I seem to be having great difficulty in recalling any of the Group Theory that I have learnt over the last 4 weeks. It has been particularly difficult to decipher some of the questions and what they are asking for, as the use of special meanings for everyday words, is just piling up. Symmetry, means something different if it is a symmetric group; order, isn't what you do at a restaurant and index is not a catalogue shop. Hmmm!
So I have had the strange experience of learning a unit and then have got to the examples at the end, only to find that it doesn't bear any resemblance to what I have just read. So I have started going through all the exam questions from 2008 onwards, to get a flavour for what I absolutely have to know, to pass the Groups bit of the paper.
I shall learn the question structures and hopefully it will start to make sense.
Goodness knows what Group Theory B has in store for me.
You'll probably find that this point marks the beginnings of "maths by definition". :-)
ReplyDeleteThe terminology will come thick and fast throughout M208, and MST209 if you do that, but you'll quickly get used to it.
I always write the term down, then a colon, then a one or two line definition in non-maths words of what it is/what we're trying to achieve.
You'll get bombarded with ...morphisms in a bit. I was disappointed to learn they're not made from plasticine. :-)
I'm having a similar problem with topology but think I've found a way forward. Keep writing the definitions out over and over again. Until you know them by heart keep testing your self at odd moments during the day and don't try and force it. Pure maths unfortunately is like that it's quite different from solving a complex integral and there really is no alternative but to keep plugging away. I can finally see some light at the end of the tunnel as far as Topology is concerned and the definitions and theorems are slowly beginning to make sense. So perhaps a similar tactic will work for you.
ReplyDeleteBest wishes Chris
I have gone past the point of worrying about whether I can remember a particular definition, theorem or strategy. There are so many of them that I just couldn't keep on top of them all. I am afraid I intend to rely on the handbook and whatever vague feelings I have about how to solve a particular problem.
ReplyDeleteThe problem with Group Theory and a lot of the other stuff is its abstract nature. It seems to be instantly forgettable. Also the pace of the course at one book per week doesn't give you much time to assimilate ideas. My hope is that with practise the ideas will eventually stick.