Maths Paper (Remarking Advice)...

Bob · 2011-08-22 21:08:19

hi zetafunc

I've had a reply from my son, David. I'll leave you to judge how hard it's going to be to master the subject and how long it will take you.

Here's what he said:

I didn't learn Galois Theory until I was 20 and learnt it mostly from the book "A first course in linear algebra" by John B. Fraleigh (now in its 7th Edition), although I didn't really understand all the finer points until I had to teach the subject later in Germany. The student will first need to understand linear algebra, groups, rings and fields. These are all contained briefly in the earlier chapters of the above book. An alternative book is "Galois Theory" by Ian Stewart which assumes more previous knowledge, but then goes deeper in to the theory and its applications.
These days there are lots of lecturers who put their lecture notes on line for free. I have no idea how good they are or how much previous knowledge they assume. There are also the dangers of mistakes, non-standard definitions or obscure notation which may not be apparent to a student studying a particular subject for the first time. Books are generally more reliable because they have been checked and proof-read many times, but they are quite expensive for a student.

Hope that helps,

Bob

zetafunc. · 2011-08-25 00:38:58

Hello,

Thanks for your replies. I just got my GCSE results today - I am still shaking. I didn't get what I wanted but I think I did okay - 8A* 2A 2B. 8A* were in Physics, Maths, RE, Eng, Eng Lit, ICT, Spanish, Geography. 2A were in Biology and Business Studies, 2B were in Chemistry and Statistics. If I had bothered to actually hand in the coursework for Chemistry and Statistics on time they could have been easy A*s and my grades would have looked a lot better! But I am happy, still. Especially with getting 300/300 in physics and maths!

I have to make up my mind about A-level choices by August 31st. I achieved the mandatory BBB in Triple Science and have an APS of 7.5, meaning I shouldn't have trouble getting into any courses. At the moment, my definite choices are:

Further Maths
Further Maths (Additional)
Physics
Chemistry

Still wondering about the Biology though. I don't know if I should pick it. These were my results for biology;

Unit 1 - 43/50
Unit 2 - 44/50
Unit 3 - 83/100 (puking in middle of exam)
math coursework with C grade (not handed in on time)
Avg = A

I am not sure about picking A-level Biology because of this. I don't want to pick anything that I won't get A/A* in. It's a bit of a gamble and I'm not certain I'll find the course interesting. I will talk to them about it. The first A-level Biology exam is in 139 days; I could start preparing now and memorise the whole textbook, do past papers, etc. but I would have to be careful with my time management, since it is entirely self-study. The results above seem like I wouldn't get an A* in Biology A-level even if I tried.

Thank you for e-mailing your son about Galois theory. I will try to find out more about rings, groups and fields with the time I have left of my holiday. His e-mail was very helpful. I will see if I can find that book he mentioned ("Galois Theory" by Ian Stewart).

Overall I'm not sure what I should think about these results. I was predicted 12 A*. I should have got 11A* + 1A if I had not been lazy with coursework. Well, that's life I suppose... you don't take your opportunity, you get punished. I am thankful I did not get shockingly bad results.

"I'm just leaving this one for the rest of you as I feel the practice will be of benefit to you!"... I like that, haha.

I will try not to take too much notice of all the pressure. It is difficult. This morning I almost puked from being nervous about results.

I am tired now. Got to sleep at 5 AM doing maths to ease the pressure of results day, woke up at 9 AM. But I am still shaking.

zetafunc. · 2011-08-25 01:33:52

zetafunc. wrote:

math coursework with C grade (not handed in on time)

Should say "bad" not "math"

zetafunc. · 2011-08-25 01:39:08

Does anyone know what the points mean? e.g. next to Physics it says A* - 58 points. Do they serve any purpose? The exam board websites say nothing about them (as far as I can see) and I was wondering what they meant. I gather that 58 points is equal to one complete GCSE, but I got A* in RE which says 29 points, which was a short course (half course). Do these get added up on UCAS, do I have to enter these somewhere...?

bobbym · 2011-08-25 02:29:16

Hi;

300 out of 300? That sure sounds good to me. Biology is fine, biologists make me puke.

