere decent, do well. Then see what comes. It is niot where you get into, but WHAT YOU DO THERE that matters. (caps intended.)

bless you, young foolish person.

So there's no actual benefit to being taught analysis by say Timothy Gowers (Fields Medal) than by anyone else?

 

[mathwonk]

forgive me, but unless you yourself are a future timothy gowers, and perhaps even then, no it probably means very little.

the time you want to be taught by tomothy gowers is in grad school, or even on a postdoctoral appointment.

but i suppose the reason you ask me twice the same question, is either you did not get it the first time, hence are not very bright, or you doubt me, hence think of yourself at least, as extremely wise beyond your years.

this is the last time i will answer it however.

 

[JasonRox]

Listen to mathwonk.

I just went to a decent school when I had the chance to go the much better school. (Money played a role.)

Of course, the courses aren't the best, but like he said, if you know what's going on and you have a future for yourself, then it doesn't matter. Just keep at it. Do work on the side and learn things on your own.

I think I'm getting more out of the school I'm at now then I would have anywhere else. I know great professors that will help direct me with anywhere I need to go, or simply talk to see that I got my ideas or the ideas straight. I got a position as a research assistant in which I probably wouldn't have got in a highly competitive school.

Personally, I see a future for myself. I do have a lot of catching up to do in some places, but I do put in my own work and that in itself is great. For those reasons, I think my current school is doing just fine although a lot of things do irritate me.

 

[J77]

Get into the university with the best reputation - if only for it to look good on your CV.

I did maths at Bristol - it's a nice place and still holds a reputation amongst UK unis. It's too late to choose Oxford now, is it not? (Or is it just too late for med/law. ps: I prefer Oxford to Cambridge as a place of study; from visiting and knowing people from both camps.)

Other places: Warwick, Manchester, Nottingham, Imperial... the list is pretty obvious.

(The above posts are more about the US system, where they chop and change between schools a lot.)

 

[JasonRox]

Get into the university with the best reputation - if only for it to look good on your CV.

I did maths at Bristol - it's a nice place and still holds a reputation amongst UK unis. It's too late to choose Oxford now, is it not? (Or is it just too late for med/law. ps: I prefer Oxford to Cambridge as a place of study; from visiting and knowing people from both camps.)

Other places: Warwick, Manchester, Nottingham, Imperial... the list is pretty obvious.

(The above posts are more about the US system, where they chop and change between schools a lot.)

I think mathwonk knows what he's talking about.

 

[J77]

I think mathwonk knows what he's talking about.

Sorry, do you know me?

mathwonk has some good advice but I don't know his experience in the UK system.

 

[JasonRox]

Sorry, do you know me?

mathwonk has some good advice but I don't know his experience in the UK system.

His experience as a mathematician speaks for itself.

 

[cristo]

Get into the university with the best reputation - if only for it to look good on your CV.

I did maths at Bristol - it's a nice place and still holds a reputation amongst UK unis. It's too late to choose Oxford now, is it not? (Or is it just too late for med/law. ps: I prefer Oxford to Cambridge as a place of study; from visiting and knowing people from both camps.)

Other places: Warwick, Manchester, Nottingham, Imperial... the list is pretty obvious.

(The above posts are more about the US system, where they chop and change between schools a lot.)

I think application dates have passed for all UK universities now (the end of january is normally the deadline) so I can only assume that the OP is looking to apply for the academic year 2008/09.

Also, I agree that, in the UK, one should look at attending one of the top 10, say, institutions (employers, for example, look at where the university is from, as well as the classification). It is a lot different to the US; firstly, we have less universities here! Secondly, it is almost unheard of that students do the first year or two, say, at one university, and then move to another.

 

[J77]

Also, I agree that, in the UK, one should look at attending one of the top 10, say, institutions (employers, for example, look at where the university is from, as well as the classification).

Exactly.

We don't want to be giving roger advice to go to the "Univeristy of Centrally West and In a Bit to the Right" because in the UK it does matter.

Not only when potential industrial employers look at CVs but a lot of academics over here on the continent will know the reputation of the big-name UK unis and, perhaps unwittingly, base a reputation on that.

