Making constructive use of my time.

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A student completing A-Level exams in the UK is seeking advice on how to effectively utilize a three-month gap before starting university to study mathematics. They have a solid foundation in manipulative mathematics and are considering whether to delve into analysis or extend their calculus knowledge. Discussions highlight the importance of motivation and suggest that first-year university courses may largely recap A-Level content, alleviating stress about preparedness. Recommendations include exploring stochastic calculus and engaging in volunteer work to enhance their CV. The student is also balancing the need to earn money with their desire to continue learning.
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Hi there,
I'm currently finishing my A-Level exams (UK system) and provided I achieve my offer will be going to university in autumn to studying single honours mathematics (4 Yr MMath/Msci).
I'm going to have a 3 month gap between my last exam and starting university, so I obviously want to make good use of my time.
While I obviously want to enjoy myself a little and I have to work to earn more money I'd like to keep learning throughout the summer.
By mathematics background is that of two A-Levels in maths. I've studied up to things such as: De Moivres theorem, maclaurin and taylor series, vectors(mostly just the equations of planes/lines), proof by induction, differentiation and integration of inverse trig/hyperbolic functions and reduction formulae etc. [I can easily provide a link to the syllabus I've been following if that is necessary]
Basically my question is: What should I try to learn in the time that I have? Obviously my background is mostly manipulative mathematics (or so I hear) so would it be best to try to learn some analysis or should I try to extend my calculus knowledge to partial differentiation etc.?
Thanks for any advice.
 
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What about stochastic, if you haven't done any of that at school?
 
De Moivres theorem, maclaurin and taylor series, vectors(mostly just the equations of planes/lines), proof by induction, differentiation and integration of inverse trig/hyperbolic functions and reduction formulae etc.
I never thought that the CAPE exams was this close to A levels (we do use A level books) because I did CAPE and we did all those topics, maybe not the De Moivres theorem, maclaurin and taylor series, but I'm going to look up those to see if I've done it but under some other heading.
 
What about stochastic, if you haven't done any of that at school?
What distinguishes stochastic calculus from other varieties? Is it the type applied in statistics? I haven't really done much statistics at A-Level (I chose 'pure' and mechanics) so perhaps I should look into it. I do prefer things like problem solving to computation though(the piece of stats I do remember is the tedious formulae for the product moment correlation coefficient).

I never thought that the CAPE exams was this close to A levels (we do use A level books) because I did CAPE and we did all those topics, maybe not the De Moivres theorem, maclaurin and taylor series, but I'm going to look up those to see if I've done it but under some other heading.
There's a link to A-Level specifications on this page if you want to compare what you're doing with A-Level: http://www.edexcel.org.uk/quals/gce/maths/adv/9451/
 
i'm glad you brought up good use of time. I'm logging off right now and getting back to work.
 
Gaz031 said:
What distinguishes stochastic calculus from other varieties? Is it the type applied in statistics? I haven't really done much statistics at A-Level (I chose 'pure' and mechanics) so perhaps I should look into it. I do prefer things like problem solving to computation though(the piece of stats I do remember is the tedious formulae for the product moment correlation coefficient).


There's a link to A-Level specifications on this page if you want to compare what you're doing with A-Level: http://www.edexcel.org.uk/quals/gce/maths/adv/9451/

Sup Gaz, I was in the same boat 3 years ago when I finished my A-levels. Basically if you're not prepared for it at the time mathematics may be the initial struggle you encounter. Usually univervisities teach maths for physicists course in the first 2 years, so check out the dept web pages and the syllabus for these courses. They may even have listed there recommended books etc. one that I recommend is it covers a lot of topics and I'm still using it in my fourth year.
 
Gaz, I reckon your motivation will be the biggest helping hand here. When I was at your stage, I was all "woo, I've finished my A levels, now what can I do to waste 3 months of summer?". I assume you've got a further maths A-level, that'll give you a hand.

First year will be a pretty swift re-cap of your A-levels anyway, I wouldn't stress about it too much. Just have a good summer, earn some cash, and perhaps get to know the city you're moving to a bit better, if you don't already.

Which uni, may I ask?
 
Gaz031 said:
What distinguishes stochastic calculus from other varieties? Is it the type applied in statistics? I haven't really done much statistics at A-Level (I chose 'pure' and mechanics) so perhaps I should look into it. I do prefer things like problem solving to computation though(the piece of stats I do remember is the tedious formulae for the product moment correlation coefficient).

hmm... well I'm talking about this kind of stuff: http://www.math.uah.edu/stat/
 
brewnog said:
Gaz, I reckon your motivation will be the biggest helping hand here. When I was at your stage, I was all "woo, I've finished my A levels, now what can I do to waste 3 months of summer?". I assume you've got a further maths A-level, that'll give you a hand.

First year will be a pretty swift re-cap of your A-levels anyway, I wouldn't stress about it too much. Just have a good summer, earn some cash, and perhaps get to know the city you're moving to a bit better, if you don't already.

Which uni, may I ask?

True if you did Further maths then you will learn very little new maths in your first year. If I recall in my first year the main things we learned were Taylor Series, vector and basic complex analysis. So you should be fine. Do some back ground reading on some of the subjects. What I recommened you do is to find a job and do some volunteer work, that always looks good on your CV.
 
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Thanks for the replies people.

Basically if you're not prepared for it at the time mathematics may be the initial struggle you encounter.
I heard that but am prepared to work on it, provided it doesn't require divine inspiration! I've heard analysis tends to be one of the hardest first year courses.

one that I recommend is http://www.amazon.com/exec/obidos...0005548-5099655&tag= it covers a lot of topics and I'm still using it in my fourth year.
That looks quite good. I was looking at also as a methods reference but the one you suggested looks good too.

When I was at your stage, I was all "woo, I've finished my A levels, now what can I do to waste 3 months of summer?"
Heh, I would be like that but I've been bored since mid-March where I finished learning all the content. I'm doing further maths AS+A2 in one year so after 9 modules this year having nothing to do is a tad unnerving.

Just have a good summer, earn some cash, and perhaps get to know the city you're moving to a bit better, if you don't already.
I'm going to try to earn some cash but the part time job I had over the year and which I have held open now is actually working in a supermarket :zzz: I hate the job so much but I don't think companies would employ someone for 2 months.

Which uni, may I ask?
It will be either Warwick(AABb/AABMerit) or Bristol(AAB). I was a little apprehensive about picking a high insurance offer but can't really see myself dropping the As in Maths or Further Maths.

What I recommened you do is to find a job and do some volunteer work, that always looks good on your CV.
Voluntary work will probably be a lot more interesting than working where I have done this year but we aren't overly well off so I need to save some money. I know experience in a supermarket isn't going to impress employers though so I obviously need to look into finding something more challenging at uni/in the later holidays.

hmm... well I'm talking about this kind of stuff: http://www.math.uah.edu/stat/
Thanks for that link. It looks better than the 'plugging numbers into formulae' stats I've done previously.
 
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