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    (Original post by Physics Enemy)
    Perfect. Thumbs up from me. Thread over! STEP = Brains, Uni = Volume of Knowledge. Well I know which I admire more, I guess others can admire the latter if they prefer. Each to their own and all that.
    I think it's the university mathematics that contributes to actual useful advancement in Mathematics. Things like the BMO are just for fun, or for a bit of competitiveness really. Our society isn't scientifically/technologically advanced because Mathematicians were doing BMO questions all day.

    So I'd say that university mathematics is probably more important than Olympiad mathematics - even though being good at BMO questions is "admirable" in the sense that most other people aren't so good at them. But they don't really serve any purpose in mathematical advancement.

    STEP seems to be somewhere in between A-Level Maths and Olympiad Maths - it's a bit of both really.
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    (Original post by Farhan.Hanif93)
    Actually I think the issue is more because it's time consuming to post FULL solutions to STEP questions, all 'LaTeX'ed up.
    And it's time consuming to do the question in the first place as well. The applied tends to be harder to "do at a glance" as well - you often need to draw diagrams etc.

    To be honest, other than me, I'm not sure there's *any* graduate (or undergrad) currently on TSR who regularly posts STEP solutions. And I don't do it terribly often either. So drawing conclusions about "manchester students can't do STEP " from a lack of posted solutions is somewhat unsound...
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    (Original post by Farhan.Hanif93)
    IThe other MAJOR flaw with your argument is that you're forcing your opinion of what mathematical talent is upon others. You seem to think that being good at maths is being able to do puzzles (i.e. STEP). Others on here are arguing that a good mathematician will be one that can memorise proofs, learn from them and use them to prove other results. As I said before, I can't judge which is the better definition yet but I'd be more inclined to agree with the mathematicians rather than the physicist (with no disrespect to you).
    There's two things here.

    Firstly, in mathematics, you don't get ignorance marks. That is, you don't get any bonus because you solved a problem from scratch, as opposed to having seen something similar before. (In fact, in so much as you get marks for 'style', you're more likely to get them when you have seen something similar before, because you're more likely to remember "I solved something like this before, but I used 1/n^2 as a test function, and I wished I'd used 1/(2n+1)(2n+2) because it would have made the next bit a bit easier". And so, you leave a little space to 'fiddle' the fraction this time, and so the examiner sees you magically pick 1/(3n+1)(3n+4) which makes everything cancel and thinks "My God, I'm in the presence of genius!" (or at least he would if he was PE)).

    The second thing is that a lot of university mathematics is about building complex structures, theories, and abstractions. This is very different from both A-levels and STEP; the problem is that it's very hard to test for pre-uni, because it often takes months to learn how one of these structures is built - you can't do it in a 3 hour exam. Many people find this difficult (I'd say pretty much everyone does at some level or other). Just as you might have someone who can add a column of numbers at a glance, but is completely floored by the idea of (x+y)^n, you'll get people who can do great at STEP, but just cannot get to grips with the idea of a G-delta set in measure theory.

    That said, to be a successful mathematician, you are probably going to be solving problems. But they are bigger, harder problems, and you're not expected to do 6 of them in 3 hours.

    On the other hand, you do need a certain core competence. Without getting bogged down in details here, read the STEP examiners report, see the things the examiners say let candidates down, and ask yourself "Is this really something that only super-elite mathematicians should be expected to do, or is this something that you'd expect a decent maths graduate to be capable of?".
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    (Original post by DFranklin)
    And it's time consuming to do the question in the first place as well. The applied tends to be harder to "do at a glance" as well - you often need to draw diagrams etc.

    To be honest, other than me, I'm not sure there's *any* graduate (or undergrad) currently on TSR who regularly posts STEP solutions. And I don't do it terribly often either. So drawing conclusions about "manchester students can't do STEP " from a lack of posted solutions is somewhat unsound...
    Agreed. What I've found (as I would expect) is that you tend to get a lot more solutions being posted in the March-May period each year simply because there's usually at least one person who is taking STEP as part of their offers i.e. last year Unbounded posted a lot of solutions; the year before, SimonM/nuodai etc posted a lot of solutions; the previous years, yourself, nota, scipio and many others were doing it; I've got an interest this year so I've just started posting up a few solutions to the remaining applied ones as I was focussing on them earlier in the year. It's clearly been dying down as the number of unsolved pure questions have been reducing rapidly so it's also probably down to the fact that there fewer 'short' and easy-to-type-up questions left to be solved.

