Last book

Well, I am finally on the last book of M208, AB4, which is on power series and I am excited by the prospect of nearly completing my studies of this course. Once I have finished this book, I just have TMA06 and 7 to do and the exam in October. I have made a start on TMA06 and 7 is based on the whole course.

AB3 on integration didn't represent too much of a problem. There was some discussion of integration techniques, reduction formulae, inequalities, Wallis' formula and Stirling's formula. I am glad to see that finally in M208 for a substitution of u=x² they don't shy away from writing du=2xdx as a way of rewriting an integral. It makes me laugh that this should appear in the 'rigorous' realms of M208 but scrupulously avoided in the 'less rigorous' earlier courses of MST121 and MS221.

In the last couple of weeks I have been asking other people if they read the proofs in M208 and it seems that they don't (see my previous post). This supports my opinion that M208 could have been written differently and perhaps it would have been better to have put the proofs at the back in an appendix. So, unless you are of the conscientious type or particularly keen then the most important thing is to get an idea of what the theorems are and to try and use them.

I have also been agitating on the forum about the lack of interest in errata. Here is what I said:

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I am sure I read somewhere in the blurb when I first started doing these maths courses that the OU liked students to report any errata that they found in the text and this was what the OU regarded as being a 'model student'.

Yes, I am correct. Here is a quote from the back of the pink pages for MST121:
"Some handy hints on how to be a model student!"
"Think you've found a mistake? Check the Stop Press and the course website to see if it's mentioned there. If not give your tutor a ring. You may save other students a great deal of heartache!"

I have always taken this advice seriously and I am a keen nitpicker. One of the reasons for this is that if I find something in the text that jars it could mean one of two things - either I haven't understood the text properly or there is a genuine mistake. So I am always keen on these sort of issues. I often find that by pursuing them I get a much better understanding of what is being said and there is always the 'prize' of finding a mistake that no-one else has yet reported.

I also think that it is important in maths to be pedantic. It is in the very nature of the subject to make absolutely sure that the text is 100% accurate and I agree with the sentiment that inaccurate text leads to confusion and heartache.

When I was doing MST121 I did find a reasonably significant error that had to be corrected in both the book and the handbook. I have also managed to get a couple of mistakes from book I1 of this course recognised as errata. However, I do feel that it is an uphill struggle and it isn't easy getting these things recognised! Tutors are busy people and there is no obvious direct channel for managing this kind of thing.

This I think is a pity. What better way to refine the text and at the same time get students really understanding what they are reading. However, if there is no easy way to report potential issues or it seems an uphill struggle, then the motivation for students to be active diminishes.

Personally, I am motivated to do this (I am a natural pedant!) but over the course of M208, I have become less inclined to report things because I am not really sure that the OU is that interested. Personally, I think the OU should be giving out real prizes to students who find mistakes in their material - it would be a great way to get students to really understand what they were reading and to focus on it with the intensity of a laser beam.

Another problem is that every time I find something that is an error it undermines my confidence in the material. After all, I am just learning this stuff. If I can find a mistake then just how good is it? What would someone find if they were a real expert? It's another reason why all mistakes (including printing errors) should really be rectified and new editions of the material published.

But, hey ho, who am I to tell the OU what to do!
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I am pleased to say that since I have agitated about this there has been a good response from the course module team and they do now seem to be taking notice of any new errata and will be issuing a new errata pdf in the next couple of weeks (rather than postponing this until the beginning of the next course). However, I wish there was a more direct channel for this sort of thing and more encouragement for students.

Happy

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!

More of a challenge

I have been tackling TMA05 on and off over the last week and it definitely seems more of a challenge. Actually, I quite like the situation where I am faced with a question which, at first glance, I have no idea how to start. I have got to the part of TMA05 that asks about homomorphisms, kernels and images (GTB2). One part seemed very straight forward but the other half was a bit of a devil (but worth the same marks, strangely enough). I wrestled with it for an hour or so and then I had to leave it. The next day I was out shopping and suddenly I had an idea about how to go about it. This is always such a thrill and why I like questions that are a challenge. Then comes the delicious joy of nailing it completely and seeing all the arguments and theories stack up in one neat pile. Ahhh...It is the reason why I love maths.

Unbelievably I am still finishing off AB2 - just a couple of pages to go. This has been about l'Hopital's rule for finding limits of functions of the form f(x)/g(x) where the limit is required at x=c but f(c)=g(c)=0. I watched the dvd about this topic and was pleased to see David Brannan appear on the screen - the David Brannan who wrote the book on analysis. The dvd must have been a video at one time as it is all looking a bit dated now - not quite kipper ties but verging towards that.

I reckon that at this rate I will have completed the course by about June. That will give me plenty of time for consolidation and, almost certainly, a bit of a much needed rest. The exam has now been pencilled in for Wednesday 17th October, so it will just be a case of getting through this and then I will be a free agent again. Yippee!

Or will I....