Maths Paper (Remarking Advice)...

Au101 · 2011-08-19 12:04:56

I didn't resit C3 and C4 because I took them this June and I made my offer so there is no need lol

I was not interviewed by SOAS, so unfortunately I can't help you, but general interview technique is what would matter I think. Just relax, talk through your reasoning - especially at Cambridge, they're looking for people who think in the right way and have interesting opinions. Clearly you are somebody who is interested in maths - so let that come across, show your enthusiasm, engage in a discussion, like you would with the people on here. It's almost something you can look forward to - if it didn't mean so much to you, I think that if you do it right, then it's something that you would otherwise rather enjoy.

It may be optional, but I know a lot of people who filled this form out, so I assumed that it was compulsory, at least for certain subjects. Perhaps I am wrong about this, but I can only assume that it will help.

Well, this isn't the place for a political rant, but I very strongly disagree with the government's policy here, but let's not get drawn into politics. I have a great interest in the subject, but there's a time and a place lol . However, you will be aware that you do not have to start paying this money back until you can afford to and a good degree should help you to achieve a reasonable salary. Honestly, though, I know it's easier said than done, but the reality is that the money isn't what matters. 'Find a job you love and you'll never have to work a day in your life' in the wise words of Confucius, unless I'm very much mistaken. The money doesn't have to be paid back immediately, so I think you should follow your dreams. You seem to be somebody with a passion for mathematics - follow it through, or you'll regret it. What difference does a few million make on your death bed - but if you can look back at a life like that of Erdős - look back on everything you've done, the contributions you've made, pursuing what you love, then I would say you are far better off.

zetafunc. · 2011-08-19 12:32:52

Au101 wrote:

I didn't resit C3 and C4 because I took them this June and I made my offer so there is no need lol
I was not interviewed by SOAS, so unfortunately I can't help you, but general interview technique is what would matter I think. Just relax, talk through your reasoning - especially at Cambridge, they're looking for people who think in the right way and have interesting opinions. Clearly you are somebody who is interested in maths - so let that come across, show your enthusiasm, engage in a discussion, like you would with the people on here. It's almost something you can look forward to - if it didn't mean so much to you, I think that if you do it right, then it's something that you would otherwise rather enjoy.
It may be optional, but I know a lot of people who filled this form out, so I assumed that it was compulsory, at least for certain subjects. Perhaps I am wrong about this, but I can only assume that it will help.
Well, this isn't the place for a political rant, but I very strongly disagree with the government's policy here, but let's not get drawn into politics. I have a great interest in the subject, but there's a time and a place lol . However, you will be aware that you do not have to start paying this money back until you can afford to and a good degree should help you to achieve a reasonable salary. Honestly, though, I know it's easier said than done, but the reality is that the money isn't what matters. 'Find a job you love and you'll never have to work a day in your life' in the wise words of Confucius, unless I'm very much mistaken. The money doesn't have to be paid back immediately, so I think you should follow your dreams. You seem to be somebody with a passion for mathematics - follow it through, or you'll regret it. What difference does a few million make on your death bed - but if you can look back at a life like that of Erdős - look back on everything you've done, the contributions you've made, pursuing what you love, then I would say you are far better off.

I think I can show my enthusiasm - I don't want them to think I'm bull*****ing myself through the interview by being overly enthusiastic though. I have things to talk about if they asked me in the interview (e.g. research I've done independently). However the weird questions they supposedly ask during the interview scare me; I've heard easy ones like differentiating e^e^e^e^e^e^e^x (use chain rule multiple times) and really awkward ones like deriving the equations for SHM using a bowl with a malteser inside as a model. My parents say to do what I enjoy but that I might not be able to. I would love it if I could go on and do maths and physics for the rest of my life, but it's not free. I understand that I can start paying it back when I'm able to, but when thinking about jobs it scares me. I heard of someone on PF talk about having a PhD in astrophysics but having to work in Sainsbury's for almost a year because he couldn't get a job, or something. I don't want to put so much effort in to go and sort shelves for prolonged periods of time... my parents always say to do what you love but in reality I may not be able to afford to do so.