    It is completely absurd to assume that undergrads and grads from Universities outside COW (not COWI, since he doesn't believe that Imperial grads can do STEP) can't do STEP simply because they aren't posting solutions on TSR.
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    Ok. I've just had a look at the STEP website and seen a couple of papers. They look hard, but given that the format is best of any 6 questions out of quite a wide range, they don't look quite so intimidating. I think it would require a lot of preparation, but it helps that there are 12 years worth of past papers and answers which would help with getting into the right mindset. So, to contradict what I claimed earlier, I suspect I probably could give them a decent shot... and actually I think probably most reasonable maths graduates should be able to do so
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    (Original post by Farhan.Hanif93)
    I've got an interest this year so I've just started posting up a few solutions to the remaining applied ones as I was focussing on them earlier in the year. It's clearly been dying down as the number of unsolved pure questions have been reducing rapidly so it's also probably down to the fact that there fewer 'short' and easy-to-type-up questions left to be solved.
    There seems less general interest in the solution threads anyhow. Since 2007, I've done solutions to most of the questions shortly after the exams, but last year I didn't actually see much reason to post them. (And the STEP III paper never seemed to get posted - I didn't see it until it got on the STEP website).

    Sadly, results when searching for the 2010 STEP threads are pretty much dominated by bickering between PE and myself, (with occasional help from Owl_432 (or whatever the number was)).
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    (Original post by Chwirkytheappleboy)
    but it helps that there are 12 years worth of past papers and answers which would help with getting into the right mindset.
    If the candidates looked a bit further, they would also be able to find all the papers since 1987 so all-in-all 69 past STEP papers i.e. over 1000 similar questions to be working on (although very few people will have the time, the knowledge and the ability to do all of them before actually sitting the examination as part of a offer).
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    (Original post by Chwirkytheappleboy)
    Ok. I've just had a look at the STEP website and seen a couple of papers. They look hard, but given that the format is best of any 6 questions out of quite a wide range, they don't look quite so intimidating. I think it would require a lot of preparation, but it helps that there are 12 years worth of past papers and answers which would help with getting into the right mindset. So, to contradict what I claimed earlier, I suspect I probably could give them a decent shot... and actually I think probably most reasonable maths graduates should be able to do so
    Which years did you look at? There's always random variation, but overall I think there's been quite a sharp drop in STEP I/II difficulty over the last few years - at least from the point of view of a maths graduate. (When I did the "how many 'cheap' 2010 questions would you get with a uni degree?" post, I was expecting it to be 2 or 3 questions, but it was actually about twice that).

    Conversely, there are questions from pre-2000 where I've seen hints from the examiners and I'm still not actually sure how you were supposed to do the question in a reasonable amount of time.

    (In case it's not obvious, my "STEP I/II is a perfectly reasonable ask for a maths graduate" posts are in reference to the difficulty of recent exams, as those are the ones people would be taking now).
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    (Original post by DFranklin)
    And the STEP III paper never seemed to get posted - I didn't see it until it got on the STEP website.

    Sadly, results when searching for the 2010 STEP threads are pretty much dominated by bickering between PE and myself, (with occasional help from Owl_432 (or whatever the number was)).
    These events were not mutually exclusive.

    The STEP III 2010 paper was in the discussion thread somewhere (that's where I found it IIRC) so I think it's safe to say that the bickering over the glory of STEP caused the paper to be buried deep in the thread and thus made it difficult to be found - I found myself digging through the thread for quite some time to find it.
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    (Original post by DFranklin)
    In case it's not obvious, my "STEP I/II is a perfectly reasonable ask for a maths graduate" posts are in reference to the difficulty of recent exams, as those are the ones people would be taking now.
    To be honest, I'm expecting some sort of a reaction to the relative ease of this year's papers. I'm expecting STEP II to be much more difficult this year.
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    (Original post by DFranklin)
    Which years did you look at? There's always random variation, but overall I think there's been quite a sharp drop in STEP I/II difficulty over the last few years - at least from the point of view of a maths graduate. (When I did the "how many 'cheap' 2010 questions would you get with a uni degree?" post, I was expecting it to be 2 or 3 questions, but it was actually about twice that).

