My exams...

...are over!

Topoggaly was horrible. I am not in any danger of failing, but I don't think I did well.
The main problem, in hindsight was the fact that I insisted on going for the Part 2 question on edge equations. In all the practice I did, this was dead easy, and before I even went into the exam hall, I knew I would do it. And as I was struggling my way through Part 1, I was always happy to know that some easy points, that also wouldn't take long, were on their way. It was also going to be a gift in that, generally, it entailed doing the same thing twice, for two different edge equations. This was true again.

Only it wasn't dead easy. First of all, I should have relabelled everything, rather than stick with the fiddly x₁, x₂, x₃ labels they used. That would have made things much easier. But there was the added fiddliness of the edges being separate and having to be combined before working to canonical form. I kept on doing this wrong. I got myself in quite a tizz, and eventually, having eaten into half of the time for my other Part 2-er, opted to move on without finishing the second half. For this I chose one on topological spaces, connectedness and so on. This started off straightforward, but proving condition T2 on the intersection of open sets involved about a hundred different cases to address. That's what it seemed like at least. The following questions about connectedness were easy, and just as we got to the last minute, there was a two point question on path-connectedness which I managed to scribble through just as the time ran out. If only I had chosen a different first Part 2-er, or given up on the edge equations sooner, perhaps I would've got through the rest in time. I think I should've gone for the one on metric spaces.

I also skipped one Part 1 question, because I took one look at it, thought "I don't remember having to do this for a shape with two types of face" and for once, used my brain and just moved right on. I did have every intention of coming back to it, but never had the time. Both of the people I spoke to after knew what to do, so apparently we had covered it, which made me feel rather stupid.

Oh yes, and I wasted far too long trying to prove that a sequence of functions was uniform convergent, without once realising that perhaps the reason I couldn't get the conditions satisfied was because it wasn't. This question in particular has burdened me with a week's worth of flashbacks! I think it was worth three points, and I probably got 1 for saying what I had to do, so it likely only cost me 2. Despite the fact that skipping the question above cost me 8, and the unfinished Part 2 ones cost me about the same, THIS is what kept bothering me.

Groups and geometry, on the other hand, was much kinder. I only didn't finish one question in Part 1, which are only worth 5 each. Although, I suspect that I didn't give enough information on another one. The one I left part of involved proving that a set H-intersect-N was a normal subgroup of H (or something). I kept getting muddled on proving inverses, and I don't know whether I got closure right. Rest assured, I got the identity. I wonder if I should have gone for the old if its non-empty, and if x and y in it implies x^-1y is in it, then its a subgroup routine. I did afterall, in my collection of bullet points of things to remember, note three times (unintentionally by the way; I must've thought each time I came across it, "Oh yes, I should make a note of that"), not to forget that you can do this.

For Part 2, you choose two from geometry and one from groups or the other way round. I would have been overjoyed if one of the questions on the specimen paper was in it. Question 13 I think it was, just asked you to classify three wallpaper patterns. This was really easy and took less than five minutes. For 15 points! I knew it was too much to hope that'd be in it though, and it wasn't. Nevertheless, I did choose a question on wallpapers. That was the second Part 2-er that I did; the first was on colourings of a brooch. This was fairly straightforward, but coming up with the pattern index was very very fiddly. I was overjoyed then, when I divided by the order of the group, 12, that I got integer results for the various equivalence classes of colourings. It took a long time though. Polya's Theorem, I think is the result we used for this.

My groups question was on Abelian groups. That old chestnut of find the Abelian groups of a certain order. This wasn't very hard, and I had had much practice at it. The final part of it, which involved finding how many elements of order 45 each of these groups had, took the longest. And there was plenty of scope for basic arithmetic mistakes, and I must have made some along the line somewhere. Then again, this wasn't worth too much. The whole final part was worth 5 points, and this bit of it came after "stating" (which is always nice since no justification is required) how many elements of order 9 there are in Z₂₇ and of order 5 there are in Z₂₅, something which even if I didn't know already could be worked out quite quickly. They were probably worth 1 or 2 of the 5 points already.

