x Turn on thread page Beta
 You are Here: Home >< Maths

# TSR's Best Mathematicians? watch

• View Poll Results: Best Mathmo?
47.21%
10.15%
21.83%
7.61%
6.60%
27.92%
22.84%
8.63%
6.60%
4.57%
10.15%
Unbounded (Pre-uni)
24.37%
Farhan.Hanif93 (Pre-uni)
25.89%
Small123 (Pre-uni)
7.61%
JChoudhry (Pre-uni)
9.14%
Goldfishy (Pre-uni)
6.09%

1. (Original post by DFranklin)
I'd distinguish between 'learning by practice' and memorization.
I guess this is a fair point - I'd forgotten (at some level at least) that a formula booklet is available at A-level, largely because I never used it and I would still like to believe that for most people its benefit is marginal.

I was imagining a first year student faced with an exam question something along the lines of: "show that if a_n -> infinity and b_n -> L > 0 then a_n/b_n -> infinity".

(From an Oxford-centric viewpoint) this is not bookwork and a robotic 100% rote-learner would not be able to field an answer; it's hardly a particularly difficult sting-in-the-tail to a question either. So let's consider it a middle-part of the question, but the sort of thing that a student needs to be completing for any hope of a 2.1.

What experience and learning does the examinee need to bring to bear to get through this?

I would like to hope there is an au-fait-ness with the situation, that the student has, which is certainly not rote-learning but which I wouldn't want simply to classify as practised either. It's more than familiarity and I'd hope there wouldn't be a reaching for past memories of similar examples akin to this question but a mindset prepared for what needs to be done. Through practice, mental dots have been joined, and there should be an appreciation of what makes the question tick (an appreciation of why it's true) and some well-honed translation of these first instinctive ideas (which may well need tweaking) into well-quantified formal mathematics.

I don't think that's an unrealistic description of what's going through the head of a decent first year undergraduate in this situation, but even if the situation is routine I'm fairly reluctant to call this memorized or practised. It's certainly not practised the way making a hoop with a basketball is, there really is a whole new mindset to what even a first year undergraduate needs to appreciate and the BA has barely begun.
2. (Original post by gozatron)
What is the furthest anyone on TSR has been in the Olympiads?
If I recall correctly, Agrippa made it into the IMO squad (last 8 or so), but didn't make the actual team.
3. (Original post by gozatron)
What is the furthest anyone on TSR has been in the Olympiads?
Nerevar got a silver medal in the 2006 IMO.
4. I don't know about the older guys as my questions were too simple for them probably

I voted for Farhan.Hanif93 and JChoudry.

I would have also voted for Unbounded as he is an extremely cool guy but I didn't see him

I also failed to read the OP before voting
5. (Original post by Mr M)
You don't even have to have a GCSE in the subject you teach. If my Headteacher instructed me to teach Mandarin Chinese and Expressive Dance tomorrow, that's what I would be doing.
Gosh, that's pretty depressing. What's it like teaching in a high school? The 11-16 kids would drive me nuts, I really don't get on well with most kids in that age group (the ones who don't want to learn and spoil the class for the ones who do, ugh...) Teaching in a sixth form wouldn't be too bad I suppose as at least by that stage, kids are only taking a subject if they have at least a bit of vague interest in it.
6. (Original post by nuodai)
Solution
Let , so that , and complete the square on the LHS
I actually knew how to do that!
7. (Original post by Simba)
Gosh, that's pretty depressing. What's it like teaching in a high school? The 11-16 kids would drive me nuts, I really don't get on well with most kids in that age group (the ones who don't want to learn and spoil the class for the ones who do, ugh...) Teaching in a sixth form wouldn't be too bad I suppose as at least by that stage, kids are only taking a subject if they have at least a bit of vague interest in it.
I teach ages 13-19. Don't assume all sixth formers want to learn. Quite a few do GCSE resits because they are forced too and are not interested. Others are there because they have nothing better to do and to qualify for the Education Maintenance Allowance.
8. (Original post by RichE)
I was imagining a first year student faced with an exam question something along the lines of: "show that if a_n -> infinity and b_n -> L > 0 then a_n/b_n -> infinity".
I agree it's not bookwork, but you still need to know the definition of and . You see enough examples of people getting this wrong on TSR to know this is a high hurdle for many.

