I think that it would be very dangerous to underestimate the 'introduction' part of the Open University course M208 Pure Mathematics. The intro consist of 3 books which cover the required knowledge, that you are expected to have under your belt; before embarking on the course.
It covers logic, set theory, functions, complex and modular arithmetic and is a sudden and violent introduction to a level of rigour, that you tend to only get at a Funeral home. I have found, coming straight off of the back of MST121 Using Mathematics, that there are some gaps in my knowledge base. They are little things that the course never really taught; Including the rigour that is required, to answer even the simplest of example questions on M208.
What has been a shock to me, and has been by far the most difficult part of the last 3 weeks of study; has been the way that you are required to explain results, that seem so bloody obvious. You can quickly get confused and muddled, trying to explain something that is ostensibly so simple, in such formal terms.
As an example, I struggled for hours, trying to prove that set A was contained in set B and set B was contained in set A. When I first looked at the question, I instantly knew what the correct answer was, and why it was so. But could I explain it in the convoluted mathematical way, required in the model answer? Could I hell. I have literally had to rote learn the structure of some of those phrases that seem to crop up, including those charming "hence's" and "therefore's".
It reminds me of the time that I learned to speak French. It took forever to get used to the way that a sentence was structured, and it took much practise to learn and then repeat those structures. The only problem is; that I have worked myself silly for the last 3 weeks and yet I am not quite confident,. that I can produce any good, exam style answers, from previously unseen questions.
It has been thoroughly enjoyable so far, but really quite taxing. It feels like I need to do 30hrs a week, not 15-20hrs, before I can gain that confidence, that I am seeking. I do think, though, that once I am used to the rigour; things will settle down and the 'newness' will not be causing such a disturbance within the force.
On the bright side, I now have a tutor and a set of 5hr day schools at Aston University on Saturday mornings. I am hoping that some tutor input, will allow me to shave some fat off my study regime and allow me to revise what I need for the exam, without any superfluous bits added on. This should help me settle down and gain some confidence as the months progress.
Things will get better. The fact that you have accepted the need rigour, rather than rejected it out of hand, is progress in itself.
ReplyDeleteWhat you are doing is deconstructing much of the maths that you believed to be true and reconstructing it on a firmer footing. That is a very reassuring and worthwhile exercise.
By going backwards for a short while you can also develop techniques that have the potential to take you significantly further forwards than would otherwise be possible.
You might even learn to love pure maths - some people do! ;-)
I concur with anonymous it really is like learning a new language. However it does pay off. Like most people on M208 I found the epsilon delta definition of continuity really quite baffling However in My M338 studies which I have just started I managed to zip through the introductory sections which revise this topic quite quickly. It even passed the '3 pint test' namely can you solve a problem from scratch in a pub whilst drinking a few beers or glasses of wine. Like anything new it's practice practice but then it will gell. Anyway keep going the steep learning curve is worth it.
ReplyDeleteThanks chaps, your words are encouraging at the end of an exhausting week.
ReplyDeleteDan
May the force be with us!
ReplyDeleteLet's hope so!
ReplyDeleteI had real problems with proving the equality of sets too and it came as a bit of a shock to me as well. It seems to be a recurrent theme and so you will get more practise as you go along. I still have a big mental block about it but it can't be helped. Some things appear easy and others more difficult. I have already had to put the structure of the proof in the back of my Handbook (actually it is the proof about the image of a function, but it is similar)
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