Over the last couple of weeks I’ve been making my way cautiously through Unit GTA4 – I say cautiously because there are a couple of warnings in the text about how relatively difficult some students find the last section of this unit, so I wanted to make especially sure that I had a good understanding working with cosets before I tackled the intimidating Section 6.

Actually, I think I struggled more with Sections 2 and 3 than with the final section; there were a few questions that I just didn’t even know how to begin to answer (thankfully the solutions given at the end of the book did make sense when I eventually read them – so at least it wasn’t completely incomprehensible!).

Section 6 itself, which is about infinite quotient groups, was much more manageable than I expected – quite good fun, in fact! Earlier on in the unit, I was wowed by the fact that you can divide an infinite group, such as $(\mathbb{Z},+)$, into a finite number of cosets – I was even more impressed with the bit in Section 6 about dividing $\mathbb{R} / \mathbb{Z}$ into cosets that form an infinite quotient group. I’m not sure why exactly, but an infinite group having an underlying structure which is isomorphic to another infinite group pretty much blows my mind!

The question in TMA02 that relates to this unit was more straightforward than I expected; I think the questions based on GTA2 and GTA3 are a bit more challenging, although it could just be the fact that I’ve had a long time to get used to working with groups and subgroups now. So the first draft of TMA02 is now pretty much finished, bar any changes due to the feedback I’ll get from TMA01.

Now it’s on to the first unit of the Linear Algebra block, which is about vectors and conics. I must admit, I’m not particularly looking forward to this unit – I’d much rather get straight on with Group Theory Block B, but unfortunately I’ve got five units of linear algebra and four units of Analysis Block A to get through first!