I had to read and re-read this a few times to make sure I wasn’t hallucinating, but it turns out that I’ve somehow managed 80% on the M366 exam! And even more luckily, it seems that the examining board were in a particularly lenient mood, since they’ve decided that my overall course result is a Distinction, rather than the Pass 2 that it should technically have been. I’m overjoyed – I really thought I’d either fail or scrape a Pass 4 for this course. It’s a huge relief to know that I won’t have to resit the exam, or substitute a different Level 3 Computing course into my diploma and degree. Phew!
I registered for M208 this week, and I’m really looking forward to the delivery of my course materials next month, so I can carry on with the Group Theory A block. In the meantime, I’ve been reading another Marcus du Sautoy book, Finding Moonshine, which is a very apt choice to pass the time with, since it’s about group theory and symmetry.
Finding Moonshine is split into twelve chapters, one for each month of one year of du Sautoy’s life, and each chapter combines the history of group theory with more personal anecdotes about the author’s own career. I was a bit ambivalent about this approach at first, but over the course of the book I really warmed to it. I enjoyed getting a glimpse of what it’s like to be a professional mathematician; particularly the little details of du Satuoy’s working style, like the yellow legal pads he prefers to write on, and stories about the overseas trips he makes over the course of the year.
Actually, aside from the wonders of group theory, the main thing I got out of reading Finding Moonshine was an increased urge to travel! I particularly enjoyed the passages about the Alhambra, and I’m now determined to take a trip there myself, most likely in 2012 when I’ll hopefully be taking M336: Groups and geometry. I also really want to visit the glass pyramid at the Louvre, too. I can only imagine how awe-inspiring it must be to see it in person.
Louvre Pyramid, Paris by batigolix
As for the mathematical content of the book, I think it’s more enjoyable in that respect than The Music of the Primes; I’ve certainly come away from Finding Moonshine with group theory fever, and I can’t wait to get back to studying it formally. I do think that the book might have been a bit over my head if I hadn’t already met the concept of symmetries as transformations in MS221, though, so perhaps this wouldn’t be a great choice for someone completely new to the subject. The next book on my reading list is Ian Stewart’s Why Beauty Is Truth: The History of Symmetry, so it’ll be interesting to see if it turns out to be a gentler introduction to the awesome world of group theory.
Surprisingly, I managed to scrape a distinction with 87% in the exam, along with an Overall Continuous Assessment Score of 94% – I’m so relieved that I won’t have to resit this exam, and to be honest I was expecting a Pass 3 or maybe a Pass 4. Well done to everyone who sat the exam, and I hope you all got the grades you wanted!
I must admit, I haven’t done very much studying at all over the last couple of weeks. I can’t seem to gather up the motivation to finish Unit AA1, knowing that I’ll probably have to go through the entire unit again next year once the Analysis Block A assignment(s) is/are actually due. Instead I’ve been reading Marcus du Sautoy’s The Music of the Primes, and falling in love with prime numbers!
A couple of years ago I attempted to read a different book about the Riemann Hypothesis – I think it was Prime Obsession – and I just couldn’t get into it, so I was half-expecting to find myself bored by The Music of the Primes. Thankfully it was much a more compelling read than I anticipated! Or perhaps I’m just better equipped to understand the appeal of the primes these days.
The Music of the Primes is a really enjoyable book, and the only criticism I’ve got is that some of the material was quite familiar to me – the bit about cicadas and their prime-numbered breeding cycles, for instance – so perhaps if you’re a seasoned reader of popular maths books then you might find The Music of the Primes a bit boring. But otherwise, I’d recommend it to anyone interested in primes and their mysteries.
For me, the main attraction of prime numbers is that they are fundamental, and at the same time infinite; it seems odd that there are an infinite number of the building blocks out of which the integers are made. Imagine if there were an infinite number of chemical elements! One of my favourite daydreams is imagining the primes stretching out across the far reaches of the real number line, getting bigger and bigger, but more and more sparsely dotted around the line – on and on forever!
