I must admit, this one went by in a blur. First section was on describing groups, and introduced the idea of a group presentation. Second section was "conjugates, centralisers and centres", presenting some new concepts, followed by "groups of small order" which described how to work out what smaller groups were isomorphic to. The whole chapter ended with "finite p-groups" which discussed groups that were direct products of other groups of prime power order. This leads neatly to the next section which seems to be almost entirely be talking about groups of prime power order.
The learning curve is real.
One of the whole points of me starting this site was to write about the things I got wrong. Making mistakes is how you learn, right? My first assignment on number theory has been returned to me and it turns out I received 100% for it. Which is good. But it's also frustrating, because I don't feel that assignment reflected the difficulty of the material. Worrisome. Well this was assignment 1, I'm still at the beginning. Plenty of time to screw up yet.
Despite the fact I am speed-reading for the sake of catching up, this chapter did seem to go by suspiciously quickly.
Direct products was an interesting new topic, cyclic groups added to some knowledge I already had, and the chapter finished off with group actions which was mostly revision.
Next chapter is just "Finite Groups", though I'm guessing with a whole chapter ahead of me, it turns out there's quite a lot of stuff I don't know about finite groups.
This was a standard speedy revision session in group theory. Axioms, subgroups, cosets, normal subgroups, quotient groups, isomorphisms and homomorphisms.
It was nice to get back into something that was familiar to me.
Next chapter is vaguely named "Towards Classification". Seems to introduce the concept of a direct product, and revise orbits and stabilisers. I'm hoping I'll be able to get through this quickly, as I'm starting to fall behind slightly...
…is learning mathematics.