More generally, in any question, there's both knowledge expected and facility with the ideas. But at A-level, many are used to needing very little knowledge indeed. The fact that people can spend a day learning a module and still get an A-grade in it shows how little is needed.

If you have that mindset, then I would still argue the amount of stuff you need to learn at university really is a shock. In any event, it's quite different from A-level. In very simple terms, I did virtually no rote-learning at A-level (and then only a couple of things I tended to get wrong otherwise), whereas I learned lots of stuff by rote for the degree.

I don't think that's an unrealistic description of what's going through the head of a decent first year undergraduate in this situation, but even if the situation is routine I'm fairly reluctant to call this memorized or practised. It's certainly not practised the way making a hoop with a basketball is, there really is a whole new mindset to what even a first year undergraduate needs to appreciate and the BA has barely begun.
To be clear, I'm not saying there's not lots of *other* things you do beyond bookwork (though Littlewood seems to have disagreed - I would love to see the papers from that era). But without knowing the bookwork, you're not well placed to even attempt the rest of the question.

Also, the question you posted is reasonably minimal on the material needed. At somewhat the other end of the spectrum, here's a 2nd year question from Cambridge (would have been 1st year when I did IA):

What does it mean to say that a function f on an interval in R is uniformly continuous? Assuming the Bolzano–Weierstrass theorem, show that any continuous function on a ﬁnite closed interval is uniformly continuous.

Suppose that f is a continuous function on the real line, and that f(x) tends to ﬁnite limits as x → ±∞; show that f is uniformly continuous.

If f is a uniformly continuous function on R, show that f(x)/x is bounded as x → ±∞. If g is a continuous function on R for which g(x)/x → 0 as x → ±∞, determine whether g is necessarily uniformly continuous, giving proof or counterexample as appropriate.
So, in this case, you need to give a moderately detailed definition (and be clear on the difference between and ), then a proof that you pretty much have to know before you've started (*):

Then there's a couple of straightforward proofs to do 'cold', and an easy proof/counterexample conclusion.

Certainly when I did the Tripos, this is a very standard question format. And if you don't know the definition and proof that start the question, you're in trouble.

(*) At least when doing IA. By part IB, B-W proofs are perhaps a bit more routine. This is perhaps another part of the discussion: at A-level, a good student will probably have progressed to the point where rote-learning isn't particularly necessary. At degree level, a good student might be at the point where rote learning of the previous year isn't much needed, but I'd say it's more unusual to be familiar enough with the current year to not need it.
9. (Original post by DerBoy)
Ha, hello there! I'm afraid I cant contribute much to this thread, since I frequent mathlinks rather than here, i'm pretty sure all candidates are worthy ones

For olympiads, got into the kangaroo kind of boring and all, got certificate of something etc kind of boring really. Although I've improved significantly! Just solved IMO 1995 question 2, the inequality, but looking for another solution. I wouldn't say i was IMO standard yet but for example i solved questions 1 and 4 of this year's IMO. That's not to say i've mastered bmo2 or anything, although most bmo1 questions are actually pretty easy now. I've been so immersed in olympiad maths i haven't done any proper maths, so that's what i'm doing just now. e.g. Had even forgotten how to differentiate a week or so ago ; but i've now done adv higher differentiation.

i'd imagine you would have improved significantly as well! i recall our discussions back in the IMC thread, i was saying how i could only do geometry although maybe you haven't gone down the olympiad route, which i suppose is more sound in the long-term?
I still uberly suck at BMO !
10. (Original post by Small123)
I still uberly suck at BMO !
you still have plenty of time! you should be able to be bmo1 standard by this year's bmo (maybe with help), if not you still have another chance
11. one of my maths teachers got his degree from the open university. the other one was only slightly better. some good lines i remember:

" is called a line integral and is called a surface integral"

"you can't divide through by 2" (actual numbers may have been different)
12. No winner has been announced here? I guess everyone realised the silliness of this?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 23, 2010
Today on TSR

### Happy St Patrick's day!

How are you celebrating?

### Stay at sixth form or go to college?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE