Well, I think things are going ok at the moment and I am happy with how things are turning out. I had TMA02 back a couple of days ago and I managed to score another 100%. Given that I am completing the TMA's ahead of the tutorials I feel pretty pleased with myself. However, TMA02 didn't have anything in it which I thought was particularly tricky and so I must expect a reality check at some point.
I have now completed TMA05. I did a couple of questions whilst I was away at Easter. I seem now to have a good grasp of the counting theorem and can see better how it works. This means I have now nearly caught up with myself as TMA06 is on the final block of the course which I am now working on.
AB2 on differentiation is done and I am into AB3 on integration. I quite like this business about upper and lower Riemann sums and how you can still determine whether a function is integrable even though it has discontinuities (though the function has to be bounded). It is hard to get your head round initially because of using infima and suprema instead of maxima and minima, but I can see that it is more sophisticated.
One thing I still dread are the proofs. I think the only reason I still manage to get through these is because I have a conscientious nature and I like to complete things. However, having worked through a proof and understood how one step leads to another I am often left at the end feeling that things could have been explained in a much better way.
I think the trouble is that M208 is possibly trying to do too much by proving most of the theorems that it uses. This means that perhaps not enough time is devoted to the proofs and evidence of this is that they are often labelled as 'optional reading'. Sometimes I absolutely pull my hair out trying to follow where the proof is going and I expect this is because it has been compressed into a page or so. Further explanation and post proof discussion would be a great help here. Perhaps it would have been better to include fewer proofs but explain those that were presented in more detail. It is very off-putting.
My belief is that maths should be understandable by everyone and often the only reason it is not is because of poor explanation and leaving too much to the reader. What is more useful? A short block of hieroglyphics that is a dense as a piece of iron and only readable by those who have been initiated into the rights of the temple or a longer, well described proof that everyone can follow. I know what I favour!
Cracking result on TMA02 Duncan. Well done. I share your views about the volume of proofs. Some of them seem rather superfluous at times. I often get to the end of a unit and my list of 'essential' got to know knowledge, for the exam, rarely includes having to have a deep understanding of the numerous proofs that they throw in. It is a shame, as it feels like skimming, sometimes.
ReplyDeleteI think we both did Ok didn't we! It is an odd situation that really ought to be remedied. There is a sort of schism in the church of the OU. On the one hand they are very keen to prove nearly everything, but on the other, when it comes to testing its students, we are only expected to 'calculate' stuff and rarely prove anything. This division is unsatisfactory for learning. We would all suddenly find the proofs much more interesting if we were asked to prove theorems in an exam (as happens at Cambridge).
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