 

[JasonRox]

Exactly.

We don't want to be giving roger advice to go to the "Univeristy of Centrally West and In a Bit to the Right" because in the UK it does matter.

Not only when potential industrial employers look at CVs but a lot of academics over here on the continent will know the reputation of the big-name UK unis and, perhaps unwittingly, base a reputation on that.

Don't you understand what you're saying.

mathwonk is speaking of exceptional students. For them, it makes no difference literally. It can help, but if you have a bright future and great potential, then you will go as far as you'd like as long as you use that potential.

So, you're saying, if you're anything like Andrew Wiles or any other well-known mathematicians, then you will go nowhere unless you go to one of the top universities.

 

[J77]

So, you're saying, if you're anything like Andrew Wiles or any other well-known mathematicians, then you will go nowhere unless you go to one of the top universities.

You'd have a much easier time of it if you did go to a top uni - not only in the quality of teaching but also through the networking opportunities.

<google's andrew wiles... e2a: he did Oxford and Cambridge, so that's a bad example... >

 

[JasonRox]

You'd have a much easier time of it if you did go to a top uni - not only in the quality of teaching but also through the networking opportunities.

<google's andrew wiles... e2a: he did Oxford and Cambridge, so that's a bad example... >

Not really. E-mail him and ask him what he things about this.

He is no doubt grateful to his professors, but I'm sure he knows more than enough people who got up the ranks without going to Oxford or Cambridge.

 

[leon1127]

In many foreign country, reputation of university plays the fundamental role when you join the society (saying this as a foreigner who studies in US). As a student who has experience in good school, bad school, US system, UK system, traditional society and US society which really stands alone.
Of course the most important is THE LAST SCHOOL YOU WILL ATTEND before you join the workforce. However for many people they don't know what is the highest degree they shall get. Thus it is better to get into the best school you can go. In addition, my professor who had the statistic told me that 29/30 NSF scholarship recipent came from a famous school in his son's application year. Thus you will be given a lot more chances if you can attend famous school.
Technically, undergraduate topics are fairly standard. You can't learn too much less if you attend a normal school. On the other hand, the attitude of particular school has major infleunt to learn. For example, if everyone in your topology class trying to understand the proof of poincares' conjecture, i suppose you will more likely to look at the proof also. In the opposite, if everyone is playing sodoku in your class (like the university that i am attending), you are less likely to focus in academia.
To answer the original question in a practical sense, apply every school you can and wish yourself luck. But isn't it a little bit too late for this year?

 

[JasonRox]

In many foreign country, reputation of university plays the fundamental role when you join the society (saying this as a foreigner who studies in US). As a student who has experience in good school, bad school, US system, UK system, traditional society and US society which really stands alone.
Of course the most important is THE LAST SCHOOL YOU WILL ATTEND before you join the workforce. However for many people they don't know what is the highest degree they shall get. Thus it is better to get into the best school you can go. In addition, my professor who had the statistic told me that 29/30 NSF scholarship recipent came from a famous school in his son's application year. Thus you will be given a lot more chances if you can attend famous school.
Technically, undergraduate topics are fairly standard. You can't learn too much less if you attend a normal school. On the other hand, the attitude of particular school has major infleunt to learn. For example, if everyone in your topology class trying to understand the proof of poincares' conjecture, i suppose you will more likely to look at the proof also. In the opposite, if everyone is playing sodoku in your class (like the university that i am attending), you are less likely to focus in academia.
To answer the original question in a practical sense, apply every school you can and wish yourself luck. But isn't it a little bit too late for this year?

I'm pretty sure it's too late here (Canada) as well, as it is the US.

PS. If my whole class was trying to understand the recent proof to Poincare's conjecture, than I'd be wondering if this was planet Earth!

You do make a good point though.

 

[leon1127]

You know what I am wishing after all these years in undergraduate? I wish I went to a school with a bigger mathematical collections... Then I will learn much more than I know now.