Au101 · 2011-08-19 12:47:18

Hmmm, well I'm pleased to see that you're not naïve, but there are a lot of horror stories out there which - in reality, in the general case, just aren't really that bad. I don't think that they will think that you are jut bs-ing your interview, if you just behave naturally, like you would if you were discussing maths with a mathematician - which is what you will be doing at the end of the day. I have a friend who - during his physics interview - decided that since he had nothing else to ask at the end of his interview at Imperial, I think, although it may have been another, just derived i^i for his interviewer.

Oxbridge interviews are famously hard, that's the point, but if you are genuinely interested - which I know you are - then it should be right up your street. I assume you know the answer to that derivative, you would just have to talk your way through it. Anyway, even if you get it wrong - they're testing how you think - if you reason through it, you can still impress.

No, nothing is free, I'm afraid, but I can't urge you enough to chase your dream. Even if you have to work hard for it, if you love it, then you really will reap the rewards. Why couldn't you just continue at university - you could lecture? Do you have any ideas about what you'd like to do in future? It's not necessarily an easy life, but it's far more enjoyable and when you go to meet your maker you can go with your head held high - proud of a life well-lived doing what you love and believe in. That's gotta be better, hasn't it?

zetafunc. · 2011-08-19 13:00:39

You say that he derived i^i? How exactly did this come about? That seems a little random...

I suppose it will be better but sometimes I wonder if this is the right way. I could lecture; I have tutored people before and taught sample maths, physics and biology classes to younger kids (the maths was introducting limits to a year 10 class, biology was introducing oocyte cell differentiation to year 8s, physics was signal processing to year 11). That could be the road for me, but I'd like to do my own research too. I just don't know if they're likely goals. I just have the feeling that most applicants will be better than me in practically every department for most of my university choices, and it seems as though my ambitions aren't realistic.

zetafunc. · 2011-08-19 13:03:34

I just derived i^i which you mentioned, this doesn't seem special... it's literally only 2, maybe 3 steps... are you sure this wasn't part of another problem? Sorry if it's a silly enquiry

Au101 · 2011-08-19 13:16:38

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.

zetafunc. · 2011-08-19 13:28:16

Oh okay, sorry if I sounded insulting in any way, it's just that it seems like an odd thing to show your interviewer at the end of the interview... I agree that it is interesting that it is real.

Thank you for the poem and I agree with it. I think I'm about an average mathematician, maybe less so for my age - I want to work as hard as I can, always give 100% to try and match the level of my competition. Even though I know that a lot of people out there are much better I still want to try. Plus, there are places I wanted to be a few years ago at 16, and I'm not there yet. For example, when I was 14 I set the goal that I would understand basic Galois theory at 16-17 and I didn't reach that goal. So, I'm disappointed with myself and will try harder next time to focus and reach that goal.

I have seen people do incredible things that I could only dream to do. I have seen many lecturers and I don't think I could match their ability or come close. I can try though.

Au101 · 2011-08-19 13:39:06

No, you didn't sound insulting at all I just hoped to make the point clear.

Yes, it's a rather famous poem. I can't remember who it was by, or I would have given it an author - I once saw it signed anon, but I read that it has been attributed to Author Napoleon Hill, so let's go with that.

Basic Galois theory is said to be very beautiful and, I'm sure, once you see how it's done, it's not that bad, but it's quite a target - it is not easy to self-teach something like that, so early on.

Well, it's good to be focused on your goals, but it's better to enjoy the process, the important thing is to enjoy the maths you're doing and enjoy the life you have whilst you still have it. It is unwise to become too focused on targets and forget to enjoy the process of getting there, so, if you've had a good time reading about it, don't worry if you haven't quite got it yet, because you will do.

I don't know you at all and so I can hardly judge, but you seem to have an incredible knowledge. There are good people, bright people, people who are, as we speak, preparing to be doctors in my year who have struggled their way through C3 - and when I say that, I mean really have found it difficult and that's not a sleight on them at all.

