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Maths at Cambridge.
Hey, everyone, I'd better introduce myself. I'm in Year 12 at a (catholic) comprehensive in Doncaster. I'm doing Maths, Further Maths, Physics, Chemistry and Electronics, and Re: Philospophy and ethics. I just wondered whether I should give Cambriddge a try next year, as I've realised I've given my future very little thought. It's pretty famous, that's for sure.
I got 4A*s, 4A's a B(geography) and a C (Technology) at GCSE. Due to the timetabling, I can't take further maths next year, so I'll only get an AS. Will that affect my chances?
And one more thing. It's not strictly to do with Cambridge, but it's to do with the subject. Can anyone please recommend me something to help me get back "into" maths. The reason I say this is because when I was in Year 7, I loved the subject. A teacher picked up on this, and let me do a GCSE that year, and I came out with a B. Unfortunately, I couldn't make any more progress after that, because just before the end of Year 8, I had to move to another country! I returned to the UK a year later, in year 10, to a different school. I thought there wasn't much point attemtping anything early, so I just did my normal GCSEs. Thorough slacking off and bad behaviour led me into wasting the last two years academically, and for some reason I lost a lot of the interest in Maths that I once had. Now, in sixth form, I'm just as lazy as ever, but my interest in maths is starting to return. I just wondered if anyone else felt like this, and if someone could tell me what to do to get back on track, I'd much appreciate it. I want to try and catch up on the last three four years that I've wasted.
Sorry if most of this sounds poorly worded and irrelevant.
I got 4A*s, 4A's a B(geography) and a C (Technology) at GCSE. Due to the timetabling, I can't take further maths next year, so I'll only get an AS. Will that affect my chances?
And one more thing. It's not strictly to do with Cambridge, but it's to do with the subject. Can anyone please recommend me something to help me get back "into" maths. The reason I say this is because when I was in Year 7, I loved the subject. A teacher picked up on this, and let me do a GCSE that year, and I came out with a B. Unfortunately, I couldn't make any more progress after that, because just before the end of Year 8, I had to move to another country! I returned to the UK a year later, in year 10, to a different school. I thought there wasn't much point attemtping anything early, so I just did my normal GCSEs. Thorough slacking off and bad behaviour led me into wasting the last two years academically, and for some reason I lost a lot of the interest in Maths that I once had. Now, in sixth form, I'm just as lazy as ever, but my interest in maths is starting to return. I just wondered if anyone else felt like this, and if someone could tell me what to do to get back on track, I'd much appreciate it. I want to try and catch up on the last three four years that I've wasted.
Sorry if most of this sounds poorly worded and irrelevant.
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I would imagine Cambridge would be impressed by your story of your first attempt at GCSE Maths. Hopefully they'd recognise it as an indicator that you're naturally very gifted in the subject.
My recommendations for getting into the subject a bit more would be to start working on some AEA, or preferably STEP papers this year, it sounds like you'd take to them particularly well. A couple of people on this board took STEP1/2 in their first year doing further maths on this board, I know theone is one of them, and he has an offer from trinity. I'm sure he'll be along later with some good recommendations. In the meantime you may wish to have a look at http://www.math.cam.ac.uk/undergraduate/advancedproblems .
You'll probably also want to read a little, there's standard books which your school/college will undoubtedly stock, Fermat's Last Theorem, The Code Book, there's a book by Korner which I meant to read before my application, but I didn't realise how intensive and large it was, so I never got more than a couple of chapters in. But you have time, and I think it would be an ideal starter.
Best of luck.
Lex.
My recommendations for getting into the subject a bit more would be to start working on some AEA, or preferably STEP papers this year, it sounds like you'd take to them particularly well. A couple of people on this board took STEP1/2 in their first year doing further maths on this board, I know theone is one of them, and he has an offer from trinity. I'm sure he'll be along later with some good recommendations. In the meantime you may wish to have a look at http://www.math.cam.ac.uk/undergraduate/advancedproblems .