I do not agree that you should only take courses you know that you are going to do great in.

zetafunc. · 2011-08-25 02:48:50

But the thing is, if I don't get a good grade in it, I am in huge trouble if universities decide to make that one grade part of my offer. For example, if I get A*A*A*A*A*B in my A-levels, and they have an offer of A*AA in Further Maths, Physics and Biology, I won't get in because I got B in Biology. This is what makes me not want to pick it, because, even if I can enjoy it, it can also make me miss an offer... I don't want that to happen.

Thanks! I am very happy with that mark. As for the puking thing, I had a stomach bug that day, but I was forced to do the exam with the others. It was torture. I was half trying to explain convergent evolution while half puking in a bag...

zetafunc. · 2011-08-25 02:49:49

Forgot to say -- if such a case did happen, in some cases you can convince them to put you on another course, if they let you.

bobbym · 2011-08-25 03:28:03

That is an amazing coincidence. While this big blowhard bio guy was insisting to us that evolution was a fact, I began to wretch violently. Yes, I tossed my cookies but that did not stop him from going on and on about his favorite theories being so wonderful they just had to be true.

What classes do you take for enjoyment or just interest?

zetafunc. · 2011-08-25 03:54:27

At GCSE I took Business and Geography for interest -- but for A-level, especially when applying for top universities, they look for specialisation. To be honest, the only subjects I am interested in are Physics and Maths; I'm taking Chemistry to make up for the B I got at GCSE. For Biology, I want to try and prove I can get an A/A* at A-level, because it's the one subject that I'm not confident I can get a great grade in.

bobbym · 2011-08-25 04:12:00

How about some Music, Creative Writing, Literature, Poetry, Art, Computers...

zetafunc. · 2011-08-25 04:23:37

Over here you can't take an A-level in something if you didn't do the GCSE - can't do music, or art. For computing, I don't like the courses, because you have to do web design and animation, and other things that are boring for me. I am learning a few programming languages at home. I used to do creative writing when I was younger (Year 7-8) but I found that a bit boring after a while and stopped. I don't enjoy it anymore. They offer English Lit & Lang, but I hated English for the 2 years that I spent on the GCSE. I used to play cello, guitar, piano and harmonica for a couple of years, but then something happened and I just lost interest. I still don't have the same interest in it as I used to...

I like public speaking but you can't really apply that to any A-levels, and no opportunities out of school come to mind.

Basically I'm a very boring person

bobbym · 2011-08-25 05:03:45

What you need is a few yikes' in your posts. Seriously, I do not think you are boring.

Just try find some time for yourself. Some time to relax. Watch a movie, go out, socialize. A little time with nature. Over exertion of brain cells can cause baldness and brain strain.

Au101 · 2011-08-25 05:30:33

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.

Au101 · 2011-08-25 05:34:18

I think, also, that bobbym is right - there is far more to life than A-levels - and even if you don't come to realise that, then they will soon take their toll and you are likely to end up pretty disenchanted with the whole thing. You are clearly an academic and you enjoy studying and learning for its own sake, so you should keep that up, but you should also take some time to relax and socialise - that's very important. You can do public speaking as an extra-curricular activity; you can just do it for fun - perhaps there is a club or a society which you can join within or without your school. It is important to do these things which you enjoy as well.

And no - you aren't boring

zetafunc. · 2011-08-28 04:45:52

Thanks for the replies.

Hmm... well, I watch tennis sometimes but that is pretty much it. I exercise too but I don't have many hobbies, really. I don't go out much, except to buy groceries, or to go for walks on my own (3 mile walk or so to my house and back). I don't really have many friends.

I guess it's a little sad to say but I think mathematics is my outlet. It's one of the few things I enjoy doing as well as do well in at school. Is that okay? It's irritating to have to say 'I have no hobbies'. I hate going to the cinema and watching movies.

Plus my parents are having a go at me for not getting the best results in my school, e.g. I get shouted at because there were people who got more A* grades than me.

I think I've decided not to do Biology for AS/A-level. So my choices for definite will be:

Further Maths
Physics
Chemistry
EPQ (Extended Project)
Further Maths (Additional) -- still need to find out if this is possible. And whether it will be done solely in Year 13, or in Year 12 and Year 13, etc...

