Ok momentary panic over. I've decided after the tutorial to stick with the Topology. I get the impression that we are all struggling with it. Even our tutor Alan says he's not sure about some bits of it. Anyway the tutorial clarified some issues or at least showed how to go about tackling questions. My mate Neil showed a brilliant insight into one of the questions involving whether there was a path in Z between all elements of Z for a topology which consisted of {0,z} U (Subsets of even numbers). Our tutor had showed that there was indeed a path between odd and even numbers and was about to go through the same tortuous reasoning to show a path between the even numbers and a path between the Odd numbers. When Neil interjected and said that if there is a path between an odd and an even number then there is also a 2 step path to an even number or odd number if P(a,b) is a path from a to b where a is odd and b is even there is also another path

P(b,c) from b an even number to c an odd number so there is also a path from a to c which is the sum

P(a,c) = P(a,b) + P(b,c) and as a and c are both even or odd then this shows that there is a path for all elements of Z. Anyway it's battling on with the TMA this week. I feel a bit more confident and hope to finish by the end of next week. One of the problems as Alan admitted is that the course material gives very few examples to illustrate the definitions and there does seem to be little or no motivation for them. I will probably do M303 the new pure maths course when it comes on the scene even though it is an excluded combination as it will help me consolidate my meagre understanding of the course material for M338, also as I wont be doing the group theory course M336 then its a chance to cover that also M303 contains an introduction to groups rings and fields. So I will put this into my third (!) open degree. I'll be concentrating on Music for the next 4-5 years so don't think I want to embark on postgraduate work for either maths or philosophy. I want to do at least the new philosophy 3rd level course and there is going to be a new third level music course appearing on the scene as well. I might also include the two third level astrophysics courses and the second level Chemistry course we'll see.

The Festival starts for me on Wednesday and I'm going to quite a few of the concerts in the Usher Hall I will also be taking a few days off. I'll give reviews of the concerts I'll be going to over the next few weeks. The itinery for this week is

Wednesday 15th Tristan and Isolde

Thursday 16th Syzmanowski Symphony No 1 and Brahms No 1 this includes a performance with Nicola Benedetti

Friday 17th Syzmanowski Symphony No 2 and Brahms No 2

Saturday 18th Syzmanowski Symphony No 3 and Brahms No 3

Sunday 19th Syzmanowski Symphony No 4 and Brahms No 4

I must confess I don't really know the Syzmanowski Symphonies and so I'm looking forward to getting to know these pieces.

Anyway I may bump into some of you who read this blog there. I'll usually be in the Traverse theatre bar after the concerts.

The piano practice is coming on I'm doing at least 1/2 hour per day before I get to work, This week I want to consolidate what I have done so far namely scales and broken chords for C major, D major and G major. The left hand and right hand parts for two of the Grade 1 pieces separately and a rather pathetic attempt to put them together and Chapters 1 - 4 of Fanny Waterman's book volume 1.

Next post I'll tell you how the Key system of Western music and the circle of 5ths can be reduced to modulo arithmetic.

Glad to hear you are sticking with topology Chris. Hope you are getting on ok.

ReplyDeleteNice as it is to hear myself described in a good light, I'm sure that Alan was going to say exactly what I said!

ReplyDeleteGlad to hear that you aren't giving up on the topology; Graham and I were beginning to feel a wee bit depressed that you might be giving up on pure maths. We have hopes of brining you over to the light side of the force.

arb

nellie