Mathematics is a beautiful subject and people can do amazing things with it, but they have all had to start somewhere, they have all had to learn their stuff to begin with - they are experienced mathematicians - who have learned from good people and if you follow your dream then you can too. If you do not, you will always be wondering what if.

bobbym · 2011-08-19 16:49:11

Hi All;

If you are the zetafunc that was working with me on the Fourier transform then you have nothing to worry about. Grades, schmades! Keep on trying!

There was a 98 year old guy who was determined to run in the NYC marathon. The whole 26 miles. The race started and he ran 13 feet and fell over from exhaustion. But do not worry, he is going to try again next year.

zetafunc. · 2011-08-19 23:32:24

Au101 wrote:

No, you didn't sound insulting at all I just hoped to make the point clear.
Yes, it's a rather famous poem. I can't remember who it was by, or I would have given it an author - I once saw it signed anon, but I read that it has been attributed to Author Napoleon Hill, so let's go with that.
Basic Galois theory is said to be very beautiful and, I'm sure, once you see how it's done, it's not that bad, but it's quite a target - it is not easy to self-teach something like that, so early on.
Well, it's good to be focused on your goals, but it's better to enjoy the process, the important thing is to enjoy the maths you're doing and enjoy the life you have whilst you still have it. It is unwise to become too focused on targets and forget to enjoy the process of getting there, so, if you've had a good time reading about it, don't worry if you haven't quite got it yet, because you will do.
I don't know you at all and so I can hardly judge, but you seem to have an incredible knowledge. There are good people, bright people, people who are, as we speak, preparing to be doctors in my year who have struggled their way through C3 - and when I say that, I mean really have found it difficult and that's not a sleight on them at all.
Mathematics is a beautiful subject and people can do amazing things with it, but they have all had to start somewhere, they have all had to learn their stuff to begin with - they are experienced mathematicians - who have learned from good people and if you follow your dream then you can too. If you do not, you will always be wondering what if.

I found this article on Galois theory (remove spaces); h t t p : / / n r i c h . m a t h s . o r g / 1 4 2 2

I don't know if it's very good, though. Could you tell me how you learned Galois theory? Did you use a website, a specific book?

Making targets for myself in the long-term doesn't usually work for me in most cases, but I sometimes feel like I have to catch up to something; e.g. at 17, I should be at such-and-such level, or something. I hope I will understand Galois theory in the near future.

To be fair on those who may be struggling their way through C3 - I may have struggled with it if I hadn't had the background I previously had. Just before my 14th birthday I started learning concepts like the chain rule, product rule, quotient rule, limits, cusps, related rates, etc. which is why I find a few areas of A-level maths a breeze, because I've already experienced a lot of it. I consider myself to be quite lucky, because I know chunks of other units, such as FP1-3, without having studied them. Maybe if they had the background I had they wouldn't struggle...

Sometimes I just wonder if this really is my dream though. When I was 15 I hated maths because of my teacher. As a result, I averaged only 80-85% in GCSE maths papers and a few times people got higher than me, then I had to deal with the teacher saying that she thought I was special and I haven't proven it, etc. and I just thought 'screw it'. I took a long break from mathematics. In many ways I think it's good that I had that experience because hating mathematics led me to develop a loving for physics, too, which I never thought existed.

One thing that also motivates me a little is to know that in a couple of years time, I can look back on a piece of mathematics that seemed alien to me and understand it wholly. I like that feeling because it shows that I am improving and my mind is not stagnant, though it feels like that a lot.

zetafunc. · 2011-08-19 23:37:16

bobbym wrote:

Hi All;
If you are the zetafunc that was working with me on the Fourier transform then you have nothing to worry about. Grades, schmades! Keep on trying!
There was a 98 year old guy who was determined to run in the NYC marathon. The whole 26 miles. The race started and he ran 13 feet and fell over from exhaustion. But do not worry, he is going to try again next year.

