Archive for February, 2009

This week I’ve been working through MS221 Chapter A2: Conics, and although I’m enjoying the chapter, I’m having a huge amount of trouble with sketching curves. I’m not sure whether my hands are particularly unsteady, or whether I’ve got terrible hand-eye coordination, but when I draw an ellipse it always ends up looking feathery and lumpy. A bit like a cross between one of these:

and one of these:

So I’m drawing a few practice curves every day at the moment, in the hopes that drawing eleventy billion hyperbolas, parabolas and lemons ellipses will train my hands to be steady enough to cope with drawing curves in the exam.

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Not only did I use this phrase in my TMA, I actually understood the cancellation I was referring to!

Not only did I use this phrase in my TMA, I actually understood the cancellation I was referring to!

I spent yesterday working on the first three questions of MS221 TMA01, and I’m pleased to report that the Cassini-type identity question, which I expected to struggle with, went very well! I think it was probably a bit easier than the questions in Exercise Book A, either that or I’ve just become more confident with the topic.

I’ve decided to word-process my MS221 TMAs rather than hand-writing them, so that I can easily print out another copy if the original printout gets damaged or lost. I always used to worry about the possibility of my hand-written MST121 assignments getting rained on, torn or otherwise ruined in transit, so I kept scans of the pages, along with the rough notes that I based the final draft on. Even so, sending the package containing my precious hand-written TMA off was always quite nerve-wracking!

Word-processing the TMAs for MS221 means that I won’t be getting as much practice hand-writing my solutions, though, which could put me at a disadvantage when it comes to the exam; luckily, there are five past papers available from the OUSA Web Shop, so I’ll be able to make up for that during the revision period. I wish there were that many past papers available for M366 – there’s only the 2008 paper listed at the moment, which would make for a very brief revision session!

Actually, it’s not Cassini-type identities themselves that have been perplexing me, it’s the simplifying and cancelling involved in exercises like the one below:

Show, by substitution, that the sequence
un = 7n-(-5)n
satisfies the Cassini-type identity
un-1un+1-(un)2 = -144(-35)n-1
for n = 1,2,3,….

I always seem to get stuck at the same part of the process; I’m fine with the bit where we substitute the sequence into the left-hand side of the identity – in this example, substituting 7n-(-5)n into un-1, un+1, and (un)2 – but I have a lot of trouble manipulating the resulting expressions into the form required by the question.
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Pepsi is no longer a valid input

I’ve decided today that I’m finally going to give up Pepsi Max, and I have ScienceBlogs and the OU to thank for this. First, there’s this post on SciencePunk, which features a very funny parody of Pepsi’s marketing, and a link to a painfully silly real article about Pepsi’s marketing. Second, and more importantly, I worked out how much money I’m actually spending on Pepsi per year: £720! I would be an idiot to continue spending this much on what is basically just sweet, fizzy water. Especially since next year’s OU course won’t cost that much!
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My MS221 books finally arrived on Wednesday, and it wasn’t until I’d opened the package that I realised I was supposed to use the copy of Mathcad that I’d been sent for MST121 a couple of years ago – if I’d realised sooner, I could have been installed it days ago! I had a brief panic when the installation wizard asked for a password, but thankfully the OU Computing FAQ page contains a valid password (this is the link, which I presume will only work if you’re currently enrolled on MS221).

So with that little crisis out of the way, I’ve been working through Section 3 of MS221 Chapter A1, which is about finding closed forms for linear second-order recurrence sequences. In particular we looked at Binet’s formula:

Binets formula, a closed form for Fibonacci numbers

Binet's formula, a closed form for Fibonacci numbers

So now I can impress and astound Alex by quickly calculating any term of the Fibonacci number sequence he likes!

The activities in this section were lots of fun, but there were a few bits where I suffered from being clumsy and out of practice with various algebraic techniques. In particular, I couldn’t remember how to solve simultaneous equations, so I had a look at the very helpful Simultaneous Linear Equations leaflet from, which sorted the problem out fairly quickly.

It’s embarrassing not to remember stuff like that, but I suppose it’s to be expected when you don’t practice a certain technique for a long time. Which is a good reason to keep doing maths courses – or at least, to keep doing maths problems, even if they’re not in the context of a formal qualification or course; I’m sure if ever I run out of money for OU course fees, I’ll end up haunting the educational textbook section of my local library every evening and weekend!