Math Is Fun Forum

The points could be UCAS points - but I didn't think that UCAS points were awarded for GCSE - perhaps this is a new addition - I am not sure about those points, none of my GCSE results came with points.

I think whether you can take a subject at A-level without having a GCSE depends upon your school - my school would have allowed it, but it's obviously very very difficult for you to do so.

I think that those are incredible results and you should be very proud. You have done very well and shouldn't worry about what courses you take next year - with results like that you can definitely do well in biology - remember that you yourself said you could have done better were it not for your coursework. Anyway, universities are unlikely to make you an offer based on more than three subjects - possibly four, but not five or six, so you can afford to drop to a B in biology. Now, I've never heard of universities specifying three subjects - you may get an offer excluding one subject, or specifying an A/A* in a specific subject (e.g. maths for maths, or biology for medicine) but I can't see why any university would offer a mathematician or a physicist an offer requiring an A in biology. My friend was offered ABB with an A in geography to study geography with Chinese studies. He got AAB with a B in geography and missed the A by one mark. He did fail his offer, but he got a remark and made it. So yes, sometimes you will get a rigid offer which is subject specific - but I can't see why biology would be a problem for you.

I know a lot of people who missed their grades for Cambridge - including one who failed his STEP offer and one who missed his grades for classics, but they still got in. There are a lot of horror-stories, maths is a difficult and competitive course - as is physics - and nobody's saying that it will be easy; but I really do think that you're worrying unnecessarily - if you're seriously considering doing six A-levels, then that is really quite something and I think that you'll be fine. The highest offer I've heard of is 2 A*s and 2 As and that was this very competitive year - the last year of £3, 000 tuition fees, when lots of people will want to be going this year, instead of taking a gap year.

I think both of our esteemed bobs have given great advice. The best thing you can do is just enjoy your maths for yourself and if people think you're getting dumber - what does it matter? They will be wrong, of course, but even if they're not, does it really matter if you're still enjoying the maths that you're doing? The thing is, when we are younger our brains are designed for soaking up information - I'm not a neuroscientist, so I don't know, maybe learning does become harder as we get older, maybe we do forget things - but we're always learning. Maths is an incredibly broad discipline - and it's always growing. We can never know all of the maths that there is to know and we can always learn new maths and build on the old maths we've learned. I don't think we peak at 21, I mean, you'd have to know an awful lot of maths to be at your best then - surely more than anyone could learn in 21 years. And hey, I can't remember during which years Oliver Cromwell was Lord Protector of England and I learned that, what, five or six years ago, but it doesn't matter, because I can remember de Moivre's theorem. I think we tend to forget what we don't use, whether we're 21 or 101, but we can still pick it up again if we have to and keep going with what we can remember.

I think the bobs are right though - as I said at the beginning. Some people used to consider me a bit of a maths wiz in my class, but I was never considered the acid test for whether a problem was doable, but either way, I mean, I do the maths I do because I enjoy it and if people think I'm really good, then that's awfully nice of them to think so and say so - although it's not particularly true - but whether they do or they don't - and if they tell me I'm rubbish - it's not gonna stop me doing and enjoying the maths I can do. And I think that's the attitude to take to your studies. I have self-taught a fair bit - and clearly so have you. It can be done, but studying maths at school and university is a very useful way to learn the maths - so see it as a chance to learn more maths and to have fun, rather than worrying about how well, or not, you're doing. That's my advice anyway.

The best suggestion I've heard so far, though,is bob bundy's that you become a member - I think we'd all be richer for having you.

Okay, thanks everyone

On a related note, if you can express the idea that:

As:

How would you express:

Thanks

I am quite sure that if they had had your background these brilliant people would not have struggled, but that is very much the point - you are not below average, very few people have had your background, you are far above what one would really expect.

I'm sorry, I know very little Galois theory, I merely know of it, I was told that it was something which is well worth learning, though. It seems like quite a good resource, though, I may have to have a proper read of it soon. I'd really like to finish FP3 first, though

He is the sort to just take something up and run with it. He just seemed to do it because it seemed like an interesting thing to do - I wouldn't advise it as such, but I don't think they'll consider you to be bs-ing unless you go about your interview in the wrong way.

Why are these unlikely goals? People do it - why can't you? Why do you think that people will be better than you? You are clearly a talented mathematician, with knowledge far beyond what is expected. Think about STEP - all of the prerequisites are on C1-C4, I believe, certainly most of them - I believe. I don't think it's about breadth, it's about talent, and understanding of mathematics. You can go very far, but you have to have some faith in yourself. I don't want to sound like a motivational speaker, or a life coach or something - they tend to annoy me anyway, but:

'If you think you are beaten, you are;
If you think you dare not, you don't.
If you'd like to win, but think you can't
It's almost a cinch you won't.

If you think you'll lose, you've lost.
For out in the world we find
Success begins with a fellow's will:
It's all in his state of mind.

If you think you're outclassed, you are:
You've got to think high to rise,
You've got to be sure of yourself before
You'll ever win that prize.

