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    (Original post by Noble.)
    Are you an undergrad at the moment?
    No I'm in Year 12. But to be fair on myself, I have read quite a few undergraduate level maths books, and have enjoyed it. So I'm not completely naive.
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    (Original post by arrow900)
    No I'm in Year 12. But to be fair on myself, I have read quite a few undergraduate level maths books, and have enjoyed it. So I'm not completely naive.
    Ah ok, I didn't really ask to see whether you were "informed" or not, I was mostly interested to ask what area and where you were wanting to do a PhD if you were a current undergrad. To be honest though, I find reading maths books for enjoyment and reading them because you've got weekly problem sheets, and are going to be examined on it, two completely different things. Last summer I started reading about a topic I was going to take the next academic year, and it was an entirely different (i.e. more enjoyable) experience than when I had to 'revise' the course for problem sheets and for examination :lol:
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    (Original post by Noble.)
    Ah ok, I didn't really ask to see whether you were "informed" or not, I was mostly interested to ask what area and where you were wanting to do a PhD if you were a current undergrad. To be honest though, I find reading maths books for enjoyment and reading them because you've got weekly problem sheets, and are going to be examined on it, two completely different things. Last summer I started reading about a topic I was going to take the next academic year, and it was an entirely different (i.e. more enjoyable) experience than when I had to 'revise' the course for problem sheets and for examination :lol:
    :eek:
    Aren't you allowed time to sort of "absorb" the material or is everything taught in an exam focused way?

    I was hoping it would be the former, since the latter is the approach taken at A level and can be quite depressing, especially if you previously enjoyed the subject. Now I can barely stand statistics after suffering through S1 ( I found it incredibly boring).



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    (Original post by arrow900)
    :eek:
    Aren't you allowed time to sort of "absorb" the material or is everything taught in an exam focused way?

    I was hoping it would be the former, since the latter is the approach taken at A level and can be quite depressing, especially if you previously enjoyed the subject. Now I can barely stand statistics after suffering through S1 ( I found it incredibly boring).



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    Nothing is really taught, in university mathematics, in an "exam focused way". It's not as clear cut like it is at A-Level where you have a set list of things you need to know and if you know them it's not difficult to get full marks. At Oxford, at least, nearly half the exam is made to be unseen problems, so obviously it's going to be difficult to make the material 'exam focused'. The way I see it, the material taught is the bare minimums you need to know and the rest is down to experience/hard work and ability (mostly the former). Of course you are given time to absorb the material, I've always found I end up much preferring the material covered in the first term as opposed to the second (and the third) when it comes to being examined (not even necessarily because I've spent more time on the material in the first term, but because I find concepts become a lot more familiar the sooner it's been taught - which is partially why I like getting started in the summer).

    I wouldn't really write off statistics because you don't like it at A-Level, I don't really associate A-Level mathematics (inc. further) with the kind of mathematics I do now (and even the kind of maths you get started on straight away at university) - needless to say stats at university is very different, that said I'm still not a fan of it.
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    (Original post by Noble.)
    Nothing is really taught, in university mathematics, in an "exam focused way". It's not as clear cut like it is at A-Level where you have a set list of things you need to know and if you know them it's not difficult to get full marks. At Oxford, at least, nearly half the exam is made to be unseen problems, so obviously it's going to be difficult to make the material 'exam focused'. The way I see it, the material taught is the bare minimums you need to know and the rest is down to experience/hard work and ability (mostly the former). Of course you are given time to absorb the material, I've always found I end up much preferring the material covered in the first term as opposed to the second (and the third) when it comes to being examined (not even necessarily because I've spent more time on the material in the first term, but because I find concepts become a lot more familiar the sooner it's been taught - which is partially why I like getting started in the summer).

    I wouldn't really write off statistics because you don't like it at A-Level, I don't really associate A-Level mathematics (inc. further) with the kind of mathematics I do now (and even the kind of maths you get started on straight away at university) - needless to say stats at university is very different, that said I'm still not a fan of it.
    That sounds like the sort of University Maths experience I would enjoy. Although, I have heard that it is possible to get through a course purely through rote memorization. Perhaps not at Oxford but I just wanted to know whether or not this was true in your experience?
    One of the reasons I want to do maths is to get away from rote memorizing material. I just don't understand how someone can enjoy doing this ( I know people in my Biology A level class who enjoy memorizing a textbook). Surely a computer can do this far more efficiently and in less time, so the effort put into this is pointless.

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    To Arrow900, sorry my tsr is messed up for some reason. It doesnt let me quote and even though I write in paragraphs, the spaces won't show up. Read the edit in that :')
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    (Original post by arrow900)
    That sounds like the sort of University Maths experience I would enjoy. Although, I have heard that it is possible to get through a course purely through rote memorization. Perhaps not at Oxford but I just wanted to know whether or not this was true in your experience?
    One of the reasons I want to do maths is to get away from rote memorizing material. I just don't understand how someone can enjoy doing this ( I know people in my Biology A level class who enjoy memorizing a textbook). Surely a computer can do this far more efficiently and in less time, so the effort put into this is pointless.

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    Sorry for the late reply, there was quite a lot I wanted to say in response to this and I didn't have the time yesterday.

