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    (Original post by und)
    It's very similar to a STEP question I've seen, but I can't remember which paper. DJ will know obviously. I think it could have been posed as a general question, because numbers are yucky. :yucky:
    That's quite a good idea and would probably make the question more STEP style.
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    (Original post by und)
    It's very similar to a STEP question I've seen, but I can't remember which paper. DJ will know obviously. I think it could have been posed as a general question, because numbers are yucky. :yucky:
    I do actually know which one you mean (I think they use a chicken crossing a road in the specific question as well) but I can't for the life of me remember which paper it was from.
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    (Original post by DJMayes)
    I do actually know which one you mean (I think they use a chicken crossing a road in the specific question as well) but I can't for the life of me remember which paper it was from.
    That's the one. I believe it was a STEP I Q9, but I don't know which paper.
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    (Original post by und)
    That's the one. I believe it was a STEP I Q9, but I don't know which paper.
    1997 STEP I Q9. Will have to go back and do that tomorrow as I skipped over it when I first saw it (Which was back in November, but still).
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    (Original post by Felix Felicis)
    Do I really have that many holes in my solutions? Would you mind pointing one or two out?

    No of course not. I was joking, with slight innuendo
    Posted from TSR Mobile
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    (Original post by bananarama2)
    Well all of particle physics is to do with symmetry groups, which slightly related to sets (isn't it?), so....there is potential.

    Heck. The Higgs mechanism is to do with symmetry breaking.
    Groups to Sets is like Chemistry to Physics.
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    Problem 47 *** (came across this nice problem thanks to a friend )

    For 0 < p< q, evaluate

    \displaystyle \int_{-\infty}^{\infty} \dfrac{x \sin x}{(x^2 + p^2)(x^2 +q^2)} \ dx

    and deduce that

    \displaystyle \int_{-\infty}^{\infty} \dfrac{x \cos x}{(x^2 + p^2)(x^2 +q^2)} \ dx = 0
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    (Original post by ukdragon37)
    That's exactly what I've been thinking, but I can't come up with anything either.
    (Original post by shamika)
    blah
    http://en.wikipedia.org/wiki/Causal_sets

    might be of interest
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    (Original post by ukdragon37)
    That's exactly what I've been thinking, but I can't come up with anything either.
    have you done topos theory?
    http://math.ucr.edu/home/baez/topos.html
    has some nice links to physics
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    (Original post by ben-smith)
    have you done topos theory?
    http://math.ucr.edu/home/baez/topos.html
    has some nice links to physics
    A little, yes. But then topos theory is quite a different beast to set theory.
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    I just wanne say Math is sexy !!

    ( more i dont know because i am a musician/and former model )
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    (Original post by Noble.)
    ...
    Spoiler:
    Show
    While evaluating the triple integral in spherical polar coordinates, I got to evaluating the integral in the middle (with respect to theta) and by using the substitution u=a\cos \theta , both limits ended up as a and so the integral is just zero. This meant that I ended up integrating zero with respect to phi to get a non-determinable constant... is that supposed to happen?

    I only taught myself a little vector calculus a few days ago, so I'm still a little hazy on some parts.
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    Solution 47

    \displaystyle\int_{-\infty}^{\infty} \frac{x\sin x}{(x^2+p^2)(x^2+q^2)}\,dx=\frac  {1}{q^2-p^2}\left(\int_{-\infty}^{\infty} \frac{x\sin x}{x^2+p^2}\,dx-\int_{-\infty}^{\infty} \frac{x\sin x}{x^2+q^2}\,dx\right)

    \displaystyle \begin{aligned}f(t)=\int_0^{ \infty} \frac{\sin tx\,dx}{x^2+\lambda^2}\,dx \Rightarrow \mathcal{L} \{ f(t)\} &=\int_0^{ \infty}e^{-st}\int_0^{ \infty}\frac{x\sin tx\,dx}{x^2+ \lambda^2}\,dx\,dt\\&=\int_0^{ \infty}\frac{x}{x^2+ \lambda^2}\int_0^{\infty}e^{-st}\sin tx\,dt\,dx\\&=\int_0^{\infty} \frac{x^2}{(x^2+ \lambda^2)(x^2+s^2)} \,dx\\&= \frac{\pi}{2(s+\lambda)}\end{ali  gned}

    \displaystyle \mathcal{L}^{-1}\left\{ \frac{\pi}{s+\lambda}\right\}= \frac{\pi}{e^{\lambda}}\quad \left( = \int_{-\infty}^{\infty} \frac{x\sin x}{x^2+\lambda^2}\,dx\right)

    Hence \displaystyle\int_{-\infty}^{\infty} \frac{x\sin x}{(x^2+p^2)(x^2+q^2)}\,dx = \frac{\pi}{q^2-p^2}\left(\frac{1}{e^p}-\frac{1}{e^q}\right)\end{aligned  }
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    (Original post by Lord of the Flies)
    k = l = m = 1,\; p = n = 3 satisfies that equation. Is there something missing from the question?
    (Original post by metaltron)
    What's even more worrying is p isn't congruent to -1mod8. I just spent ages on this question!
    Gentlemen, I beg your pardon. The condition should be p > 3.
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    (Original post by Star-girl)
    Spoiler:
    Show
    While evaluating the triple integral in spherical polar coordinates, I got to evaluating the integral in the middle (with respect to theta) and by using the substitution u=a\cos \theta , both limits ended up as a and so the integral is just zero. This meant that I ended up integrating zero with respect to phi to get a non-determinable constant... is that supposed to happen?

    I only taught myself a little vector calculus a few days ago, so I'm still a little hazy on some parts.
    I ended up with zero as well, all though I didn't have to substitute anything. I thought I'd got it wrong and I couldn't see why, so I gave up.
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    (Original post by ukdragon37)
    Groups to Sets is like Chemistry to Physics.
    So one uses the other a little bit?
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    (Original post by bananarama2)
    I ended up with zero as well, all though I didn't have to substitute anything. I thought I'd got it wrong and I couldn't see why, so I gave up.
    Maybe it is so... but then how to link the next part with the previous part...
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    Guys, Indeterminate's integral should actually be problem 47.
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    (Original post by bananarama2)
    So one uses the other a little bit?
    Somewhat, yes.

    If set theory is Physics, then
    group theory is Chemistry,
    field theory is Biology,
    and category theory is Philosophy.

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    (Original post by ukdragon37)
    Somewhat, yes.

    If set theory is Physics, then
    group theory is Chemistry,
    field theory is Biology,
    and category theory is Philosophy.

    (quantum) Field theory looks so interesting!
 
 
 
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