 

[JasonRox]

You know what I am wishing after all these years in undergraduate? I wish I went to a school with a bigger mathematical collections... Then I will learn much more than I know now.

How small is the collection right now?

 

[^_^physicist]

Look for a college that will be as flexible or as stuctured as you want it to be. For instance, at my university, maintaining membership with the honors college allows me to waive a large number of required classes. Additionally, the university I attend does not pour funds into the math department, so the department is made up of about 15 professors/graduate students. This allows me to get to know my professors and as a result be able to waive pre-requists for courses, allowing me to design my minor (math) and my major (physics...we have about 12 full time professors...if that) pretty much however I want to, so long as it fits within particular guidelines.

Granted I am expected to take a set of required courses, and these almost never get waived; however, prerequists for many courses (almost all of the courses) are negociable. And this works great for someone like myself.

My friends on the other hand, go to universities that have larger departments, and nearly no flexiblity. For some of them, they love having an order and a path already constucted, as it keeps them focused and sometimes gives them more "free-time" for research and other activies.

You just have to play it by ear.

Then again you are talking UK, so...I am not quite sure how the system works out. Prestiege is great, but it only helps if that is really what you are looking for. If for instance you want some flexiblity, and the ablity to round yourself for future obligations, a school that is not quite as "important" could work out just fine.

 

[AlphaNumeric]

So there's no actual benefit to being taught analysis by say Timothy Gowers (Fields Medal) than by anyone else?

I didn't have Gowers for analysis in my first year, but for 'Numbers and Sets'. Though I didn't get most of it (proper pure maths was a bit of a shock to the system for me!), he was an excellent lecturer, very lively and explained things very well.

However, do not expect all Cambridge lectures to be the same. Gowers is well known and well liked. Some Cambridge lecturers are well known for the opposite reason. Terrible organisation, illegible handwriting and/or accent, closed off, unable to answer questions or explain things properly. While some people are excellent solo mathematicians, mathematicans are not well known for their communications skills (really doing myself a favour here aren't I? )

Failing to get into Cambridge would hardly be the end of a maths career before it started. I know of a few people who hated Cambridge, dropped out, went elsewhere and their enjoyment and results shot up. Every university will have a few brilliant lecturers you'll remember forever, a lot of decent ones and a few who'll make you wonder how they got their jobs. They will not always be correlated with intelligence.

If you're applying to Cambridge, you'll be aiming top 10 unis for all your 6 UCAS choices. Whichever one you end up in will give you an excellent education and will still allow you the possibility of doing a PhD pretty much anywhere you want if you're good enough. Also, remember there's more to uni than just the reputation of the department of your preferred subject. Cambridge is a small town and if you like 'big nights out' or anything other than student nights, it's not that great for night life. Plenty of nice (if not a little expensive) pubs though and in the summer it's wonderful. It's certainly 'differerent' to more typical unis in the UK. You end up thinking nothing of people walking around in suits and gowns

 

[mathwonk]

As to the size of the maths collection, that is irrelevant. if you merely learn thoroughly the contents of courant's calculus, both volumes, and artin's OR van der waerdens OR jacobsons algebra, you will already know infinitely more than the average applicant to graduate school in maths.

note the word "thoroughly".

This is literally true in US, and I welcome knowldgeable opinions about the UK.

Of course I have seen many lists given here of hundreds of topics supposedly learned by undergrads/ Thia is a joke. most professional mathematicians do not pretend to know all those topics.

e.g. I myself know very little well after over 40 years study, perhaps basic calculus and basic algebra, and some tpoics in riemann surfaces and algebraic curves, and their moduli, and moduli of abelian varieties. note i do not feel expert in topology at all, even though on this forum i am considered by some a topology expert. that is apparently because there are no such genuine experts here.

of course many people know far more. it depends on your level of dedication. i knew much more when i came out of central washington state college in 1974 than when i came out of harvard in 1965, because at central i studied.

it is not the level of the university but the level you yourself achieve that matters. And that is universal.

people who advise you to go to university such and so to piggyback on their reputation, are insulting your ability to show your own mettle. This is ironic in a subject famous for distinguishing between a statement and its converse. you are less likely to succeed by going to a great university than you are to be invited to a great university because you are a success.