You'll probably also want to read a little, there's standard books which your school/college will undoubtedly stock, Fermat's Last Theorem, The Code Book, there's a book by Korner which I meant to read before my application, but I didn't realise how intensive and large it was, so I never got more than a couple of chapters in. But you have time, and I think it would be an ideal starter.
Best of luck.
Lex.
Well the motivation bit is a bit difficult! By your GCSE results they look very good really, and i would say are good enogh to give cambrige a try, thats assuming your alevel results are basically straight a's. The further maths is prob ok, but make sure it goes on your form somewhere that you couldnt actually carry it on, and you didnt just drop it. You have to take nasty papers called STEP to get into cam if you get an offer, so theyre worth a look at. Theres a new book out called the magic of the primes by a guy called marcus de sautoy(or something like that) which is supposed to be good. I actually went to a lecture thing by him in oxford whch was very good, so the book would be too. This would also give you something to talk about at interview, and might get you into maths again. I think you just have to get motivated by what you want to do, try and have a thing in your mind to aim foe and it really helps. Thats how i stayed on track anyway!
Hope this helps but im not actually a mathmatician so im not an expert! I have a friend who got in to cam for maths, and i think he read a book, but thats about all he did!
Good luck
Hope this helps but im not actually a mathmatician so im not an expert! I have a friend who got in to cam for maths, and i think he read a book, but thats about all he did!
Good luck
I echo everything that fishpaste has said earlier. If you are serious about studying maths at cambridge, you need to be certain you enjoy the subject, as the course is very difficult and can get frustrating I imagine without any enthusiasm. You ought to read books and do difficult questions and generally try to improve your standard of maths. If you take an AEA (probably more sensible since you won't have done f. maths this year) that will be looked upon favourably. Also, don't learn along with your class, make sure you get ahead, read upto P3/P4 at least, as you're bound to get asked questions on this material at interview, and you need a basic knowledge of these books before you start any real difficult questions. In terms of books, I recommend the man who loved only numbers, what is mathematics?, a mathematician's apology, the mathematical olympiad handbook (if you can find a copy cheaply) as well as whatever you are interested in. I'm sure there's a recommended reading list on cam's maths website: http://www.maths.cam.ac.uk . Best of luck whatever you decide,
Chris
Chris
Hey, thanks a lot guys! Much appreciated. There's just a few problems though. I do further maths after school, so it's out of normal timetable. And the way the subject blocks are arranged, I'll have to drop my normal maths classes in order to take up further maths, and I'd have to change maths blocks., which the school doesn't allow. Also, I have absolutely no evidence saying that I did my GCSEs in year 7, apart from an old school report from back then. I don't have a clue about how to get a certificate or whatever. My current school doesn't think I'm lying or anything, I just expect Cambridge to want some concrete evidence.
I'll definitely read those books. Heh, funnily enough, what got the attention of my year 7 maths teacher was the fact that I read that "Fermat's Last Theorem" book and wrote about it in some non fiction book report for English. My English teacher told him or something, and he was impressed. I was such a precocious( is that the right word? ) little **** back then.
Bleh, I'm all rubbish now. I did rubbish at the Senior Maths Challenge. But It can't help to try I suppose.
So yeah, thanks a lot everyone, I'll be following your advice for sure, with the AEAs and books.
I'll definitely read those books. Heh, funnily enough, what got the attention of my year 7 maths teacher was the fact that I read that "Fermat's Last Theorem" book and wrote about it in some non fiction book report for English. My English teacher told him or something, and he was impressed. I was such a precocious( is that the right word? ) little **** back then.
Bleh, I'm all rubbish now. I did rubbish at the Senior Maths Challenge. But It can't help to try I suppose.
So yeah, thanks a lot everyone, I'll be following your advice for sure, with the AEAs and books.
kart
Also, I have absolutely no evidence saying that I did my GCSEs in year 7, apart from an old school report from back then. I don't have a clue about how to get a certificate or whatever. My current school doesn't think I'm lying or anything, I just expect Cambridge to want some concrete evidence.
Did you not get a certificate posted to you (or your school) a few months after you got your results?
I found 'How to Solve It' by G. Polya to be pretty good too.