Someone suggested going to university early. I don't know if this is a good idea. That means applying this year (2011) and going around August 2012. I would get to do what I love the most -- mathematics/physics -- without having to stick around with subjects like Chemistry at A2. What do you think about this?

zetafunc. · 2011-08-28 06:05:49

Do universities ever make offers based on AS as well as A2? e.g. A*A*aa + 1,1 in STEP?

Au101 · 2011-08-28 06:32:23

Sometimes they will. If you don't continue a subject to A2, then it will still score UCAS points (half as many as the equivalent grade for a full A-level) so they can contribute to some pure points offers (although many universities will specify that the points must come from a certain number of full A-levels). Further, as we've discussed - although not the be-all-and-end-all, module scores can work in your favour and they will definitely contribute to the overall grade, you always need a certain UMS score overall. Sometimes, they will include references to AS scores. However, I admit that I didn't pay that much attention so I could be wrong - on this issue, though, I don't believe so. Here, allow me to quote an example offer for you:

This offer is subject to you obtaining a minimum of 320 UCAS Tariff points. Score to be taken from 3 A Level subjects only, excluding General Studies. Alternative conditions: A minimum of 340 UCAS Tariff points. Score to be taken from 3 A Level subjects and one AS subject only, excluding General Studies.

As for your grades this year - you did exceptionally well - why should it matter what another person has done or failed to do? You have still done brilliantly. I think you would enjoy university and excel there. You may well be able to take advantage of entering university early - it will be less frustrating for you certainly. It is, however, a lot of work for you to do by then and a decision which only you can make.

There's nothing wrong with being an academic and enjoying your mathematics and other such things, but I do think that there're more important things.

Also, on the Further Maths (Additional) front - it is possible. Even if your school don't offer it, you can purchase your own textbooks and learn the courses for the other modules. If your school won't let you sit the exams there (which they probably will) then you can sign up to sit them at a registered centre. It may cost you a little to sit the exams and, of course, so will the textbooks, however, you can sit those modules with or without the support of your school.

bobbym · 2011-08-28 07:15:29

Hi;

Obviously I am not going to change your mind so I am going to have to toughen you up.

I don't really have many friends.

That happens. It is their loss, but they will get through it too.

I guess it's a little sad to say but I think mathematics is my outlet. It's one of the few things I enjoy doing as well as do well in at school. Is that okay?

Sure, that is fine.

Plus my parents are having a go at me for not getting the best results in my school, e.g. I get shouted at because there were people who got more A* grades than me.

That happened to me too. You will get over it. My brother points out here that your life parallels mine in some ways. I did not turn out so bad. Actually I did but let's ignore that.

zetafunc. · 2011-08-28 07:44:52

Thanks for the replies.

I have all the textbooks I need (to be honest I just downloaded them off of some site) for the Further Maths (Additional) course -- I don't know how I would get a centre to let me do it though. Does this have to be another school, or can a 'centre' be something else?

I have discussed going to university a year early with my parents and they don't think it is a good idea, especially because I need another year of maturity and I'm not independent enough. Is it worth it to go to an average university in Year 12 rather than go to a top university in Year 13?

As far as doing other things apart from maths and studies and watching tennis (and sometimes other TV shows from internet) I don't have a life apart from that. Very boring.

Bobbym, I am curious to hear about your mathematical background... what is your level of education? What was your experience of university? What did you work as after your education (maths degree?)... etc?

The problem lies in that my college might not agree with doing only 2 subjects at school for A-level; e.g.

Year 12
A2 Further Maths
AS Physics
AS Chemistry
EPQ

Year 13
A2 Physics
A2 Chemistry

Other people would be doing 4 AS x 4 A2 over two years. Maybe my school will have a problem with this...?

bobbym · 2011-08-28 10:18:54

what is your level of education? What was your experience of university? What did you work as after your education (maths degree?)... etc?

A lot of people are asking me this question recently. I am loathe to discuss it. I am not ashamed of my decisions about my education. I am ashamed of decisions about how to use it.

Rather I would ask you some questions. Which would be more amazing to you? That I aced my SAT's with 1600 out of 1600? That the tests actually put me to sleep. Hardest part was finishing them! I was wishing I could vomit, that at least would have kept me awake. Turned down Columbia and went to MIT and they taught me everything I know.

Or, that I dropped out and have no formal education at all. That I taught myself everything I know? Got it all from books and working math related jobs. Continuous pressure to get the answers faster than anyone else. People hired me because they knew I would get the job done not because MIT said I would get the job done.Which story is more impressive to you?

