pure mathematics


Bumps on the road.

As ever there was a blog.

what’s involved here?

This is a sixty-point course. I found it hard, really hard. I found it hard because of the workload, because of the content and because of me. Don’t let that put you off.

A sixty-pointer is always going to be harder, the ante is seriously upped compared to a thirty-pointer; you have twice the work to do in the same timespan. We did seven, yes seven, TMAs and some of the material requires [at the very least] a second look. At times I felt that all my life consisted of was a hellish series of TMA deadlines. This course requires a serious commitment: of your time, of your mind and of your mental stability.

Still, horrors aside, there are hearty morsels on offer here. More than enough to make skirting with failure and exhaustion worthwhile for the brave student. This was the first course where I really began to see what maths, pure maths, has to offer the mind. [Of which more later.]


I’m guessing that most of my readers will be doing, or will have done, M221 and are now pondering M208/MS209. Their question will be, “how hard is M208?” Not too hard is my answer. However that answer comes with some caveats.

Some of the content is difficult, I’m not going to say hard, because there’s nothing here that you should have trouble understanding, it just takes a lot more effort to wrap your head around things than it did for MS221. But there isn’t a huge crevasse to be leapt here. Most of the concepts are grokkable once they’ve been explained, how people originally came up with these, ‘good ideas’ is another matter. Indeed I developed a creeping sense of inferiority when I realized that, without help, I could never have got here by myself.

One leap is that you are expected to be very comfortable with things like algebraic manipulation, or a proof by induction—technique as I call it. The forums were full of questions about, “how did we get from here … to here?” If you want something to work on in the run-up to this course, work on the basics until they are second nature.

The other great leap is accuracy, there can be no sloppiness on this course. You have to follow a strict way of doing things. You will lose marks for not stating the method[s] and results that you are using, for not checking that the pre-conditions of said method[s]/results are satisfied and for not stating your answer in terms of the question.

what’s involved? [redux]

This is a fairly stable course—things don’t change much. So you can be fairly confident that what follows will be much the same as what you will face. [The, excellent, videos are ancient and for those of us of a certain age will bring a tear to the eye.]

There are six blocks, but four really. The introductory block doesn’t really count [except in the exam and TMAs] it’s mostly a re-hash of the stuff that we learnt during MS221, the two Group theory blocks are co-joined [although not seamlessly], the Linear Algebra stands alone and the analysis blocks go together [again not seamlessly]. However by the end of the course I was beginning to see that there was only one block really—maths.

That’s what I really took from this course—I’m beginning to understand why, “that curve” may have something to say about prime numbers. We learnt techniques and ways of thought here that will stand us in good stead for out future maths progress. I may still swim with the minnows but I now know something about what the big fish are talking about.

what did you do neil?

Mostly it was last-minute panic rush. And the exam was pure hell. I did not give of my best. Such is the nature of the OU, sometimes life gets in the way. I let myself down on this one, partly that was down to circumstances, partly it was down to me. I didn’t manage my time well and I left too much to the last minute. Staying ahead of the game is important.


Although I did pretty well on the TMAs the exam blew up in my face. That happened because I didn’t treat it seriously enough. However much you understand the material the exam requires technique,and technique requires practice. I didn’t practice enough, not during the course nor during my revision.

With proper preparation the exam shouldn’t be daunting. In fact I’d go as far as to say that you could probably do it, and the TMAs without any real understanding of the material. I did several TMA questions simply by cribbing the answers in the unit-texts, this was a bad thing—it gave me a false idea of my understanding.

a good course?

Yes, brilliant. Despite my moaning [which is down to my cocking things up] I loved it. True, it was hard in places, the workload is heavy and the pace, for me, felt relentless. But the maths was lovely. Even if I never do any maths ever again, which ain’t going to happen, this course opened a window to higher mathematics for me. I suspect that I might have got a better result if I’d plumped for MS209, but I’m glad that I chose this course.

Here’s what others have said about M208.