I wasn't there. I mean the content of the course really as opposed to anything else. Why was this lecture so rubbish?
It was pretty much entirely devoted to a proof that if R is an Euclidean domain, so is R[X] which was long, tedious and boring. Also, I'm not enamoured by the recent material we've covered (ex. 3 is probably going to be horrifically boring). I suppose once we get on to modules though it will start perking up again.
Out of curiosity, does anyone know why the Archimedeans' IA lecture notes were taken down?
Apparently, one of the Caius first years let it slip that they were available to one of the lecturers, who wasn't happy that they'd put them up there without his permission. Just a rumour though.
Anyone know how to do question 5? I've missed too many lectures and I've got no idea what's going on.
I'm reading the notes and it's confusing me: they say the gradient vector is normal to the line, even though it'd surely be tangent to it (as it's the gradient?!)
My working for part (a):
Put f(x,y) = 1-(x^2)(y^2) Gradient of f(x,y) = (-2(y^2)(x), -2(x^2)(y)) with x=2, y=-1/2 which evaluates to (-1,4).
Shouldn't (-1,4) be the tangent vector of the curve? My notes say it's normal.
Anyone know how to do question 5? I've missed too many lectures and I've got no idea what's going on.
I'm reading the notes and it's confusing me: they say the gradient vector is normal to the line, even though it'd surely be tangent to it (as it's the gradient?!)
My working for part (a):
Put f(x,y) = 1-(x^2)(y^2) Gradient of f(x,y) = (-2(y^2)(x), -2(x^2)(y)) with x=2, y=-1/2 which evaluates to (-1,4).
Shouldn't (-1,4) be the tangent vector of the curve? My notes say it's normal.
Your notes are right, grad f is normal to the level sets of f. Grad f points in the direction of greatest increase of, for instance in this case f(x,y) = x^2*y^2.
Anyone know how to do question 5? I've missed too many lectures and I've got no idea what's going on.
I'm reading the notes and it's confusing me: they say the gradient vector is normal to the line, even though it'd surely be tangent to it (as it's the gradient?!)
My working for part (a):
Put f(x,y) = 1-(x^2)(y^2) Gradient of f(x,y) = (-2(y^2)(x), -2(x^2)(y)) with x=2, y=-1/2 which evaluates to (-1,4).
Shouldn't (-1,4) be the tangent vector of the curve? My notes say it's normal.
Yves' lectures are really quite useful, whereas the notes are a little less clear (immediately, at least). I've realised they and LAG (only because notes are put up way too late) lectures are the only ones worth going to. A little annoying that Calculus is a 10am and 9am though.
I still need to hit up klute before my friend graduates. Is it as bad as all that?
(Sorry for dredging up a fairly old post) I didn't think it was that bad... I mean the music is pure cheese but the quaddies are pretty good for getting you wrecked.
(Sorry for dredging up a fairly old post) I didn't think it was that bad... I mean the music is pure cheese but the quaddies are pretty good for getting you wrecked.
Is the definition of a tautology that your reasoning from an empty set like the thing that it follows from is empty? Or is the definition of a tautology that the valuation is 1. Like gave weird definition for empty being the empty set definition. However, thought a tautology is something like P or not P, not vacuous reasoning.
I haven't come up with a way of proving that the compact linear operators are a closed subset of the bounded linear operators without invoking some horrible notation like that.
I haven't come up with a way of proving that the compact linear operators are a closed subset of the bounded linear operators without invoking some horrible notation like that.
I think by being careful you can WLOG the nasty notation out.