Well that's that then. All over. I am quite happy with how that one went, and it cheered me up a lot after the debacle that was my topogally exam. Too bad it had to be that way around, because it doesn't really reflect how much I liked each course. Or perhaps it does reflect it, in that it's the opposite :)
That said, I enjoy M336 much more this week than I did last. Not because of the exam, but because in the course of revising it, I think I finally "got" a lot of it. And now feel that groups in particular has potential. Too bad a lot of the year was wasted on wallpaper patterns, when we could have gone onto rings and fields...

And so, onward, to my final level 3 course, MT365. I am not happy about the fact that a lot of people choose this because it is supposedly quite easy, as I don't want that to be thought about me. My reason, in fact, is a conversation I had with my topology tutor a few months ago, about how I don't really enjoy applied that much, but am all out of level 3 pure courses. He said that although it is not a pure maths course per se, it is a lot purer than any of the other level 3s. As well, I am interested in the connection between graphs and topology.

Good luck with your results, those of you who also took exams recently. And I hope you enjoy the few days break before the next course(s).
Neil H

Phew

"Phew #1" because my M336 TMA returned today. Which means that the young man I referred to, who my tutor thinks was probably her son, did not think it would be amusing to burn, rip up, or otherwise dispose of my assignment instead of give it to my tutor.

"Phew #2" because I did indeed get somewhere in the 80s as my tutor told me she thought I had at the tutorial. Actually, I got 81, which is apparently this year, my go-to score for uncompleted assignments based on un-studied units.

Curiously, I just realised that my total score for both courses is also exactly the same, but due to the different weightings, I assume they'll end up with slightly different overall results.

I set out my revision schedule last weekend, which basically alternates two days of topology and one day of groups and geometry, until the topology exam, and then every day groups and geometry until the groups and geometry exam. Conveniently, the day I set this gave me exactly the same number of days studying each. Not-so-conveniently, I was a bit rubbish and didn't stick to it, and today which is a groups and geometry day, I will actually start with two hours of topology, simply because I like it more. Then after getting five hours of work done, I will try to do three or four hours of what I should be doing.

The week gap between the exams is really quite a gift in this respect, because I would otherwise not get enough groups and geometry revision done, since basically topology rocks and that doesn't.

I think I am doing enough topology revision due to the fact that I am coming up with answers to stuff at weird times, like walking the dog. For example, in the last assignment we had a set in R2 which we had to use Heine-Borel-Lebesque to show was compact. In particular, my explanation of why the set was closed sucked immensely, and went on for about 1/3 of a page. Which I kind of thought was about 1/3 of a page minus two or three lines longer than it should have been. I emailed my tutor to ask if there was a neat trick for the annulus part of the set. But before he could reply, it came to me while playing ball with B'elanna a couple of hours later. So I emailed him again and asked what he thought of this way. Well, he replied the next morning and said that it was exactly the way he would have suggested. Woohoo! Go me!

Anyway, that's enough procrastinating. I've read all the news today, squinted at Facebook for anything new and interesting to pop up, sorted out some housework, and even written here. Probably it's time to actually do something. Once again, I have managed to do nothing of use in the a.m. despite being up since 8. I wonder is that better or worse than the same when I get up at 6?

