Well posted TMA05 off this lunch time this covered the second part of group theory B and I'm afraid I didn't enjoy it at all. The questions seemed biased towards visualisation something I'm hopeless at. I totally bombed the last question as I couldn't get the results from the counting theorem to tie up with the pictures but having spent 3 frustrating hours on it last night I gave up in disgust.
Recap of questions
1 a long tedious question about symmetries of a 3d object and various conjugacy classes
2. A reasonably straightforward one on matrix groups and their subgroups
3. A question on homomorphisms the first part is straightforward, but the second part covers some really deep stuff on the relationship between the Image of a homomorphism and the quotient group which is the
normal subgroup formed from the group and the Kernel. I haven't fully digested all of the links but essentially the image of a homorphism f is isomorphic to G(f)/Ker(f) and aided by some solutions to past exam questions I was able to complete the TMA but definitely need to go back and understand why.
4. A relatively straightforward question on group actions and their orbits.
5 The tedious flag colouring question alluded to above.
In general I feel it unfair that this group theory question is biased to those who have visual skills. Also colouring flags made me feel like I was back at primary school. I'm expecting my lowest score for this assignment. Bring on the last part of the analysis course.
I must admit to being quite disappointed by the treatment of Group theory in M208. Far to many confusing examples which obscure the underlying structure. Why not provide us with a brief introduction to what Lagrange was trying to do with the symmetry groups of polynomials. Why not provide us with an introduction to the rotation group and the special unitary groups that play such an important part in physics. Instead we are expected to count ways of colouring squares or flags and mentally rotate 3 d objects in our head. Very disappointing.
Chris,
ReplyDeleteIf it's any help, TMA5 drove me crackers last year for the same reason - needing to visualise and rotate things in your head.
The answer is somewhere in the associated DVD but I never did quite fathom it.
I think TMA5 also gave me my lowest mark.
On the upside, while the analysis in TMA6 looks complicated at first glance, it's really one large exercise in applying very standard results and should provide a bit of a grade booster. I'm pretty sure I did better on analysis 2 than analysis 1, in terms of TMA marks, anyway.
I avoided as much group theory as possible in the exam and went straight for the analysis stuff.
Cheers its good to know some one else feels the same on the Forum most people seemed to enjoy it
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