oh for fuck's sake

[ajva]

The result mentioned at the top of the page here is an important result in my current course that there are always questions on in the exam. e.g. I will be working out how many equivalence classes of (= different ways of) colouring there are for a particular shape with a certain number of colours. It's also piss easy to say what the colourings are (ie. Oh yes, there will be one all red colouring and one all blue colouring, three one red and five blue etc. etc. blah blah - you just stick it in the formula, and it's easily understandable why it works).

Except... when the theorem is stated like it is on that webpage, it's so fucking impenetrable that I barely recognise it.

Bloody mathematicians and their abstruse ways. Grrr. No wonder people think maths is impossible. I reckon it's 'cos lots of them are ugly and need to prove their superiority in other ways, like intellectually excluding people.




Disclaimer: No, not all mathematicians are ugly. I know that. Some of my sexiest friends are mathematicians. I'm being facetious. Chill.

Comments

[ciphergoth.livejournal.com]

Update: I now understand the first sentence.

I've done some searching on "cycle-index polynomial" and gained a little enlightenment but not much.

What books are you using for group theory? It looks like I could do with learning some more...

[ajva.livejournal.com]

*ROTFL*

Many congratulations - always knew you were a genius. ;o) Actually, I'm only using dedicated OU material at the moment. They're very good at teaching maths as their books explain it very clearly and they link things together usefully. The section on Polya's theorem is brief and just looks at how considering symmetry groups acting on sets leads to an easy way of figuring out how many different colourings there are of certain three-dimensional objects. The trickiest bit, I always think, is making sure you've got the symmetry group right: it's easy to mess up on that one but after that it's plain sailing. Your man on the web page is obviously about to launch into a broader exploration of what Polya's Theorem can cope with.

I can explain cycle index polynomial but I'll leave it till Monday if you don't mind as it's home time and I want my dinner.

My current course is called M336 Group Theory and Geometry and is an interesting mixture of group theory and wallpaper patterns/three-dimensional lattices (stopping just short of detailed work on crystals, really). Interesting stuff. :o)

[ajva.livejournal.com]

Doesn't have to be "certain" objects, of course - can be anything. It's just that's what we tend to use.