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    (Original post by DFranklin)
    Galois Theory / Number Theory if it's no trouble (they're the 3rd/4th year courses where I seem to most generally still know how to do the questions, or at least vaguely understand them!).

    Interesting (to me) that Measure Theory comes under the title Analysis for a couple of these universities - it was a separate course at Cambridge. (Sadly a course I never really got to grips with - one of the bigger holes in my mathematical education).
    The galois theory is a level 5 course so it can be done in the 3rd year as all the pre-requisites are 2nd year courses. Saying that, level 5 courses are generally seen as 4th year courses. Out of all the 4th year courses i'd say this is the most accessible in terms of the stuff needed beforehand so i could see people doing this a fair bit in 3rd year, possibly myself included.

    The number theory course is from what i've been told a "baby" number theory course. We don't really do any until this course. I personally know someone who is doing it in the 2nd year, but officially it is a 3rd year course.

    There was also an analytic number theory course available, but i think the lecturer must be somewhere else as at the moment it isn't available. It was a 3/4 year course, probably more 4th year.

    Again this is the university of Leeds. What do you think? Looking at first year exams i think cambridge's are harder, i think oxford's are harder but not massively so and i haven't looked at many others. I'd probably say the league tables are fairly accurate in gauging difficulty, Leeds is probably of manchester's standard.galois.pdf

    number theory.pdf

    analytic number theory.pdf
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    (Original post by DFranklin)
    Interesting (to me) that Measure Theory comes under the title Analysis for a couple of these universities - it was a separate course at Cambridge. (Sadly a course I never really got to grips with - one of the bigger holes in my mathematical education).
    I think it could be because Measure Theorists are a bit thin on the ground. If there's someone in your department with such leanings it's likely to be through their work in Analysis or in certain branches of set theory, which is then the context in which it's taught to undergraduates (kind of in the same way that most undergraduate education on the topic of Lie Groups is conducted via differential manifolds or representation theory).
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    (Original post by DFranklin)
    n
    So, have you taken a look?
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    (Original post by DFranklin)
    Because if you don't understand the material in the first year, chances are you're going to do really badly in the 2nd year.

    No. You can't judge from one course. (And you also have to judge by more than the name of the course).

    Realistically, there's not a lot of point commenting in this discussion unless you have already completed a good amount of university level maths. (Even if you have a full maths degree it's not easy to make sensible comments, I am finding!)
    Sorry i don't mean to hassle you, but i'm interested in knowing what you think about the papers i've posted?
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    Here are the 2009 papers for two 3rd year courses at lse. The maths department isnt very strong so I hope this will be useful re op. Note these are half units so each is only worth 1/8 of your final year.
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  1. File Type: pdf MA303.pdf (38.9 KB, 305 views)
  2. File Type: pdf MA305.pdf (33.2 KB, 272 views)
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    (Original post by George231086)
    Sorry i don't mean to hassle you, but i'm interested in knowing what you think about the papers i've posted?
    Sorry - I've found assessing these beyond "gut feel" more difficult than expected.

    I'd say there's a little less content than Cambridge, but it's not a huge difference. (And in practical terms, the question is how much content a good student typically learns. Cambridge has a lot of courses, but no-one does all of them).

    The big difference is that the Leeds questions give a *lot* more guidance. Each question is typically divided into 4 or 5 parts, and then each part is usually broken into 3 or so pieces.

    In contrast the Cambridge questions typically range from a question broken into 4 parts that aren't subdivided up to a question that isn't broken up at all. The following is fairly typical format

    (Original post by Tripos)
    State and prove the Arzela–Ascoli theorem.
    Let N be a positive integer. Consider the subset SN of C([0, 1]) consisting of all
    thrice differentiable solutions to the differential equation
    f'' = f + (f')^2 with |f(0)| < N , |f(1)| < N , |f'(0)| < N , |f'(1)| < N .

    Show that this set is totally bounded as a subset of C([0, 1]).
    [It may be helpful to consider interior maxima.]
    first you're asked for a bit of bookwork, then to do a concrete example. Usually the book work will be worth about a quarter to a third of the marks.

    I think that is quite a significant difference - what are your thoughts?
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    I'd say bookwork counted for a little bit more. Especially with something like Arzela-Ascoli which is a fairly chunky proof with 3 definitions to boot. Stating and proving A-A is probably worth a low beta (10/11 marks). Other questions though you do only get 5/6 marks for a state & prove part of question. Other questions are entirely bookwork

    Looking at those Leeds exams. Galois Theory could deffo manage, same with Number Theory (from doing courses of same name in third year Cambridge) The analytic number theory is different. Have seen a fair bit of it before but not in too much depth (some in the Number Theory Course, some in the Number Fields course).
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    (Original post by KAISER_MOLE)
    I'd say bookwork counted for a little bit more. Especially with something like Arzela-Ascoli which is a fairly chunky proof with 3 definitions to boot. Stating and proving A-A is probably worth a low beta (10/11 marks). Other questions though you do only get 5/6 marks for a state & prove part of question. Other questions are entirely bookwork
    Thanks. I suspect I didn't choose the best example (I couldn't remember how much you were expected to assume for the proof of A-A).
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    (Original post by DFranklin)
    Sorry - I've found assessing these beyond "gut feel" more difficult than expected.