Neil H

Last tutorials for M338 and M336

Yesterday I had a tutorial for both of my courses in Leeds.
That bloody city! It has taken me years, literally, to chart a course to Leeds Met for my tutorials, without getting stuck on one-way roads taking me in the wrong direction, getting lost, or any other mishaps that only ever happen to me in Leeds. Once I even gave up trying to get there, rang my wife (or girlfriend as she was), ranted, and drove back home!
But finally, now, I've worked it out. I intentionally make a mistake somewhere along the way so I end up missing the university, then when I find myself driving up a long dual carriageway past The Library pub, I turn back on myself and follow the road back down, and veer to the left. That way, I always make it to the multi-storey across the road from the university. Easy.
Yesterday, the multi-storey was closed. And all the other parking anywhere nearby is pay and display, which is not that useful when you only bring your card to pay at the machine in the multi-storey. As well, the road that not getting into the carpark sent me down ushered me back toward the motorway, which is really not what I needed. I pulled a U-ey.
In the end I was parked in a random (but legitimate looking) break in the double yellow lines way up past The Library, near to a travelling fairground that was just setting up.
The fifteen minute hike back to the university was boring and hot, but I made it, albeit late.
Nevermind. So my M338 tutor had organised to have the whole day there, from 10:30 to sometime in the afternoon. But my M336 tutorial was at 13:30, so I could only stay until the break we had at about quarter past one. I love topology, more than groups and geometry, and I would have happily stayed there longer. But I had, for various reasons, never made it to an M336 tutorial, and thought it would also be nice to actually see my tutor, what with this being the last one.
It was a tiring day, but definitely worth it I think. For two main reasons 1) we worked on one of the past papers for topology, and having not looked at any of them yet, I was pleasantly surprised by it (then again, with a topology tutor who actually researches the subject in his day job doing the questions on the board, it's always going to go well), and 2) my groups and geometry tutor said she received my assignment. She couldn't remember exactly, but thought I got 80-something. It's certainly lower than the rest of my marks, but enough to average over 90 before even the substitution rule. She thinks the person who I handed my assignment to was probably her son after all. So, for once, I am worry free on the TMA front. Though I still want to receive it back, to be sure.

Neil H

Still alive

Hi fellow OU-ers

Sorry for not posting in ages. Just a quick one, now that I am done with all the TMAs, to say that I am still alive.

I managed to get myself very very behind schedule, to the point where I found myself less than two weeks to the M338 TMA04 deadline having only finished C1. Not good. But I was determined to actually study the books rather than skim read them, so I had a really heavy couple of weeks of topology. I almost managed to stick to my catch-up schedule but slipped a little bit, and it was 9pm on the Monday, just a few days before the deadline by the time I got to C5.

Nevertheless, I stuck to my guns of actually studying it, so did an all-nighter to work through C5, finishing it at about 2pm on the Tuesday. Unfortunately I had work to do the rest of that day, so I didn't start the TMA until Wednesday morning. At least I got some sleep though, which I wouldn't have done if I was working on the TMA. I worked all day Wednesday, almost all night, and finally got through it some time Thursday.

This week of minimal sleep really took its toll on me, and I spent all day Friday regularly dropping off while trying to watch films on DVD. I expected to get nothing done, which was why I scheduled myself a day-long date with the sofa and DVD player (Kim was away for the weekend, so it was prime opportunity to vegetate). Even on Saturday, I was pretty useless, but I managed to pull myself together enough to paint the hallway, kitchen and stairs with primer (subsequent to us having got half of the house replastered not long ago).

I was worried for a long time that it never got to my tutor because for the first time I opted to use stamps rather than go to the Post Office. I went there earlier in the day with an A5 envelope stuffed with more sheets of A4 than I expected the TMA to take up, and got them to weigh it and measure it and sell me the stamps so all I had to do was drop it in the post box. In the hopes it would get there quicker, and be less likely to get stuck inside the postbox somewhere that the postman doesn't find it when collecting (apparently some of us do worry about this kind of thing), I dropped it in the letterbox on the main Post Office in town.

Every day I was checking the post, after enough time had gone for it to be marked, and every day I got more worried that it never arrived, or it arrived too late and never got marked. I was relieved somewhat when my tutor emailed everyone to say it was taking him a long time to mark them all, and that they would be finished as soon as possible. Then it turned up the next day. Relief. And I got 97%! I am more chuffed with this than I was with the 100% for TMA03, because that one was easy by comparison with this epic undertaking. Off the top of my head, I can't remember where the marks were dropped. It was good to see that some of the answers that I was really pleased with myself for coming up with, actually turned out to be right.