    Conversely, there are questions from pre-2000 where I've seen hints from the examiners and I'm still not actually sure how you were supposed to do the question in a reasonable amount of time.

    (In case it's not obvious, my "STEP I/II is a perfectly reasonable ask for a maths graduate" posts are in reference to the difficulty of recent exams, as those are the ones people would be taking now).
    Mmm. I looked at 2010. Just looked at 1998 now and they do appear harder
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    (Original post by Farhan.Hanif93)
    To be honest, I'm expecting some sort of a reaction to the relative ease of this year's papers. I'm expecting STEP II to be much more difficult this year.
    I'm sure you know, but the examiners report says as much: "In hindsight, many of the pure maths questions were a little too accessible ... Next year’s questions may be expected to be a little bit more demanding".

    My personal perception is that when the Cambridge examiners 'tweak' the difficulty, the changes tend to be a lot more extreme than intended. So I'd expect it to be unusually tough.

    [I've posted this somewhere else, but the 1983 IA Tripos was much much harder than the rest of the decade. I would normally answer a tripos question in a little under 1 side, and remember grinding out a 1983 special relativity question over 5 pages. Except I didn't finish it, because the last part involved basically doing the last 3 pages again, only with a sign change. My supervisor both thought I'd done nothing wrong, and that there was no way of doing the last part without doing another 3 pages of working.

    In which case I have absolutely no idea how an examiner could think that question was reasonable. I'd have been lucky to finish it in 3 hours, and I doubt there was anyone who'd do much better. I mean, PE may think my judgement of difficulty questionable, but heck!].

    @Chwirkytheappleboy: the difficulty is also a fair bit more variable in the pre-2000 papers. There are some easy questions that come out in a few lines, and some that take pages. Again, I struggle to understand the examiner's thinking.
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    (Original post by DFranklin)
    I'm sure you know, but the examiners report says as much: "In hindsight, many of the pure maths questions were a little too accessible ... Next year’s questions may be expected to be a little bit more demanding".

    My personal perception is that when the Cambridge examiners 'tweak' the difficulty, the changes tend to be a lot more extreme than intended. So I'd expect it to be unusually tough.

    [I've posted this somewhere else, but the 1983 IA Tripos was much much harder than the rest of the decade. I would normally answer a tripos question in a little under 1 side, and remember grinding out a 1983 special relativity question over 5 pages. Except I didn't finish it, because the last part involved basically doing the last 3 pages again, only with a sign change. My supervisor both thought I'd done nothing wrong, and that there was no way of doing the last part without doing another 3 pages of working.

    In which case I have absolutely no idea how an examiner could think that question was reasonable. I'd have been lucky to finish it in 3 hours, and I doubt there was anyone who'd do much better. I mean, PE may think my judgement of difficulty questionable, but heck!].

    @Chwirkytheappleboy: the difficulty is also a fair bit more variable in the pre-2000 papers. There are some easy questions that come out in a few lines, and some that take pages. Again, I struggle to understand the examiner's thinking.
    I'm not sure whether you've had a chance to look at the Siklos booklets but, in terms of changes, something I noticed was that the author decided to remove the difficulty ratings from the problems (if you had taken a look at the original one, you would know that the questions used to be rated from 1 to 3 stars, where 3 stars would be awarded to the most difficult problems. Not all 3-star problems were STEP III questions originally, mind you which suggests to me that they acknowledge that the difficult of questions on each paper vary considerably).

