I am still slogging on with the number theory and groups courses. Regularly I ask myself why I am doing this, but then I know that I like having something to focus on that keeps me busy. But sometimes it is just so blooming difficult!
At the moment I am trying to cram in some work on TMA03 of the numbers course. I sort of dread it in advance because these TMAs are really quite difficult. Often the questions don't relate directly to the course material. They use the ideas but in a way that you haven't seen before, so it really makes you think. There is, however, the feeling of huge elation when you do manage to conquer a problem. I take these questions a small chunk at a time. Often I will read the next part of a question and start mulling it over in my head. At first it seems impossible, but after a few glints of ideas, you get an idea of the framework for an answer and then you can flesh the whole thing out. I often go to bed thinking about a knotty problem. It is a good time to give a problem your undevoted attention without distraction, but I can't say it is a good way to get to sleep!
I have now finished NT6 on quadratic reciprocity. One more book and I would have the third block finished for M381. The groups course is going ok. The problem is that the ideas are increasingly complicated and although I tenuously understand a book when I have read it, it rapidly gets forgotten after a few weeks. I have finished GE3 and am currently on GR4 which is investigating finite groups and what we know about them.