The comment from my tutor said that in some places I had gone about things in a different way than was expected, but that my answers were definitely correct. He pondered whether I had tried these different ways 'for fun', to avoid going about it the 'standard' way. I would love this to have been the case, that I was that confident that I thought I'd play around a bit, and in fact, on one particular answer perhaps it was, but generally I think these were just the ways that came to me first.

As for M336, well the jury's still out on that one. Unfortunately, due to my catch up session for M338, that course got put on the back burner for a bit, and so I found myself in much the same situation after the M338 TMA was sent. Luckily the final book for groups was a kind of revision book, so there wasn't quite as much catching up to do. However, I had to skim read some of it over the final few days and there's no doubt that this affected my TMA-ability.

Again, I was just a couple of days before the deadline by the time I started the TMA, so I had the joy of a couple of all-nighters again.

This can't be good for me. And I had to do another one for work on Sunday night just gone as well.

Anyway, with M336, it became evident to me on the day that it should be posted, that I was only going to have half of it done in time for the Post Office, so I opted to drive it to my tutor's house the next day on the deadline. She lives in Harrogate so it was about an hour away. Although I had been there once before, I did not realise how lovely a place Harrogate is until last week. In fact, we are hoping to go and spend an afternoon/evening there soon based on the impression we got of it.

Well, by about 10.00am on the deadline, I had done all but two questions of it, totalling 8 points I think it was. I could not leave it any longer, because I needed Kim to navigate for me and she needed to be at work at 1.30pm, so I had to leave those two out. I was not overly confident with the rest of what I had done, but at the same time, could not really see where anything had gone wrong.

Now my latest worry is that the assignment actually got to her. We found her house well enough, but she wasn't there. Instead I handed it to a young man that answered the door, who told me that it was indeed her house. I have no reason to distrust him to hand it to her when she got back, but I am a worrier, so until I get it back marked, I doubt I will be at ease.

Well that's about where I am now. Currently I'm revising my TMAs, by means of an A1 flip sheet and black permanent markers. I don't know why I am doing it this way, but the child in me loves writing with big black pens on large sheets of paper. I have gone through the first three of M336, and am currently on the second one of M338. I will go back to that now, but only for a short while more, because I have a lot of work to get done by Monday and unless I make a start, I'll be looking at another all-nighter on Saturday.

Happy studying everyone!
Neil H

H U

Well, I've put in some time with varying the blog content, so I think I can get away with a classic course-related post "without loss of generality" (to sound all topological). I'll have to keep it short as I'm in the middle of an indescribably boring translation about railway crossings, that is due in at 1am. I'm a bit behind schedule (when am I ever not behind...on anything?), so it is looking like this it will be an all-day affair (again!) :(

Anyways, I got back M336 TMA02 about two weeks ago: 100%! Or "HU" as they seem to call it. A heads up on what that stands for would be gladly welcomed. I felt somewhat vindicated to get that 100%, when I robbed myself of full marks last time by not copying out one of the answers properly.

And yesterday, after waiting a fortnight and beginning to worry that it hadn't arrived to my tutor, I got back M338 TMA03. HU again! Oh my god. I couldn't believe it. I mean, I thought I had all the right answers, but I always drop marks somewhere, and the full justification requested in the final question had me sure I'd missed something. Apparently not though.

Kim played a trick on me; as I think I mentioned before, she opens it for me if I'm worried for whatever reason. Well, I wasn't worried, but she was there and offered to open it for me. So I passed it across, and she opened it and for a moment looked concerned and confused, "hmmmm". After a while...
Kim: Oh I see....
Me: Huh? What do you see!?
Kim: ...because I can see the marks for the individual sections, but there's no overall mark! (smiles)
Me: It's HU!!!?
Kim: I hate you!