 

[roger]

My results aren't good so far. So how do I know if math is for me?
I enjoy it and have a desire to learn, but that might not be enough.

 

[mathwonk]

here are a few famous outstanding mathematicians and their undergrad schools:

deRham-Lausanne;
Nathan Jacobson-Alabama;
Zariski-Kiev (in philosophy, not accepted in the schools of maths);
Harish Chandra-Allahabad;
Margulin - Moscow;
Hironaka - Kyoto;
Caratheodory - Belgian Military School;
A.N.Whitehead - Trinity College;
Julian Schwinger - CCNY;
L.E.Dickson - U. Texas;
Tarski - Warsaw;
Raoul Bott - McGill;
Lars Ahlfors (first fields medal) - Helsinki;
W.V.O. Quine - Oberlin College;
Marston Morse - Colby College;
Steenrod - U of Miami at Oxford;
R. Brauer - U. Berlin;
Irving Kaplansky - Toronto.
and grothendieck, and perhaps lefschtetz, spent some quality research time in kansas,

enough... get it?

 

[mathwonk]

roger, what is your goal? to do somethiong you enjoy, maybe not to excel but to strive as well as you can? inspire others, and learn?

or to poick the thing you are best at compared to others, earn as much money as possible, and retire early? ask your respected elders for advice, your dad, your professors, your older brother, hang in there.

the love counts for a lot, but know going in you will make material sacrifices.

 

[roger]

roger, what is your goal? to do somethiong you enjoy, maybe not to excel but to strive as well as you can? inspire others, and learn?

or to poick the thing you are best at compared to others, earn as much money as possible, and retire early? ask your respected elders for advice, your dad, your professors, your older brother, hang in there.

the love counts for a lot, but know going in you will make material sacrifices.

My goal is to discover new things which is what math professors do isn't it?
It's not just for fun or for money.

I don't know any elders actually.

 

[JasonRox]

My goal is to discover new things which is what math professors do isn't it?
It's not just for fun or for money.

I don't know any elders actually.

I would say professors just explore new things and search for new things. They don't always necessarily discover new things, but that is the intention or big goal in mind for most.

 

[roger]

Roy, could you please try to explain the differences between say research math and degree math?

 

[leon1127]

As to the size of the maths collection, that is irrelevant.

I am not speaking of some specific book. I am saying that they are lacking some very classical book. For instance, they don't even have reprinted work of Atiyah (they don't have vol. 2-4 while they have 1 & 5.) while author is referring me to Atiyah's work for detail discussion in Clifford algebras. Another example is that they don't have the calculus of variation by Carathedory. I suppose this should be a classic book every university's library should have. It bothers me more than few times when my library is lacking some classic text.
Luckily, it is getting better with my suggestion of some classical text.

 

[mathwonk]

you are missing my point i think. what they do have is far more than you can possibly master, so make the most of that.

 

[mathwonk]

in degree math as i know it, one is solving problems whose solution is already known to someone else. this makes it not so scary. in research math the problam has never been solved usually, so one takes more of a chance since it may be years of fruitless work, or even lie far beyond ones powers. so trying it takes more guts.

 

[JasonRox]

in degree math as i know it, one is solving problems whose solution is already known to someone else. this makes it not so scary. in research math the problam has never been solved usually, so one takes more of a chance since it may be years of fruitless work, or even lie far beyond ones powers. so trying it takes more guts.

But sometimes there is no problem as well, so you have to create one.

 

[mathwonk]

Jason makes a good point. there is somethig called "problem finding" as opposed to "problem solving", but it is so little taught in school that few of us know much about it.

Years ago, before obtaining my degree, I read about the remark a famous French mathematician made to a student asking for a problem: "how long have you been taking our courses here?...And in all that time have you not noticed anything needing further investigation?"

I realized I had never asked this question of myself.

 

[JasonRox]

"how long have you been taking our courses here?...And in all that time have you not noticed anything needing further investigation?"

Like everything!

Nice quote though.