For me, the best way to really appreciate the enjoyment of maths is to find/ be given a couple of number theory questions, ones that require either logic or basic shortcuts (a rule for division by 8 for example), and just sit down with an A4 pad and a pen with the knowledge that you're not going anywhere for an hour or so and... well... have fun I guess.
There are plenty more, but these are a start. Two are from a sheet we were all given at the Imperial interview, the third is question 1 from that STEP found on the Cambridge site (http://www.maths.cam.ac.uk/undergrad/admissionsinfo/steppaper/text/text.html).
1. Arrange the numbers 1, 2,..., 9 in order so that for each n the number formed by the first n digits is divisible by n. Thus 123456789 satisfies the condition for 2 because 12 is divisible by 2, and for 3 because 123 is divisible by 3, but not for 4 because 1234 is not divisible by 4.
2. You have twelve coins, one of which is counterfeit. It looks exactly like the others. The only difference is that its weight is not the same as the other eleven. It may be lighter or heavier, but you do not know which. You have a beam balance but no weights. Show that it is possible to determine the false coin (and whether it is heavier or lighter) with three weighings.
3. Find the sum of those numbers between 1000 and 6000 every one of whose digits is one of the numbers 0, 2, 5 or 7, giving your answer as a product of primes.
For me, the best way to really appreciate the enjoyment of maths is to find/ be given a couple of number theory questions, ones that require either logic or basic shortcuts (a rule for division by 8 for example), and just sit down with an A4 pad and a pen with the knowledge that you're not going anywhere for an hour or so and... well... have fun I guess.
There are plenty more, but these are a start. Two are from a sheet we were all given at the Imperial interview, the third is question 1 from that STEP found on the Cambridge site (http://www.maths.cam.ac.uk/undergrad/admissionsinfo/steppaper/text/text.html).
1. Arrange the numbers 1, 2,..., 9 in order so that for each n the number formed by the first n digits is divisible by n. Thus 123456789 satisfies the condition for 2 because 12 is divisible by 2, and for 3 because 123 is divisible by 3, but not for 4 because 1234 is not divisible by 4.
2. You have twelve coins, one of which is counterfeit. It looks exactly like the others. The only difference is that its weight is not the same as the other eleven. It may be lighter or heavier, but you do not know which. You have a beam balance but no weights. Show that it is possible to determine the false coin (and whether it is heavier or lighter) with three weighings.
3. Find the sum of those numbers between 1000 and 6000 every one of whose digits is one of the numbers 0, 2, 5 or 7, giving your answer as a product of primes.
Whilst Question 1 can be done merely by trial and error (I can never remember seeing a particularly mathematical approach, as there will be several possibilites), question 2 is a classic question. If you can do it, try replacing 12 by 13, can you still do? If you manage this, try it with 14, is this possible?
Question 3 is typical of the type of question you will find in a STEP paper. If you enjoy attempting such questions, I recommend looking at the British Mathematical Olympiad Round 1 papers from the last ten years, google 'BMOC' and you'll find a pdf of the papers on their website.
Question 3 is typical of the type of question you will find in a STEP paper. If you enjoy attempting such questions, I recommend looking at the British Mathematical Olympiad Round 1 papers from the last ten years, google 'BMOC' and you'll find a pdf of the papers on their website.
I love Q2! Those questions are so cool.
kart
Hey, thanks a lot guys! Much appreciated. There's just a few problems though. I do further maths after school, so it's out of normal timetable. And the way the subject blocks are arranged, I'll have to drop my normal maths classes in order to take up further maths, and I'd have to change maths blocks., which the school doesn't allow. Also, I have absolutely no evidence saying that I did my GCSEs in year 7, apart from an old school report from back then. I don't have a clue about how to get a certificate or whatever. My current school doesn't think I'm lying or anything, I just expect Cambridge to want some concrete evidence.
I'll definitely read those books. Heh, funnily enough, what got the attention of my year 7 maths teacher was the fact that I read that "Fermat's Last Theorem" book and wrote about it in some non fiction book report for English. My English teacher told him or something, and he was impressed. I was such a precocious( is that the right word? ) little **** back then.
