A classroom on a wet wednesday evening

Wonderful thing Open University tutorials. Number of people in the tutorial group, twenty seven; attendees at the tutorial, three.

The best one I ever went to was when I was the only bugger there but it did mean that I got two hours personal tuition on vectors and matrices from a research fellow of a Cambridge college.

To be fair the tutorial earlier in the week was not too badly attended with about 8 people showing up on a wet and cold winter evening in a sixth form school in Cambridge*. I'd already covered the subject of the tutorial but I tend to get more out of tutorials that way and I find them handy just for picking up tips on how best to do things rather than for ab-initio instruction.

This time the big take away was "how not to show a proof".

Lets say you have the focus-directrix property of a non-degenerate** conic Pd = ePF. Now what you don't do is start off by saying "As Pd = ePF then... blah blah blah ...see they are"

Rather you go

"Pd = some formula... rearrange rearrange rearrange... = x"

and

"ePF = some other formula ... rearrange rearrange rearrange... = x"

"so Pd = ePF for this conic"

If you don't do it that way then you fall victim to an argument by circular reasoning which, as a rabid athiest used to duffing up religious types when they use such arguments I should have realised.

So even if you've got down pat the subject your OU tutorial is about it's always worth going along IMHO because you're bound to pick up something.

And what else would you be doing on a wet wednesday evening anyway.



* Which follows in the noble tradition of all educational establishments by selling undrinkable coffee that tastes like hot dishwater with grit in it.

** I have a picure in my head of a "degenerate conic" as a parabola that hangs about smoking behind the bike sheds and committing acts of petty vandalism.

Madonna's Bra

I was studying chapter A2 of MST221 this weekend, working away in the office I use when I work from home. As is usual the dogs were in there with me to give me a hand with the algebra sleep on the sofa but at one point Mrs Dracunculus came in with a cup of tea and asked what I was up to.

Being all enthusiastic about my new knowledge of parabolas and hyperbolas I started to scribble some cones on my whiteboard and show what happens when you cut them up.



"Oh," said Mrs Dracunculus, " so how come you have to use Madonnas' bra in mathematics?"



She's not very mathematical, Mrs Dracunculus.

0,1,1,2,3,5,8...

Just finished Chapter A1 of MST221 in which we get to poke around that set of numbers up there, the Fibonacci sequence, an example of a second order recurrence system. All quite interesting stuff and I didn't have too many problems getting my head around the sums including the derivation of a closed form for such sequences - which given the struggle I had with wrapping my poor dragony brain around the same derivation for first order sequences last year I was rather happy with.

I did have a bit of an issue with the algebra when doing the exercise to derive a closed form for a Cassini identity as the OU have started truncating their solutions and I am assuming just expect you to be able to follow this stuff by now.... bit like this...



Anyway a quick email to the tutor (and a same day response - great service!) gave me a poke in the right direction with something that is bleeding obvious once you've been shown it, which is.

 n-1                          n       n+1
a     is a common factor of  a   and a

so 2 is a common factor of 4 and 8, 3 is a common factor of 9 and 27, and so on.

I was even happier when Question 2 of the TMA was on just such an identity.

So, onto conics