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Attack of the Cycloids

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

Cycloid


Cardoid

Cardoid


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Getting started with M208

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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I finally got TMA04 for M366 back this morning, and was very happy to find that I’ve got my best mark of the entire course for this one – 93%! Which is a well-timed confidence boost, since my M366 revision has been challenging to say the least! I’ll be happy with a Pass 4 in the exam, to be honest. Let’s just hope there are plenty of questions about Block 5, since that seems to be my strong point…

I got the MS221 TMA04 back a while ago, but I only had a quick look at the score and the summary comments, as I didn’t want it to distract me too much from the M366 exam prep I’m doing at the moment. I got a disappointing 88% for this one, which particularly worries me since Block D was my favourite part of the course, and I expected to do a lot better than that. I can’t believe I scored better on the calculus TMA than this one!

Well, I’ll have plenty of chance to go through the detailed feedback and find out exactly what went wrong with my understanding of Block D, once the M366 exam is over and done with next Wednesday. Until then, it’s back to neural networks, learning rules and search algorithms for me!

Although I’d recommend using the Black Badge Press solution booklet for MS221 revision, since it’s more detailed, I thought I’d upload the other solution documents that I’ve managed to collect over the last few months, in case anyone wants them:

https://catbear.files.wordpress.com/2009/09/ms221_97_sols.pdf
https://catbear.files.wordpress.com/2009/09/ms221_98_sols.pdf
https://catbear.files.wordpress.com/2009/09/ms221_99_sols.pdf
https://catbear.files.wordpress.com/2009/09/answers-ms221-2003.pdf
https://catbear.files.wordpress.com/2009/09/answers-ms221-2004.pdf
https://catbear.files.wordpress.com/2009/09/answers-ms221-2005.pdf
https://catbear.files.wordpress.com/2009/09/answers-ms221-2006.pdf
https://catbear.files.wordpress.com/2009/09/answers-ms221-2007.pdf
https://catbear.files.wordpress.com/2009/09/2008-ms221-answers.pdf

Happy revising, everyone!

I can’t believe it’s only 3 weeks until the M366 exam! This course has really dragged at times, but now that I’m into the revision period the days are just flying by! This week I’ve been making notes on the learning outcomes for each block, and trying to condense my notes as much as possible. There’s something very satisfying about squashing a nine-month course into a nine-page Word document!

I’ve been doing some MS221 revision this weekend too – I decided to have a go at Part 1 of the 2007 past paper, and I was interested to see that the questions don’t completely conform to the pattern in the 2008 paper. I was particularly blind-sided by the appearance of a question on combinations/permutations and binomial coefficients, since I’d forgotten they were actually covered in Chapter B1.

With MS221, I’ve mostly been concentrating on getting faster at answering questions – there are 12 questions in Part 1 of the exam, and I’m aiming to spend 2 hours on that bit, so I need to be able to do each short question in about 10 mins. So far, I’m fast enough when it comes to my favourite topics (Block D, I love you!), but in my weakest areas I have to spend far too long flipping through the Handbook and scratching my head.

In an attempt to speed the process up, I’m putting together a kind of condensed version of my most frequently-used bits of the Handbook, so that I can transcribe it into the blank front page of the actual book and take it into the exam. It’s going to be quite a challenge to hand-write all these notes into the Handbook, but hopefully it’ll allow me to spend more time puzzling over the actual questions and less time flicking through the book. And it’ll give me an opportunity to use my many colourful gel-pens – my Handbook will probably be the most gaudy book in the exam hall!

My tutor very kindly sent me a solution document for the past paper from 2008, so this morning I’ve been working through the my first ever practice exam for a maths course! I was quite curious to see what the exam paper was like, since all the exams I’ve taken with the OU so far have been in computing/programming. Luckily it seems like maths exam papers follow roughly the same pattern that the computing exams do – about a dozen short questions, one for each course unit, and then a few longer questions that require combinations of techniques from various units. And nicely, you only have to do two out of the four longer questions available, so I’m happy to say that I’ll be able to avoid at least some of the graph-sketching questions!

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I was wondering in my last post whether the MS221 unit about groups would be any fun, and quite unexpectedly it turned out to be really enjoyable! I particularly liked working with Cayley tables and isomorphisms (even if the former can sometimes feel a bit like filling in a sudoku puzzle!), and on the basis of this chapter, I’m very much looking forward to the material on groups in M208. From what I can tell, there are a whole seven units on group theory in M208, so I’ll certainly get a chance to see whether my interest in the subject is more than a passing phase!

Chapter D4, the “proof and reasoning” chapter, was good solid fun too – and very reminiscent of the material on logic in M263, so it was quite a nostalgic experience for me. It definitely helps to have encountered the idea of proof by induction before; I think I had some trouble with that originally in M263, so I think it could be a bit of a stumbling block for the MS221 students who haven’t met the topic before.

There was one bit in D4 that I had a lot of trouble with – proving statements about inequalities. I’m not sure why, but I seem to have some kind of weird mental block when it comes to inequalities. So I’m going to have to do loads of practice questions involving them during my revision work – I don’t want to have an inequality-induced freakout in the middle of the exam!

So now that I’ve finished with chapter D4, I’ll be spending this weekend wrapping up TMA04, and then I’ll need to work out some kind of revision plan – only 5 weeks and three days to go until the M366 exam, eek!

I really, really love the Algebra Workout programs that go along with the MS221 course texts – I watched the program on modular arithmetic earlier this week, and it was immensely helpful. Prior to that, I felt utterly confused about Euclid’s algorithm and finding multiplicative inverses, but once I’d seen the process worked through on the DVD, somehow made everything sense!

In fact, now that I actually understand how to do it, it’s quite enjoyable. And of course, using Euclid’s algorithm was especially good fun during the section in the course text about ciphers – there’s something really appealing about deciphering secret messages! I’ve been intrigued by cryptography and cryptanalysis since reading Simon Singh’s excellent The Code Book a couple of months ago, so I was really pleased to get the chance to do a bit of practical maths involving ciphers. I like the idea of learning how to actually break ciphers, but I think that might be a bit ambitious for a Level 2 maths student!

Anyway, now that I’ve finished Chapter D2 and its associated TMA questions, I’ll be getting started on the penultimate chapter tomorrow, which is about groups and symmetry. I’m looking forward to this chapter quite a lot, because the topics are completely new to me; there’s a chance I won’t like group theory, but either way I’m just excited to find out what it’s all about – and if it turns out that I do enjoy it, then there’s a nice chunky Level 3 course in the subject that I could aim for, which is always a good incentive to study harder!