The other thing I like about primes is the fact that they’re so important in cryptography – it amuses me that the study of prime numbers has such big practical applications, and I suppose it goes to show that seemingly abstract and academic topics can yield unexpected concrete benefits. Although of course, not everything humans have used prime numbers for could be described as beneficial.
I wonder what the practical applications of group theory are? The next book on my reading list is Finding Moonshine, also by Marcus du Sautoy, so hopefully I’ll find out soon enough!
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.
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I was kind of expecting M208 to be over my head, but so far I’m really surprised at how much material in the first few units of M208 is also covered in MS221, and at how gentle an introduction the Intro Block actually is. Very pleasantly surprised indeed! I’ve been working on Unit I3: Number systems and GTA1: Symmetry this week, and there were only really two new ideas introduced in these, so I feel like I’m getting a nice, steady warm-up session before the really hard stuff starts.
The topic in I3 that I’d never encountered before was equivalence relations. It took me a little while to get my head around the idea (and to stop thinking of the phrase “equivalence class” in its software testing context from M255), but I think I’ve got a fairly good grasp of it now. I even managed to give a coherent explanation of it to Alex, with the help of the “coloured blocks” example from the h2g2 Equivalence Relations page.
The unit about Symmetry introduces the two-line symbol notation for describing symmetries, which I’d never come across before, and to be honest at first I couldn’t really see the point of doing it this way. If I’m going to describe a reflection of a square in the vertical axis, for instance, I’d much rather write 
But later on in the unit, I watched the video section about symmetries of Platonic solids, and it certainly sounds a lot easier to write down the symmetries of a tetrahedron in a two-line symbol than trying to figure out how to represent it in the form 
Speaking of Platonic solids, I absolutely love the animations of them on the Wikipedia Platonic solid page. I could watch this octahedron spinning all day!
Octahedron image by Cyp, under the Creative Commons Attribution ShareAlike 3.0 License
This week I’ve been wrapping up Unit I1: Real functions and graphs, and making a start on I2: Mathematical language. The last few sections of I1 introduce some really interesting-looking graphs – I particularly like cycloids and cardoids. Partly because the graphs remind me of Spirograph pictures, and partly because the names sound like monster robots from a classic sci-fi film!
Cycloid
Cardoid
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I’ve been a bit lax with the studying over the last couple of weeks, but there’s only so many days I can spend on comic books and videogames, so this week I’ve been trying to get a head start on M208 using the OpenLearn materials.
I’m about halfway through Unit I1: Real functions and graphs at the moment, and I’m really enjoying it so far. It starts with a fairly gentle refresher about the graph-sketching strategy covered in MS221, and then goes on to expand the strategy so that we can sketch composite and hybrid functions. This leads to some weird and wonderful graphs, like the graph of xcosx and (sinx)/x.
I was a bit worried at first that the introductory block of M208 would just be composed of material we’d already covered in MS221, to make sure that all the incoming students were up to speed on the same topics, but there’s definitely enough new stuff to keep me interested, at least so far. I’m particularly intrigued by the idea of ‘jumps’ and ‘corners’ in graphs, like the ‘hole’ at x = 0 in sinx/x. Apparently we’re going to look at these jumps and corners in more detail in the Analysis blocks, so I’m looking forward to that very much!
But that’s way in the future, I reckon we probably won’t be doing the Analysis units until spring/summer next year – I’ve got four units of group theory, and five units of linear algebra to get through first. This winter is going to be mathtastic!
The MS221 exam was this afternoon, so I’m now officially done with both of this year’s courses! I think Part 1 of the exam went well, but Part 2 was a lot more challenging than I expected – I went for the “volume of revolution” question and the one involving propositional logic and proof by induction, neither of which went as well as I’d hoped. So I think I’ll be looking at a Pass 2 or maybe a Pass 3 for this exam, depending on how many silly arithmetic errors I made. Hopefully I’ll get a better grade for MS221 than for M366, at least!
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The exam is over, and I think it went okay, but I’m not at all confident that I’ll have passed this one – hopefully the results will be released around the start of December like they were last year, I’ll be very interested to find out whether I’ve managed to scrape a Pass 4! Anyway, now that it’s over and done with, it’s time for a good navelling-gazing session about M366 as a whole…
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