This week I’ve been making a start on TMA01, and so far I’m really enjoying it. The TMA is split into two parts, with two questions in Part 1 and four question in Part 2. Unfortunately for me, both questions in Part 1 involve lots of graph and diagram sketching! I found it a bit hard to get back into the swing of doing that kind of question, but I think I’ve just about got the hang of it now.

I’ve been dipping into Part 2 of the TMA too, while avoiding the bits that involve sketching diagrams (I thought I’d leave those bits til last, and get them over with in one big sketching extravaganza), and I particularly enjoyed the proof by contraposition question. I don’t remember covering this kind of proof in MS221, so maybe that’s why it’s entertaining me so much, but either way there’s just something very satisfying about proving $A \Rightarrow B$ by proving $\neg B \Rightarrow \neg A$.

Still, as much as I’m enjoying the TMA, I really can’t wait to get back to the GTA course units. I’m just at the start of Section 4 of GTA2 at the moment, and I’m loving it! I particularly liked the section about cyclic groups, and the video programme about isomorphisms (the bit where the presenter says “But first, let’s see what’s going on over here…” and then the camera pans across to a group of dancers doing some kind of Scottish formal dancing was brilliantly surreal. Even better than the “Symmetry counts” programme’s kitchen full of platonic solids!)

I’m very eager to get started on GTA3 too, because the unit is called “Permutations”, which gives me hope that it’s going to be something to do with combinatorics. Some of the exercises using two-line notation for symmetries reminded me a bit of finding all the possible combinations/permutations of the vertices in the figure, so I’ll be very happy if it turns out that you really can leverage combinatorics techniques to explore symmetries. At the very least, I hope the accompanying video programme is as bizarre and entertaining as the GTA2 programme!