Life's battles don't always go
To the stronger or faster man,
But sooner or later the man who wins
Is the one who thinks he can.'

Anyway, yes i^i is very straightforward - but quite nice, I enjoyed doing it myself. Interesting that it should be real, don't you think? But the point wasn't that it was hard, but that it was just an interesting thing for him to do - and it's important to show that you care and that you are special, perhaps more so than just some letters.

I believe that you are indeed both right. I was looking at the graph of y = sinh x, though, which, for large, negative values of x, approaches the graph of:

As we can see, because:

Now, my textbook wrote:

But I really didn't like this way of putting it and I quite like limits and asymptotic analysis and such areas and so I thought I'd try to make use of them, but we don't cover them in much detail and I have limited (poor pun) experience of using minus infinity, so I just wanted to check that this was a valid way of expressing the idea.

The scripts themselves will not be marked in any other way, I mean, the person marking wouldn't know nor care. There's a bit of a conspiracy theory that in the case of subjects where the January paper is only for resits, the paper itself may be more difficult (although I highly doubt that) but since this isn't the case for maths it doesn't matter at all. I'm not sure what year eleven is (I go to a school with very odd naming conventions, and we had fifth form, lower sixth and upper sixth (which is slightly more normal than the names for previous years)) but am I right in thinking that that's GCSE year. Even if it's AS year, doing the resit will probably not hold you back, because you seem to be accelerated in some way. Nevertheless, some universities don't look kindly on resits, I have to say, in fact I think there are some which won't accept A2 resits. I don't know about AS's though. I'm not really a higher education adviser, I think talking it over with that person is your best option, but I think, if you want to apply for maths at Cambridge, there are more important things than module scores. First of all, you definitely need to do double maths and secondly, STEP. You may or may not know anything about STEP, but it is very very hard, and a typical maths offer will be a 1, 1 in STEP II and III. This is incredibly hard. I know two people at my school last year - one of whom had four A*s - who failed their offer, getting a 2 in STEP III. This is where I would recommend you invest your efforts, especially as this is the real distinguisher.

Hello, zetafunc, I resat that paper myself. I have to be honest with you, I did score in the nineties - although I'd be interested to see what my mistake(s) was/were - but in my C3 and C4 modules, I was disappointed, having expected to score significantly higher. It doesn't matter to me, I am off to my first choice university next month, so all is well, but I hope that I can offer a constructive take on the situation. The first thing that I would say is that marks may be awarded specifically for correct working. I knew of somebody who happened, by chance, to get the right answer to a question, but his method was wrong. I believe that he had used an equation where a constant speed is assumed and the speed was not so. It was something similar to this anyway and - rightly, you might say - he was not awarded any marks. Is it possible that your methods were not correct? It can be difficult to remember exactly how you did something even straight after an exam. Are you also sure that you rounded correctly? Marks may be awarded for correct solution only, and you may have been a decimal place out in a question, or two. I tend to be fairly philosophical with my exam results, I am disappointed at my own performance in maths, but I am happy to accept that - in the stress of it all - I probably got the wrong end of the stick, or made a mistake in the working. What I've said above is to illustrate the fact that there can be myriad ways in which marks can go astray, especially in an exam situation and so I would advise that you ordered a photocopy and double-checked first. I seem to remember that this is possible, although if there is a problem with timing, you might have to get a remark, without checking first. Marks can go down, though, and whilst examiners can obviously make mistakes, they are moderated and maths papers can be marked very formulaically, so you're unlikely to see a large variation, as you might in an essay subject, where it is a judgement call.

With maths, of course, your results will average out, there are other modules and this is good and bad. Obviously, the higher the module marks, the better your position, so a remark would be advisable in that way. On the other hand, however, one module is not the be-all-and-end-all, a few marks here and there isn't the end of the world, especially as this is an applied module.

My advice, then, is to remember that in examinations, marks can be lost unexpectedly, which is a great shame and can obscure the real talent. As a result, I would personally order the photocopy of the script. If this is not an option, however, you can get the remark, it's not hugely expensive, but I would certainly not expect anything to come of having mine remarked. I wouldn't wish to say that the same will be true in your case, but I don't think I'd do it myself.

P.S. I don't think it is free to sit any examination, including re-sits. However, your school may be prepared to pay for you.

Nono I think you're right, I'm just having difficulty explaining the jump from:

It seems to make intuitive sense in my head, that as n tends to infinity that is the integral which you will end up with. The thing is though, at my school you could do double or single maths. I did single maths which means I didn't cover what is known as further pure, which has a lot of interesting pure maths on it which I wanted to cover. So I got a textbook and have spent my recent holidays on the first two of three modules. My method has been to write myself my own 'sort-of textbook', which is more a sort of extended set of notes with various tangents and exercises and what I wanted to do was to explain this derivation. The thing is, it makes some sense in my head, but I certainly can't write-up an explanation without sort of waving my hands and saying, well it looks about right.

I couldn't agree more