I haven't had 100% since TMA04 of MST121, which was totally undeserved, because I couldn't be bothered to study that block due to my aversion to all things statsy, and just hunted for the relevant parts to the assignment. Rather naughty for sure, but I was in my overlap with MS221 by then and was involved in much more interesting maths at that end. However, I then ended up with two hundreds in the space of a few weeks.

These results will be very useful. The M336 ones so far have given me a large buffer to work with (and alleviate a little of the fear I felt when I opened Unit GR3 only to notice I didn't understand anything on the first two pages - looks like I need to revise a bit before tackling it). And the M338 mark has balanced out my lower mark for TMA02, where I didn't manage to answer all the questions.

I say this to myself every time a good result comes back (or when a bad one comes back come to think of it), but I'm hoping this will incentivise me to start working harder. I don't make good use of my free time, especially when I have the house to myself when Kim's at work and I could potentially do many uninterrupted hours of study. So I need to sort that out. My mindset at the moment is that I'm ready and looking forward to working harder from now on, which means from tomorrow because of this job I'm doing. Hopefully, this time, I'll actually manage to fight my innate laziness and do it.

Neil H

Lots of little triangles

As if talking my dear wifey into letting us have Mobius strip wedding rings wasn't already taking things too far, I got my very first tattoo on Monday. And it's a maths one! Hooray!

I've long wanted a fractal tattoo, and for a time was interested in the Mandelbrot set or something like that, but eventually decided that I wanted one that was more geometricky. The Sierpinski triangle was the winner, as of all of the classic fractals, I find it to be particularly attractive. It is also very easy to explain to people if needs be.

Furthermore, I found many examples of Mandelbrot and Julia set tattoos, but only a couple of Sierpinski triangles online: one to one less iteration than mine, and a large one that is very cool and spans both forearms. There must be many more out there, but I would imagine the relative rareness online is reflected in the real world, so I can be sure of something fairly unique to me.

Actually, the picture was taken from Unit C5 of M338 Topology. I downloaded the PDF version, zoomed it as big as I was allowed, then print-screened, pasted, cropped, and printed. As for the size, this was just what I got when choosing the 4 copies per A4 option in Windows.

I took down a smaller print (9 per A4 size) on Saturday, and asked about it in the very professional 'The Bleeding Art' in Huddersfield town centre. They were pretty positive, but told me that with that much detail (if you think about it, there are 81 small black triangles, after this many iterations), it should be a bit bigger. There was no specific reason for the size I'd taken in anyway. Fortunately, the size mentioned above turned out to be more-or-less perfect.

When we went down on Saturday, it was actually for Kim's benefit. She's been after a realistic tattoo around her wrist of the Morning Glory plant, with the vine winding around, and a few of the (blue) flowers in bloom. I never really knew about this realistic style, so was amazed at some of the examples they have on display, and showed on the computer. She gave them some photos, and they will make up the design in time for her appointment in a few weeks (there is a waiting list for the guy that does these kinds of ones). It was only really an incidental thing, that I would ask about mine too. But here I am a few days later with a big triangle on my arm!

I was done as a "walk in." You turn up in the morning, and on a first-come-first-served basis, they allocate you a time slot during the day. I was scheduled for 3.30pm, but the lady having Pingu on her leg overran somewhat, so I got started shortly after 4. One of the staff had made my stencil on the computer earlier in the day, based on the larger print out; his version was better than mine as it had gone a bit blocky with the zooming. Anyway, it was all done and filled in by about 5.50pm, and I was on my way home. Not bad at all!

I'm really happy with it, and I've been keeping up well with the after care. I am wondering what I should go for, if I do that is, next time. One idea I had was the inverse of this design on my other arm in the same place. It think that would look good.

Neil H

Pi equals 3.0226

Okay, it doesn't, but I just finally did an experiment that I read about years ago when doing a translation on Monte Carlo approximation.

You may know it, but still, it involves drawing a circle inside a square with sides equal to the circle's diameter. Then, by some random method, you put points on the circle-in-square and work out the ratio of points on the circle to points on the square, and thereby approximate pi.

