This week I’ve been dabbling a bit in one of the other M208 units available on OpenLearn, AA1: Numbers. I think this unit is supposed to be studied after all the Group Theory A and Linear Algebra books, but it seems pretty straightforward so hopefully studying it out of sequence won’t do me too much harm. In a way, the material in AA1 is quite familiar but at the same time it seems like we’re looking at these subjects in a more precise, rigorous way than in MS221. It’s nice, but a bit intimidating! I often get a bit anxious that what seems like a simple statement might have some deeper meaning which is sailing over my head. Still, if that’s the case I’m sure I’ll find out pretty quickly when it comes to the assignments.

This unit introduced a couple of techniques that I haven’t used in a very long time: long division, and finding the fraction equivalent to a recurring decimal. Long division was quite a challenge, and I literally can’t remember the last time I actually did it – I think I’ve got the hang of it now, but I was ridiculously rusty at it, so if there are questions involving long division in the exam then I’ll need to practice until I can do it in my sleep. I really don’t want to fudge a Level 2 maths exam because I panicked over doing long division! It’s strange how you can forget something so basic, and it makes me wonder just how much of the maths I’m learning now I’ll end up forgetting over the years!

I don’t know why, but I love finding fraction equivalents of recurring decimals. There’s just something about the simplicity of the method that appeals to me, and I always get a little kick of satisfaction when using it. And of course, there’s the fact that you can use it to prove $0.\overline {9} = 1$. That’s always good fun!

I’ve been reading a couple of maths-related books this week too, one purely for pleasure and the other in the hopes that it will help me improve as a maths student. The former is Simon Singh’s Fermat’s Last Theorem, which I’ve thoroughly enjoyed. I had high hopes for it after loving Singh’s The Code Book, and if anything I think I enjoyed Fermat’s Last Theorem even more. It’s full of wonderful little anecdotes about the various mathematicians who have influenced or contributed to the eventual proving of the theorem; I particularly liked the one about Euclid’s reply to the student who asked “What’s the use of learning this?” – he threw a penny at the boy, since the student wanted to profit from his education, and then expelled him! (I have threatened to start throwing pennies at the more application-inclined Alex whenever he asks me “But why would you want to prove that..?”, but I don’t think I’d get away with expelling him from the lounge.)

The other book I’ve been reading this week is Kevin Houston’s How to Think Like a Mathematician: A Companion to Undergraduate Mathematics. This book is superb, and I really wish I’d started reading it last winter, before embarking on MS221. It’s filling a gap in my maths education, in the sense that although I’ve had feedback about individual assignments from my OU tutors, I’ve never had much in the way of guidance about doing maths as a whole. I think reading How to Think Like a Mathematician is slowly turning me into someone who explores and engages with mathematics, rather than someone just applying algorithms and cranking out solutions (which did well for me in MST121 and at GCSE level, but is definitely not enough these days!). I haven’t finished How to Think Like a Mathematician yet (it’s a whopping 278 pages!), but so far I think it’s probably one of the most generally useful books I’ve read in a while. Definitely worth giving a try if you can get your hands on a copy!