Bleh, I'm all rubbish now. I did rubbish at the Senior Maths Challenge. But It can't help to try I suppose.
So yeah, thanks a lot everyone, I'll be following your advice for sure, with the AEAs and books.
I'll definitely read those books. Heh, funnily enough, what got the attention of my year 7 maths teacher was the fact that I read that "Fermat's Last Theorem" book and wrote about it in some non fiction book report for English. My English teacher told him or something, and he was impressed. I was such a precocious( is that the right word? ) little **** back then.
Bleh, I'm all rubbish now. I did rubbish at the Senior Maths Challenge. But It can't help to try I suppose.
So yeah, thanks a lot everyone, I'll be following your advice for sure, with the AEAs and books.
if you know which exam board you did your GCSE with, contact them - I'm sure they'd be able to point you in the right direction
Suzy_vet
I dont think dropping furthser maths would really effect your chances at all, byt make sure you put it on your forms somewhere obvious that you couldnt carry it on.
The form they sent me straight after I applied had a question specifically asking if further maths was an option.
s-k
can someone post the answer to Q2 plz iam going mAD!!! 
Call the coins 1,2,3,4,5,6,7,8,9,10,11,12.
a) Show that in two weighings you can find from 4 coins, 1 of which is counterfeit, which one is counterfeit.
b) Use this to show that if we weigh 1,2,3,4 - 5,6,7,8 then the only case we need consider is when it doesn't balance.
c) So assume 1,2,3,4 go down wlog. Now either one of 1,2,3,4 is heavier or one of 5,6,7,8 is lighter than the rest. Now 9,10,11 and 12 are good coins, so weigh 1,2,5,9 - 6,3,10,11. If the LHS goes down you know either 1 or 2 is heavier or 6 is lighter. If the RHS goes down, then either 3 is heavier or 5 is lighter. If it balances then the counterfeit is either 4, 7 or 8. Show in any of the three cases you can work out which one the counterfeit coin is in just one weighing.
Suzy_vet
I dont think dropping furthser maths would really effect your chances at all, byt make sure you put it on your forms somewhere obvious that you couldnt carry it on.
Could you not just do the extra further maths modules in your own time then go and ask for help from the maths department in frees/breaks on the parts where you need it? My school said they couldn't fund teaching of further maths even to AS so I have to do a lot of the extra modules in my own time then one of the maths teachers can sometimes fit me in for a lesson when they hav frees. If they know you are aiming for cambridge i'm sure they would encourage you.
Haha..that's the problem, I don't dare tell anyone that I'm aiming for Cambridge! I'm a terrible slacker, and my reputation precedes me. My maths teacher was talking about how my sister worked hard, unlike me, and the head of the department walked by just then and said how surprised he was to hear my name and the word "work" in the same sentence. And add that to the fact that the teachers constantly ask me what plans I have for the future, and for the past few years my reply has always been "Nowt! I've got no idea at all, I'll just see what happens." So I'm gonna find it mighty odd telling my teachers about trying for Cambridge. Blaaaaarghhh.
kart
Haha..that's the problem, I don't dare tell anyone that I'm aiming for Cambridge! I'm a terrible slacker, and my reputation precedes me. My maths teacher was talking about how my sister worked hard, unlike me, and the head of the department walked by just then and said how surprised he was to hear my name and the word "work" in the same sentence. And add that to the fact that the teachers constantly ask me what plans I have for the future, and for the past few years my reply has always been "Nowt! I've got no idea at all, I'll just see what happens." So I'm gonna find it mighty odd telling my teachers about trying for Cambridge. Blaaaaarghhh.
I think it would be best if you changed your attitude and really aimed for Cambridge- tell your teachers thats what you want to go for and start to put some work in so that you get a good school reference on your UCAS form and this will be seen by all the unis you apply for. Don't dwell so much on your past reputation and you will be able to change their opinions of you- I realise A levels can become boring if you find them no challenge but make sure you look beyond the maths syllabus and try to find some material that challenges you beyond A level- it is very useful to be able to talk about extra reading etc.in interview and will impress them if you are loking beyond the basic syllabus. Good Luck!
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