Here are photos of my effort, in which I dropped grains of rice, and then (quite laboriously) counted them. I counted those outside first, then those inside. There were 227 grains outside of the circle, and 702 inside. This gave me 929 grains on the square and 702 on the circle. I had to make a judgement when they were on the line, but just went with the obvious choice of inside the circle if more of the grain is inside, and outside otherwise.

For what it's worth, the radius of the circle was 4", and so the sides of the square were 8". However, I treated them as being of unit length. Hence, the area of the square was 4 and the area of the circle was pi.
The ratio therefore was pi/4, and the ratio from the rice-approximation was 702/929, which to 5 d.p. is 0.75565. Times 4 and we get pi roughly equal to 3.0226.

It may not be that close (I was hoping for something that would round to 3.1 at least), but for what it's worth, if 28 of those that ended up in the square only had ended up in the circle, we'd have got (730/929) x 4 = 3.14316, which is pretty close.

In the hopes of getting a bit closer, I also checked the weights and got 14.85g for the square and 11.15g for the circle. This got me an approximation of pi (to 5 d.p.) of 3.00363. Oh hang on, I shouldn't be going to more decimal places than there are in the input values, should I? So actually, this just gets pi = 3. Oh well.

So there we have it. Another way of wasting time on a Saturday afternoon that should be spent studying. At least it's maths though.

The Turing Solution

Hi all,

I just heard advertised on Radio 4, a programme that might be of interest to those of the mathematical persuasion.

At 11:00am this morning is The Turing Solution, a half-hour show about the life and work of the great Alan Turing. It will be presented by someone described as "standup mathematician Matt Parker." Never heard of him myself, but regardless, the programme should be worth a listen. Coincidentally, I just last week, started thinking back to M381, and was pleasantly surprised that I could still generate URM programs for basic things like multiply and divide two numbers. Not particularly impressive, I know, but proof that I actually took something in of that course. If it weren't for the fact that the autumn start of MST209 will mean I don't have a break this time, I would be interested in going back through the logic part of that course without the distractions of number theory.

In other news, I was disappointed (but not surprised) to see that Radio 4 have not included Andrew Wiles among their list of "New Elizabethans" despite what I thought to be an articulate and well-argued suggestion. Oh well.

Right, bed time!

Neil

Metrics

Hi. I wanted to avoid making this blog become little more than the diary of an ever-repeating cycle: I got behind schedule; I had a TMA due in and stayed up all night to finish; I got the results back. That certainly seems to be the way it's been going recently, so I have decided this time, to talk about some of the actual maths we've been up to lately, namely 'metrics'.

Why metrics you may ask if you're familiar with them. What are metrics you may ask if you're not. Good questions. The easy answer to the first is that I quite enjoyed them. The easy answer to the second is below. (It should probably be noted here, that I don't have the books with me, so I'm likely to make some mistakes...)

Metrics are a generalisation of the concept of distance between two points, that satisfy three axioms:
(M1) d(a, b) ≥ 0 with equality if and only if a = b.
(M2) d(a, b) = d(b, a)
(M3) d(a, c) ≤ d(a, b) + d(b, c)
So basically, and also quite obviously, the distance between two points a and b is always non-negative, and is 0 only if the points are in the same place. The distance from a and b is the same as from b to a. And yes, (M3) is our old friend the Triangle Inequality. The direct distance between two points a and c, is not more than it would be via a third point b.

Metrics have been my favourite part of the topology course thus far. To begin with, even within the highly abstract realm of topology, metrics have a very easy to grasp real-world basis, since after all, we talk in terms of distance all the time (as it goes, the basic distance we use is the 'Euclidian metric'). One of the first different ones presented in the text is the 'taxicab metric' (e₁(a,b) = |b₁ – a₁| + |b₂ – a₂|, the sum of the horizontal and vertical distances between a and b), which gives us the distance a taxi would travel to get from a to b in a city based on a block design, where roads only run in two perpendicular directions. Indeed, without knowing, we all use such an alternate measure of distance (albeit one that's a bit harder to define than the taxicab metric) which is the distance between two places via the roads. So the concept of different definitions of distance is really not all that alien.