Bobbym, I am curious to hear about your mathematical background...

Background? I know what I like. Combinatorics, probability, number theory, numerical analysis, computational math, CAS...

I know what I hate. Group theory, topology, tensors and vector analysis, abstract algebra, logic...

You are talking a lot about tactics. How to get this grade to get into that school. I do not hear anything strategical in your thinking. What are your long term plans? Do you want to have a piece of paper that says you are good, or would you rather be good? Do you want math excellence or do want an excellent job? They are not the same thing.

Au101 · 2011-08-28 10:55:54

Well, examination centres must be registered with the JCQ I believe, but they are not necessarily schools, there are places - I believe - which are also set-up for this purpose. It is not something which I have ever looked into, though, you should speak to your school's external examinations officer or do some internet research into this. It is, however, possible to sit an examination without your school's facilitation, although it's obviously not necessarily easy or cheap.

I think Bobbym's advice and my advice has been roughly similar so far - along with the contributions of bob bundy - and I don't wish to repeat bobbym's advice in slightly different words at this stage. I shall, however, urge you to consider what he is saying - and, indeed, what he is about to say - carefully, he is a wise and very reasonable mathematician and is giving you sound advice.

zetafunc. · 2011-08-28 23:42:12

Thanks for the replies.

I can't decide which is more amazing, mainly because both stories seem equally impressive. My long-term plans are to be a lecturer of maths/physics or a research mathematician. I would prefer to have a piece of paper that said I was good along with mathematical excellence; if I were just great at maths but had no formal qualification to prove this, what would I do? How would they hire me? If there were hundreds of other applicants with PhDs in mathematics and I was applying with no formal education but just put on my personal statement that I was passionate about mathematics, surely they would accept the PhD guy in almost every case? What good is maths excellence if I can't prove it? I would like to be a good mathematician/physicist and have a rewarding job, but if I don't get a degree I don't see how I would get there. How do you teach mathematics at a university if you don't have a degree? For example, I was looking at CERN's website, and a lot of the jobs that would appeal to me required lots of qualifications, like a PhD in particle physics, lots of job references, etc...

My Director of Sixth Form still has not replied about the Further Maths (Additional) A-level; I may have to contact a private centre. But if it costs too much, then I just won't do it. He told me that the school could technically enter me for any A-level course though, since the college is so large. I will talk to my examinations officer about doing exams at another centre. The problem lies in that the school can't offer any teaching support regarding that A-level.

zetafunc. · 2011-08-28 23:53:08

Also, has anyone heard of an EPQ (Extended Project Qualification)? My college requires that I do one of these as part of my chosen package. I would like it to be maths or physics-related, but I am stuck for ideas. It is supposed to be an investigation or report-based study on a topic of interest (like your own research), but I'm not sure which would be the best thing to do? If it is physics-related, it would have to have a heavy mathematical component to it. I'm not sure what I would do for this.

Au101 · 2011-08-29 00:07:14

Yes, I did an EPQ - if you would like to hear more about it then I would be happy to explain further. What I would say, though, and I hate to be blunt - but it really was a waste of time.

Also, I do understand - you are an ambitious person and - more importantly - you would like to spend the rest of your life doing what you love and in your case - regretfully, in my opinion - you do need pieces of paper, there's no way around that. However, I think maths excellence is just as good if you can prove it as if you can't, the piece of paper is just a hoop that, unfortunately, you can't really avoid going through, but the excellence is worth just as much without it - it is still as valuable in itself, perhaps more in some ways, since it is rewarding for its own sake.

zetafunc. · 2011-08-29 00:23:31

Thanks for the reply -- why was the EPQ a waste of time?

Regarding EPQ, do you have to attend lessons on it and give them some kind of progress review on your project on a weekly basis? Roughly how much time needs to be devoted to it? Also, I was told you have to present this to an audience; is this true? What kind of audience would it be?

I do want to spend my life doing what I love doing... but I have heard of some cases where it has turned out to be a nightmare for some people. I was reading about a guy who graduated with a PhD in astrophysics, but is struggling to find a job because he doesn't have any engineering qualifications. I guess that is a case where a piece of paper doesn't always help. But I still think that having both is more important than just having one of them.

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