    I'd say there's a little less content than Cambridge, but it's not a huge difference. (And in practical terms, the question is how much content a good student typically learns. Cambridge has a lot of courses, but no-one does all of them).

    The big difference is that the Leeds questions give a *lot* more guidance. Each question is typically divided into 4 or 5 parts, and then each part is usually broken into 3 or so pieces.

    In contrast the Cambridge questions typically range from a question broken into 4 parts that aren't subdivided up to a question that isn't broken up at all. The following is fairly typical format



    first you're asked for a bit of bookwork, then to do a concrete example. Usually the book work will be worth about a quarter to a third of the marks.

    I think that is quite a significant difference - what are your thoughts?
    I think that's a fair assessment. I'm only going into the 2nd year so as of yet i'm not advanced enough to fully appreciate the differences due to a lack of knowledge in the content.

    However from looking at the papers, it does seem that book work alone could get you pretty far, just simply learning key results and their proofs. I'd also agree that there is more leading, ie show that f satisfies p, now show f satisfies q, using these results prove that f is blah. I could imagine the cambridge question being more along the lines of, "prove f is blah" with possibly a hint like, consider x.

    The leading is something i've noticed on first year courses and tends to be more pronounced in more recent papers. Papers from 5 to 6 years ago seem to have alot less leading, sometimes i've literally seen the same question asked 5 years ago but without the hints or help. From comparing first year cambridge and Leeds papers i think cambridges are harder and require more thought. The leeds questions tend to be standard applications of a result or basic definitions, whereas the cambridge questions seem to require a bit more ingenuity. That said, i don't want to do Leeds a disservice, not all courses are the same and some are more non-standard than others.

    It seems likely to me that the format of Leeds papers and some others like manchester have been designed to be more accessable to the average student. I think the uni doesn't want to fail alot of people so instead of giving a question a student can't start on they add lots of little bits so that a 2:2 can be achieved by answering those.

    It's a similar thing with A-levels. The 1970's Alevel question just asks for the equation of the circle that passes through the three vertices of a given equilateral triangle, whereas the 2008 question would ask you to find the midpoints of each side, the gradient of the side, then the normal, then find the intersection of the three lines perpendicular to the sides through the mid-point etc. It means a candidate can atleast get some marks, but would get nothing with the original question.

    I'm unsure about it all really. I don't want to get into the habit of being led and i wonder whether i'll ever get to a good level of mathematics because i'll not be used to thinking as much. I suppose doing my own work might help.
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    (Original post by George231086)
    From comparing first year cambridge and Leeds papers i think cambridges are harder and require more thought.
    It's a generalisation, but because of STEP I'd say that Cambridge students are starting from a much stronger foundation than many people elsewhere. So you get quite a large difference in the first year exams (from what I've seen of 1st year exams elsewhere), but (it seems to me that) that difference is a lot smaller by the end of the 3rd year.

    It seems likely to me that the format of Leeds papers and some others like manchester have been designed to be more accessable to the average student. I think the uni doesn't want to fail alot of people so instead of giving a question a student can't start on they add lots of little bits so that a 2:2 can be achieved by answering those.
    The Cambridge exams have also moved a bit in this direction. The exams have a certain number of "half questions" that are designed to be straightforward without much problemsolving required.

    I'm unsure about it all really. I don't want to get into the habit of being led and i wonder whether i'll ever get to a good level of mathematics because i'll not be used to thinking as much. I suppose doing my own work might help.
    I think there's quite a big difference between 1st year exams and finals, so I'd see how things progress before getting too concerned.
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    (Original post by DFranklin)
    It's a generalisation, but because of STEP I'd say that Cambridge students are starting from a much stronger foundation than many people elsewhere. So you get quite a large difference in the first year exams (from what I've seen of 1st year exams elsewhere), but (it seems to me that) that difference is a lot smaller by the end of the 3rd year.

    The Cambridge exams have also moved a bit in this direction. The exams have a certain number of "half questions" that are designed to be straightforward without much problemsolving required.

    I think there's quite a big difference between 1st year exams and finals, so I'd see how things progress before getting too concerned.
    Thanks i'll bear that in mind.
 
 
 
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