    Another thing worth mentioning about the most recent booklet is that the very last question was one of those that they branded 'too-difficult' for STEP so if you haven't seen it before, you may be interested in taking a look into it and perhaps posting your thoughts on it. I'd imagine that they will possibly be less lenient when it comes to deciding what to drop in the too-difficult-for-STEP pile this time.
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    (Original post by Physics Enemy)
    There is one flaw with STEP though; I think they should make everyone do at least 1 Mech Q and 1 Stats Q. If you think about it, it's a bit of a cop out to only do pure Qs (or applied in the very rare case), as hard as they are. I'm surprised they never incorporated this idea.
    The reason why this is not compulsory is because the content in each applied module varies a lot between the exam boards and therefore it wouldn't be fair to assume that they would be able to access enough questions to be able to meet this requirement. Plus STEP is a lot about choice, placing restrictions like that would be a step in the wrong direction.
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    (Original post by Physics Enemy)
    There is one flaw with STEP though; I think they should make everyone do at least 1 Mech Q and 1 Stats Q. If you think about it, it's a bit of a cop out to only do pure Qs (or applied in the very rare case), as hard as they are. I'm surprised they never incorporated this idea.
    Your argument is flawed, there is no way I would be able to do a STEP III stats question. This is not because I find them too hard (not that I am saying this may be the case), but I simply have not been taught stats beyond S1, nor will I by June. The stats and mechanics in STEP III requires knowledge of most of the units available at A-level (at least up to M3 and S3). However many candidates will not have been taught all of these as they are optional. However the pure maths units must be taken by all further maths candidates (with the possible exception of 1 or 2 FP- units) however this means the pure questions should generally be accessible to all, but the applied sections may well be inaccessible to some and so it is hardly fair to force all candidates to answer questions from these sections.
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    (Original post by Farhan.Hanif93)
    Another thing worth mentioning about the most recent booklet is that the very last question was one of those that they branded 'too-difficult' for STEP so if you haven't seen it before, you may be interested in taking a look into it and perhaps posting your thoughts on it. I'd imagine that they will possibly be less lenient when it comes to deciding what to drop in the too-difficult-for-STEP pile this time.
    Having had a look, what's interesting (in terms of this discussion) is that it would be a perfectly reasonable question to ask at university level (other than being possibly a little long). All the stuff that's 'conceptually' difficult would be covered at university (you'd understand the convergence issues, the idea of diffing the series and then integrating again, you'd know what a Fourier series is, and that it's periodic).

    Other than that, if you had anything in particular you wondered about, perhaps you could be more specific.
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    (Original post by DFranklin)
    Having had a look, what's interesting (in terms of this discussion) is that it would be a perfectly reasonable question to ask at university level (other than being possibly a little long). All the stuff that's 'conceptually' difficult would be covered at university (you'd understand the convergence issues, the idea of diffing the series and then integrating again, you'd know what a Fourier series is, and that it's periodic).

    Other than that, if you had anything in particular you wondered about, perhaps you could be more specific.
    I suppose what I was asking was what your opinion is on it's difficulty in relation to what you would expect on STEP. Concepts aside, do you believe that it's probably going to be slightly more difficult than what is expected on STEP II or III this year?
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    Ignoring time taken, I'd say a fair bit harder than I'd expect any question on STEP II; a bit harder than I'd expect any question on STEP III.

    I'd say it's also a fair bit longer than a modern-day STEP question, even STEP III.
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    (Original post by DFranklin)
    Ignoring time taken, I'd say a fair bit harder than I'd expect any question on STEP II; a bit harder than I'd expect any question on STEP III.

    I'd say it's also a fair bit longer than a modern-day STEP question, even STEP III.
    That's reassuring. The amount of time it took to do it (and possibly even the amount of thinking it required) was a bit worrying.
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    (Original post by Physics Enemy)
    Yes you're right. Perhaps they could impose it on STEP 1&2 though; not both stats and mech, but at least 1 (or 2) applied questions of choice. And maybe 1 applied Q of choice on STEP III. Something like that anyway.
    I guess that could work, or they could say a maximum of 5 pure questions can count towards your score, meaning you don't have to do an applied question to get a grade, but you can't get more than 100 without doing an applied question. However this is against the ethos of STEP which is all about choice and so would probably never happen. Also, I am led to believe that universities prefer aptitude in pure maths at A-level rather than applied maths (UGs/graduates feel free to correct me) so it would seem pointless to force a candidate to do applied maths in STEP if they are capable of getting an S/1 on the pure questions alone, especially if this represents the skill set that Unis are looking for.
 
 
 
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