The thing that troubles me however is that I want to have a good mathematical education... I'm a little ignorant about the content of university courses, but I don't want to feel like I'm at a disadvantage if I have a course where I'm not taught as much as someone in a course from Cambridge has been taught. No one can stop me from learning what I want to learn completely, but they can do things like bog me down with assignments, where over a four-year span I may not be able to learn the mathematics that was in that other course, or wherever. It's sort of like catching up to an 'average', I'm not sure how to describe it. I want to be a mathematician who can still communicate with and understand someone with a degree from Oxbridge, or another top university.

That was a nice story... I hope that man is okay!

zetafunc. · 2011-08-20 02:45:23

Also, do you have any tips for exam stress? I have heard that some people try hypnosis, but that doesn't work for me... I get it terribly bad before most exams; nausea (leading to vomiting in some cases), inability to concentrate due to the exam due to nerves, sweating, general ill feelings. I have sat exams with about 500 different people and I never saw any of them have to use the toilet repeatedly during the exam to wash their face in water, or ask for a sickbag, etc. so I was wondering if you had any advice on coping with that. This is a huge pain because it eats into my exam time.

bobbym · 2011-08-20 03:00:21

I think you should learn to relax a bit more. Pressure affects everybody differently. A couple of deep breaths helps a lot of people.

Do not worry about failure, lots of great mathematicians had little or no schooling. I am not saying pass up an oppurtunity, I am saying that if you are good and have the desire nothing will stop you.

Au101 · 2011-08-20 04:28:58

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

gAr · 2011-08-20 04:30:00

Hi zetafunc.,

It's because of high expectations.
I have seen some clever ones experiencing the way you do.
Try to stop worrying about the outcomes, everything will be fine!

zetafunc. · 2011-08-20 06:26:32

Thanks for your replies.

That's the trouble; I can't seem to relax... I try to take deep breaths but outside the exam hall I just feel like I'm going to throw up. That C3 exam, including the biology one, were mental battles for me. I had to use the toilet to wash water on my face and stop myself from throwing up knowing that my time was running out. I was lucky to get 92, very lucky, in my condition. This happens in too many exams and unfortunately it's not an excuse; you can't get a doctor's note for exam stress (at least I don't think you can). I think it is partly due to high expectations, as gAr mentioned... I just hate thinking about blowing my chances, or people saying that I underachieved or did poorly.

I suppose in terms of failure, I mean go through incredibly long bouts of mathematical stagnancy, to the point where there is too much I forget and make it a monumental task to get back into the rhythm of again. Or to just reach a ceiling in my mathematical career, where it just gets 'too hard'. I have heard that this has happened to some people, but I don't know this with certainty.

Au101, was your exam board Edexcel?

bobbym · 2011-08-20 06:45:28

Hi;

Or to just reach a ceiling in my mathematical career, where it just gets 'too hard'.

Yea, that will happen. Ever heard of "island hopping?" Strategy used by Macarthur in WWII. Same strategy they used to teach on tests. If you come up to something too tough then skip it for now and come back to it later. There will always be easy pickings close by. In a year or two that subject that stymied you will fall.

I just hate thinking about blowing my chances, or people saying that I underachieved or did poorly.

The heck with people! There will always be someone who will say you are a slacker. Next to him you will be. There can only be one guy that is the best. That is some sort of rule. That is no reason not to do math.

Supposing you are not meant to be great. You can still do mathematics for the rest of your life. You can still enjoy it. You can have more fun than 10 mathematicians just by being an amateur.

Au101 · 2011-08-20 08:41:33

Well said Bobbym, I don't really have much to add to that. I don't think that there's any reason to suspect that you won't become a fantastic mathematician, but you don't need to be better than all the rest to have a good time doing the mathematics that you love.

And yes, it was indeed Edexcel. I quite like Edexcel .

gAr · 2011-08-20 15:30:39

Agreed!

And there are so many interesting stuffs which are never taught.

... or people saying that I underachieved or did poorly.

Forget people, remember mathematics. That's the rule.

"Success has many fathers, failure is an orphan" !

Au101 · 2011-08-21 01:11:53

'The road to wisdom? Well, it's plain
and simple to express:
Err
and err
and err again
but less
and less
and less.'

I do know who said that - Piet Hein.

