## Wednesday, 9 March 2011

### Just a quick one

Hi just a quick one to say I finally got my GENSTAT licence key should anyone do M346 and you run into problems then contact the M346 course team directly. So I spent an exciting evening learning how to read in files, generate statistics and plot histograms and normal plots. Hopefully things will get better I'll start the TMA over the weekend.

Also got my first TMA for M208 back pleased with the result but it's early days yet. Dropped 1 mark in the induction question as I used a short cut in writing out mathematical expressions in terms  of P(k) and P(k+1) which Alan told me was meaningless as P(k) is a proposition not a mathematical expression (ouch). Apart from that most of the rest of the TMA went well. The questions were on

a) Drawing Sets and applying transformations
b) Composite Functions
c) Proof by Induction
d) Complex Numbers
e) Equivalence Classes

There has been quite a discussion on equivalence classes on the M208 forum partly because I suspect that their significance is not really bought out. In group theory they play a major part in partitioning the group by it's various symmetry relations. For dihedral groups in particular the conjugacy classes correspond to the varous symmetry operations for a triangle for example we have the identity, three rotations and two reflections. Each of these belong to a separate conjugacy class. The classes play an important role in representation theory which I hope to expand on in more posts. Essentially if we represent each symmetry operation by a matrix the sum of the diagonal elements of each type of matrix (the trace ) is the same for each type of symmetry operation so instead of using a group table to represent all the invariant operations we can still retain a lot of the essential information of the group by concentrating purely on the traces of each type of matrix. These are called characters for more watch this space .....

#### 1 comment:

1. Hi Chris,
Fascinating blog. How are you managing to do 3 courses at once? That's mind-boggling.
I think equivalence classes were a hot topic on last year's forum, too. Compared with almost all other areas of M208, ECs seemed to be the least explained (well, these and the counting theorem, which crops up in GTB and nearly sent me crazy).
I guess you'll be somewhere around the linear algebra block now? Fairly straightforward, in fairness. The analysis blocks are awesome - really well-explained and great fun.
Good luck with all your courses - I've no idea how you manage to do all three - I'm falling apart at the seams trying to do MST209 and M248 at the same time. :-)