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  • Integration "by parts" [was Re: Functions computed by Turing Machines .

    From Andy Walker@21:1/5 to Richard Heathfield on Mon May 5 13:47:43 2025
    On 04/05/2025 22:18, Richard Heathfield wrote:
    [...] I hit a hard wall (integration by parts) and never really recovered.

    Is that still a "hard wall" for you? I know how annoying it is
    to be told that something you find hard is "really" very easy, but in this
    case it really is, and the problem is usually bad teaching. That in turn
    is usually down to pay; if mathematicians can get two or three+ times the salary by going into accountancy, computing, ..., then it's not surprising
    that only the most dedicated go into teaching and the rest is left to a smattering of people with school maths who barely understand what they're trying to teach. Fair dos, some of them turn out to be excellent, but the general standard is dire. Recent prominence [at least in the UK] given to "STEM" is perhaps changing that, but it's too late for most people.

    --
    Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Wolf

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  • From Richard Heathfield@21:1/5 to Andy Walker on Mon May 5 16:49:08 2025
    On 05/05/2025 13:47, Andy Walker wrote:
    On 04/05/2025 22:18, Richard Heathfield wrote:
    [...] I hit a hard wall (integration by parts) and never really
    recovered.

        Is that still a "hard wall" for you?

    It's been many years since I last visited that part of the garden.


    I know how annoying it is to be told that something you find
    hard is "really" very easy, but in this case it really is, and
    the problem is usually bad teaching.
    I have no doubt that to real mathematicians it's a walk in the
    park, but not to me. I managed to pick out a path in which I
    never needed more than algebra, trigonometry, and a certain
    aptitude for bullying computers. The only integration I've done
    since sixth form has been integration testing.

    <snip>

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within

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  • From Andy Walker@21:1/5 to Richard Heathfield on Tue May 6 17:16:31 2025
    On 05/05/2025 16:49, Richard Heathfield wrote:
    [...] I hit a hard wall (integration by parts) and never really recovered. >>      Is that still a "hard wall" for you?
    It's been many years since I last visited that part of the garden.
    I know how annoying it is to be told that something you find
    hard is "really" very easy, but in this case it really is, and
    the problem is usually bad teaching.
    I have no doubt that to real mathematicians it's a walk in the park,
    but not to me.

    This particular topic is not even a "walk in the park"; it's
    a step back from where you must have already reached in calculus.
    Unless, that is, it was presented to you as an inexplicable formula,
    perhaps by a teacher struggling with the whole concept of calculus.
    If so, you wouldn't be the only one. Many years ago a colleague and
    I were jointly teaching a postgraduate modelling course, and a
    student who had a top first in maths shame-facedly stuck his hand up
    and said, "Sorry, but could you please explain integration by parts?".
    Gasps from the audience [he really was known to be an exceptionally
    good student], but he said he'd struggled with the concept for nearly
    a decade. We explained, and he said "Oh, is that all it is?". Other
    students said then that they had also never understood it, just done
    it by rote. It's a common problem when maths is taught by people who
    are at or beyond the limit of their own knowledge.

    I managed to pick out a path in which I never needed
    more than algebra, trigonometry, and a certain aptitude for bullying computers. The only integration I've done since sixth form has been integration testing.

    :-). No-one needs more maths than that unless they are doing
    "serious" maths. But it's a shame if people who are interested and
    competent get stuck not when the going gets tough but when something
    obvious is explained badly. I'm sure similar things happen in all
    subjects, not least computing.

    --
    Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Richards

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  • From Richard Heathfield@21:1/5 to Andy Walker on Tue May 6 17:23:46 2025
    On 06/05/2025 17:16, Andy Walker wrote:
    I'm sure similar things happen in all
    subjects, not least computing.

    In C, it's pointers.

    Pointers are /so/ easy, but I have seen them reduce grown men to
    tears. And yes, it's mostly bad teaching that's to blame.

    --
    Richard Heathfield
    Email: rjh at cpax dot org dot uk
    "Usenet is a strange place" - dmr 29 July 1999
    Sig line 4 vacant - apply within

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