Archive for June, 2009


One thing I really like about Block C of MS221 is that it reiterates the basics of calculus, which were originally covered in MST121, before going on to the more complicated stuff. Normally I’d be annoyed by the repetition of a topic across two courses, but with calculus I’m actually really glad the course team decided to do it this way. For some reason, the MS221 chapters on differentiation and integration seem way more accessible and understandable to me – I remember having a bit of trouble with Block C of MST121, but so far I haven’t had any similar problems with the MS221 version. Perhaps the material is presented or explained in a different way (I should really dig my MST121 books out and compare the relevant chapters, but they’re all the way up in the spare room and I’m too lazy to get them!), or maybe the preceding two blocks of MS221 make for a better preparation for calculus? I’d be interested to hear from other students who have done both MST121 and MS221, to see whether anyone else has found calculus easier or more interesting in the latter.

In any case, it’s really gratifying to actually enjoy calculus this time around – it’s such an important part of mathematics, I’d feel like I was really missing out on something if I still couldn’t find anything beautiful or fascinating in it. So far, the section of Chapter C1 about graph sketching has been the most satisfying bit to me – the fact that we can figure out the shape of a graph, along with its long-term behaviour, just by studying the equation of the graph is amazing! Ooh, and the Newton-Raphson method, that was pretty awesome too – the speed at which you can get a good approximation of the solution to a particular equation, and the ease with which you could implement the approach on a computer, is brilliant! I can honestly say that the Newton-Raphson bit of the Mathcad work for Chapter C1 was the most fun I’ve had with Mathcad in my OU career. I really do wish calculus had been this enjoyable in MST121!

You’ll notice there isn’t the characteristic exclamation mark on the end of this post’s title – I’m a bit embarrassed of these two assignments, since both got grades quite a bit lower than the previous ones. For M366 I got 84% (just 1% short of a distinction, dammit!), and for MS221 it was 89%. I’m actually more ashamed of the MS221 score, because almost all of the lost marks were due to stupid errors, which I absolutely should have picked up at the proofreading stage. My tutor’s comments were very nice, but I think he must be getting a bit frustrated with the trivial errors I keep making. Basically, his general feedback was:

  • Factorise expressions where possible
  • Check your work (Mathcad is useful for this)
  • Read the question carefully!

All very good advice, which I have been striving to apply today while working on TMA03. I’ve been checking everything, every little calculation, either in Mathcad or Wolfram Alpha – so far, I’ve caught some really stupid slip-ups, so hopefully I’ll be able to manage more than 89% for this assignment!

The M366 assignment got a lower mark, but I’m happier with that one because the lost marks were due to a genuine lack of understanding about various little details of the subject matter, rather than plain old carelessness. Actually, I get the impression that most of my lost marks were caused by me not fully understanding the questions themselves; some of them wanted slightly different or fuller answers than I expected. For example, in the question about the NetLogo rabbits simulation, I lost three out of six marks because I didn’t mention the details of the code behind the features I was talking about – I described the simulation at too high or abstract a level, without backing up what I was saying with a description of the “nuts & bolts” side of things. Which is an odd mistake for a programming student to make! Still, hopefully by the time the exam comes around I’ll be much better at interpreting the questions correctly. And at least there’s no NetLogo coding to mess about with in the exam!

I know I’m late to the party with this, but Wolfram Alpha really is a brilliantly useful tool for checking your maths work. Today I’ve been doing the exercises in Section 2 of the unit on differentiation, and I’ve already made good use of the site to investigate some problems that I just couldn’t grasp. In particular, I found Exercise 2.1(i) to be almost impenetrable – my solution for it was very different to the solution in the back of the book, and I just couldn’t see where I’d gone wrong.

This is where Wolfram Alpha has been coming in handy. The brilliant thing about it is that as well as calculating the value of a mathematical expression, it also displays the steps you could take to work it out yourself. This is brilliant when the solutions in the course text tend to be a bit terse! For example, the solution for the exercise mentioned above is this:

Not terribly helpful, if you’re as stuck as I was. But check out the Derivative section of the Wolfram Alpha page for the expression, and click on the “Show Steps” link – it gives much more detail about the solution, and after reading through that explanation I could see exactly where I’d gone wrong with my original answer. I suppose there’s a danger with sites like these that people might just enter TMA questions into it and copy the answers, but then again the OU apparently uses anti-plagiarism software that would probably flag up TMA solutions that were word-for-word copies of existing internet resources.

Anyway, plagiarism aside, I think Wolfram Alpha is going to be a very useful tool for me (especially if it means I can avoid phoning my tutor when I get stuck!).

M257 wrap-up

Well, the exam was yesterday afternoon, and overall I think it went OK. There were a couple of questions in Part 1 that I hadn’t done enough revision for, but I made a concerted effort to proofread, proofread and proofread some more, so hopefully I’ll have avoided most of the silly errors I made in the practice papers.

With M257 out of the way, I’m now going to be concentrating entirely on MS221 and M366, and the rest of this evening is going to be spent getting reacquainted with differentiation – I’ve missed doing maths so much during these last few weeks, I could almost kiss my course books! (Though that wouldn’t be a great idea hygiene-wise, considering how dusty they are…)

This week I’ve been typing up my attempted solutions for the M257 past papers so that I can post them in the course forum, and I’m really glad I did type them up – I spotted quite a few silly errors in the process of transcribing them! I’m still not hugely confident of my answers, but I thought I’d upload them to the blog as well, in case anyone would find them useful. Here are my attempted solutions for the three past papers:

If you spot any mistakes, please let me know in the comments (although once the exam is over on the 17th I might not be particularly speedy about correcting them!).