    It is possible to get through the course and get a 2:1 purely on rote memorisation, but that would be seriously impressive; the amount you'd have to memorise, assuming you have little to no mathematical ability, would be immense since so much undergrad mathematics is notationally fiddly (to the point where it can seem unintuitive if you have no understanding) and the amount of work, dedication and time it would take to learn everything in parrot fashion would be quite insane.

    The way I see it, students vary quite a bit in their approach to the 'memorisation' aspects of a maths degree, but I would add that anyone who views it all as 'rote memorisation' is essentially doing an undergraduate maths degree wrong and anyone with this attitude towards the degree will generally have to be quite exceptional in other aspects of their ability to end up with a first (work ethic, dedication, memory etc.)

    I agree with you that the kind of memorisation you get at A-Level is dull and it's pretty much one-dimensional (in the sense that you need to remember it for the exam, and that's about the extent of it) but the memorisation required in a maths degree has quite a few other subtle uses. When you learn a theorem/proposition this tells you the conclusion, which on its own can be incredibly interesting but there's often far more to be understood in the proof - in a way a theorem is like reading the synopsis of a book. Quite often a proof will introduce you to some mechanism that isn't directly intuitive, or at least, you wouldn't have thought to do that and this mechanism isn't just a way to prove that theorem but it becomes a part of your 'mathematical toolkit' to prove other things and actually is a part of what makes a good mathematician. This kind of memorisation isn't the same kind that you have at A-Level, instead it's a kind of memorisation that changes how you think and approach problems.

    Personally, there was very little in my second year that I considered myself having to 'rote learn'. Don't get me wrong, everyone has aspects of the course they don't like and finds themselves resorting to trying to rote memorise those aspects when it gets close to exams, but more often than not it's entirely futile because if you're finding yourself having to do this it's unlikely you're going to have a decent enough grasp of the material, as well as familiarity and confidence of the material, to even dare attempt answering a 45 minute long exam question on it. My general approach to remembering proofs to theorems is to remember the key steps that seem to come from out of the blue, because if you remember these any half-decent mathmo can then flesh out the details to make it rigorous.

    Let me give you a nice short example of a proposition and its proof where the proof is really neat and potentially useful in other contexts:

    There's quite a bit of 'backstory' to fully understand this, but for what I'm trying to point out, it isn't necessary.

    If R is an integral domain with finitely many elements, then R is a field

    The the purposes of what I'm trying to illustrate, you just need to know that a field is a ring with the added condition that the non-zero elements have multiplicative inverses, that is for all a \in R \backslash \{0\} there exists a b \in R \backslash \{0\} such that ab=1 where 1 is the identity element of the ring (required by definition of a ring). A ring R is an integral domain if it isn't the zero ring and it contains no zero-divisors - that is if we have ab = 0 with a,b \in R then we must have that one of a or b is zero (so, for example, the ring of integers is clearly an integral domain).

    So in light of this, to show this result all we have to show is that all the non-zero elements of an integral domain with finitely many elements have multiplicative inverses. That is, if we have a \in R \backslash \{0\} then we need to show the existence of a b \in R with ab=1. Initially this seems to be quite a complex idea, and it wouldn't be unnatural to think to yourself "Where on earth does the fact there's only finitely many elements and it's an integral domain property come into play?"

    All becomes clear quite quickly when you see the initial step of the proof which is to consider the map of left-multiplication by a, that is m_a : R \rightarrow R given by m_a(x) = ax and then you note that this map is injective since if m_a(x) = m_a(y) then ax = ay so a(x-y) = 0, but this is an integral domain and by assumption a \neq 0 hence we must have x-y = 0 that is x=y. Then any injective function on a finite set is also surjective (that is, for all b \in R there exists a c \in R such that m_a(c) = b which is something covered in quite early first year analysis) and so we can conclude that there must exist a b \in R such that m_a(b) = 1 that is ab = 1. Since a was an arbitrary non-zero element of R what we've shown is that all non-zero elements have a multiplicative inverse - hence our ring R is actually a field.

    The point is, this proof is not unique to rings or integral domains, it's a method that could be used any time we've got a finite set and a notion of cancellation (integral domain).
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    Career: EU/Corporate Barrister
    Why?: EU, I love languages and i find the European law fascinating. I chose being a Barrister instead of soliciting because there is a healthy balance between court appearances and office work.
    Steps: I will have to go through all the standard steps but I would love to do some work I France before I start practising. I still have a little while to think though!

    Wish me luck.
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    Career: Ward Sister in children's A&E

    Reasons: Always wanted to be a nurse from a young age. Love working with kids, want to help them when they're sick/injured and scared. Huge interest in health and disease, like the idea of the adrenaline of working in A&E. I like the way that a ward sister role combines both clinical work and management roles.

    Plan: Complete a degree in children's nursing (conditional offer for September - fingers crossed I get in!), get a job at a London hospital and work my way through staff nurse, senior staff nurse, junior sister up to ward sister


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    Hi. I'm actually stuck between Primary school teaching (Key stage 1 or 2) or psychology/therapy at the moment myself. I really enjoy working with children and I loved my work experience at a primary school but I also find psychology/therapy really interesting.
 
 
 
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