## Thursday, 22 March 2012

### That sinking feeling

Help, I think topology must be one of the densest subjects to get into. I have to say I'm really struggling with this one as it's quite alien to anything I've come across. Still I'm not alone that does seem to be the consensus of a number of people on the forum.

I think part of the problem, is that one is dealing with general relations between functions, which aren't specified at all. In the analysis sections of M208 there was usually a function which was specified and it was possible, no matter how strange the function to say something about it. For example, the notorious Blancmange function of M208, yes proving it's continuous is a real pain in the neck (See the discussion I've been having with Duncan on this )

but at least you had something to get your teeth into. The function is defined, I more or less know the epsilon delta defintion of continuity and how to test if a function is differentiable or not. OK I might not grasp all the details of the proof but I can get the gist and I hope finally to consolidate my understanding with a few pints with Duncan next week.

With topology it's quite different, the definitions are about relations, between relations, between relations (alright I exaggerate a bit). It's very often definitiion 1, definition 2, combine definition 1 and 2 to get theorem 1. Definition 3 definition 3.1 Definition 3 and Definition 3.1 gives us theorem 2 and on and on, unfortunately there is no real road map as to where all this is going so it seems like wading through treacle.

Having said that, I think I've finally developed some sort of strategy to cope with this course. (a bit too late for the second TMA due in a couple of weeks time), but I think the only way to get a handle on this course is to try and learn the defintions by heart, at least in the first instance, testing yourself at odd moments during the day once those are grasped then you can begin to follow the theorems. This seems to have worked so far for unit A2. At first I was totally baffled, by the defintion of continuity for metric spaces, in terms of balls, (Indeed one can legitimately say topology or at least metric is a load of balls !!) A ball is essentially a generalisation of an  open interval around a point in two or higher dimensional space. However having written it out a few times and more or less learnt it off by heart, it now begins to make sense and I can move on. Hopefully I've not left it too late to catch up. Fortunately we have a tutorial on Saturday and that should give me confidence to tackle the TMA over the next week. In the mean time I'll keep plodding away.

On a brighter note, I got my first TMA back from the Waves course, grade 1, but I dropped a few marks because of silly sign errors and also I had totally missed out a small section of one of the questions. TMA02 of this course is tempting, but as the school teacher said in the Pink Floyd's the Wall, "You can;t have your pudding until you've had your meat, how can you have your pudding if you don't eat your meat? "

So I have to eat the meat of TMA02 for the topology course before I can have my pudding of the waves course.

Finally in a slightly amusing way, I've left my small mark in Edinburgh. I was out drinking with some colleagues from work in the Blue Blazar a local pub just off Lothian Road, when a new guy who's just joined went to the toilet. He came up and said "Thats what I really like about Edinburgh, where else would you see Maxwell's equations scrawled next to some graffiti slagging off Hibs supporters". What is really amusing is that I had scribbled those on the toilet door about six years ago after a rather boozy Christmas do. I was amazed that they are still there.

Hopefully the mist will begin to clear vis a vis topology and I can't wait till my pudding but I must be careful not to gobble it all down quickly otherwise I'll drop some marks for silly mistakes.

1. From what I have heard Topology is one of the most difficult courses in maths at the OU and most people struggle with it, so credit to you for even attempting it. The problem with difficult concepts is that they take time to absorb and often there isn't enough time to do this. Then it starts to feel like you are hitting a brick wall because the more you read the more lost you become! All I can say to you is just keep taking things one step at a time and try not to get too disheartened.

I wish I was more like Maxwell who presented his first paper to the Royal Society when he was still at school (actually he had to get someone else to present if for him as he wasn't allowed to because of his age). I wonder if he ever scribbled anything on a toilet wall in a pub in his youth?

2. Hi Chris, Keith here. Can't post using my normal log-in for some reason.
I was just wondering how the topology is coming along. I don't plan to take it as an elective module but do need some aspects of it for further analysis work, so will study at my own pace.
Is the problem with it that it's abstract in nature? Every introductory book on the subject I've looked at so far has quickly lost me (though Mendelson's book is good http://www.amazon.co.uk/Introduction-Topology-Dover-Books-Mathematics/dp/0486663523 ).
Also, I saw elsewhere you were planning to do M347 at some point - a good choice mate. It's calculus city.

3. At the minute it's just one damned definition after another and the only way I can get a handle on them is to keep writing the definitions out to learn them off by heart. As Daniel has said it seems like it's all proof without pudding. I have this weekend to finish the second TMA and I'm only about half way through Block A.
So not going very well. I'll probably do M347 in October 2013 alongside either M3338 if it's running that year or M346. It means postponing doing the MSc but M347 could be useful as well as interesting for work. It looks like We'll finally be doing a course together in October. As for the posting problem I had similar problems but don't know why, posting as anonymous seems to be a work around but not very satisfactory I admit.

4. I've registered for M347 in October 2013, as my bargepole hasn't arrived from Amazon yet for touching topology.

Topology looks way too abstract for me.

MS324 is hard. Looking at some of the past exam papers, some parts of questions are repeated exactly. That must help.