Bob · 2011-08-21 01:38:20

hi zetafunc,

Could you tell me how you learned Galois theory? Did you use a website, a specific book?

I've emailed my son about this. It one of his specialisms. I'll post again if I get anything or he may do it himself.

bob

zetafunc. · 2011-08-22 03:33:45

Hello all,

Thanks for all the responses. Regarding the island-hopping; I suppose I can do that. I always like to try and learn something as quickly as possible, though. Sometimes I view this stage of my life as an egg-timer that will run out soon; I know that after 30 you start to forget things (neuronic decay?), and I heard somewhere that people reach their 'mathematical peak' at 21 -- not sure what that means exactly, but that can't be anything good. I agree with your point that you shouldn't let people calling you a slacker deter you from mathematics. However, it can mean that I don't get on put on certain courses... e.g. if my sixth form interviewer thinks that I didn't do quite so well, they might put me on a level 2 course instead of a level 3 course. People tend to have such high expectations of me that they think I can get 100% in everything. I always feel this pressure before and during an exam. If I didn't do so well in an exam, or think that I got less than 90%, I get upset. Someone told me that the better student can deal with it. Maybe I'm not a better student. I still enjoy the mathematics, but people never seem to see this. It's like having a long winning streak and then losing one match and people asking you why this happened, is this the end of your career, etc... it takes me a long time to get over. The only time when I can really enjoy doing mathematics is when no one cares about what grades you got, or when I can just sit down and write for hours on my whiteboard listening to music. There is an expectation in my classes that if I don't know the answer, then no one does. If someone else does and I don't, then I get questions like "are you getting dumber?" or "are you in decline?". It's sickening.

Au101, that is a nice poem; thank you for this. I hope I'm on the right road.

Bob bundy, thanks for taking the time to do that! I would love to hear what your son thinks about it. I hope Galois theory is not impossibly hard. A few years ago I remember reading the stuff on sets and groups by Ricky Shadrach. I think I probably need a much larger foundation in group theory before Galois theory? I'm not sure, I don't know much about it...

bobbym · 2011-08-22 04:03:30

Hi;

Kaboobly doo, definition: Clever but specious or fallacious reasoning.

I know that after 30 you start to forget things (neuronic decay?), and I heard somewhere that people reach their 'mathematical peak' at 21

Kaboobly doo! I am 3 times that upper limit and still getting better.

Someone told me that the better student can deal with it.

More kaboobly doo! I was the best pressure performer that ever lived. They called me stoneface. Let me say, there is only one way not to feel pressure, that is by cutting off your head.

There is an expectation in my classes that if I don't know the answer, then no one does.

I had the exact same thing. When I would be absent and teachers would ask the class a question, they would say. "let's wait till m gets in, he will know."

Keep mental poisoning like that a safe distance from you. Do not let any of that sink in.

Overconfidence is a serious weakness but lack of confidence is death.

I think you can make it. Ain't that enough?

Bob · 2011-08-22 05:05:33

hi zetafunc,

the only time when I can really enjoy doing mathematics is when no one cares about what grades you got

That's the best attitude to have.

And the response to give when everyone expects you to have an answer is "I'm just leaving this one for the rest of you as I feel the practice will be of benefit to you!".

What you do is what defines you. Not what grade you get so don't get hung up on exams. If you have done the work and practised then you know what you're capable of, so just go into each exam with the 'let's enjoy this' attitude.

I think Galois theory is hard and that it does begin with group theory. I'm still awaiting a response from my son. He went to Cambridge and then did a PhD at Manchester. When he sent me a copy of his thesis I didn't understand a single thing in it, including the title! And I thought I could do mathematics. I will find out his answer soon, I'm sure.

I hope it is wrong that one's best maths is done by age 21. I've recently done problems that I couldn't do when I was 21 so I'd say it's not true for me.

This site is called Maths Is Fun. You sound like you are an ideal candidate to become a member. So how about it?

Bob

Last edited by Bob (2011-08-22 05:08:10)

Au101 · 2011-08-22 13:00:55

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.

Last edited by Au101 (2011-08-22 13:01:54)

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