With a particular metric, one can define an open ball B_d(a, r), which is the set of all points with distance less than r (the radius) from point a, a sphere S_d(a, r), which is the set of points with distance r from point a, and a closed ball B_d[a, r], which is the set of points with distance less than or equal to r from point a. Or, simply the union of the open ball and sphere. In two and three dimensions, things are pretty intuitive; in the plane, these are a disc, circle, and disc with boundary respectively, which fits nicely with our idea of balls and spheres as being round; in 3D, it can be pictured as something like the air inside a (round) balloon, the rubber of the balloon as the sphere, and then both together as the closed ball. Take it down to one dimension, on the real line, and things are not so round. The sphere is just two points, a –  r and a + r, but it makes sense considering the definition, because they're the only points with distance exactly r from point a. Well that was all with the Euclidian metric. But what about other metrics? Well, the definitions work just as well when we have another type of distance, another metric. With the taxicab metric, for example, balls and spheres end up as squares rotated by pi over 4. Squares balanced on a corner. And on it goes, getting less and less ball-like as we take less familiar metrics.

Which is the charming thing about metrics, the weirdness of abstraction: take for example, distances between infinite sequences of 1s and 0s, or distances between functions! Not something the average human considers on a daily basis, true, but defined appropriately, they can be shown to satisfy (M1) to (M3) and therefore qualify as metrics. If memory serves, the distance between infinite sequences of 1s and 0s was something like: given two such sequences a and b, then d(a, b) = 2^-n, where n is the number of the position where they first differ. So if a = 1,1,1,0,1,0,0,0..... and b = 1,1,1,1,1,0,0,0....., then they first differ at the 4th place, so their distance apart is 2^-4 = 0.0625. (Is that right? I can't remember, but it's something along those lines anyway).

I'm starting to drone on a bit, but I wanted at least, to mention the thing that first made me ponder writing about metrics, and that was the interesting one we encountered recently, namely the 'vine-picker's metric', which was in our recent TMA. I figure it was long enough ago that it's not a problem to discuss it, and anyway, I'm not going to go any further into the question than the info on the assignment booklet. A week or so after the TMA was done, I cleaned some space on my blackboard and had a little play with the vine-picker's metric. It is defined as:
d(x, y) = |x₁ – y₁| if x₂ = y₂, or |x₁| + |x₂ – y₂| + |y₁| if x₂  ≠  y₂.
Below is a photo of my blackboard. On the left is the rule and graph, and on the right is some vine-picker distances worked out for points on the graph.

So, we end up with a situation that's as if there is something stopping you from moving in the up-down direction, unless you are above the origin, like there are impenetrable grape vines blocking your way, and the only gap between them runs vertically through the origin (for the record, my diagram simplifies it somewhat; in this case the points have integer coordinates, so the vines could be drawn in).  To travel from one point to another in vine-picker metric terms, you therefore have two cases: if the points are at the same "height", (x₂ = y₂), you just go directly horizontal, but if they're not at the same "height" (x₂  ≠  y₂), then you must walk horizontally to the axis, then up (or down) to the appropriate height, and then back out to the second point. The example on the blackboard demonstrates d((2, 3), (8, 3)) = 6 and d((5, 1), (3, 5)) = 12.

Of course, the vine-picker's metric satisfies (M1) to (M3). We had to prove some stuff about it in the TMA.

Anyway, that's metrics. Very cool indeed. It's only Unit A2 of Topology, so there's clearly plenty more fun where that came from. For what it's worth, it was the surfaces and shapes side of topology that I was really looking forward to (surely that was the case for most of us?). However, since I've been going back through (or indeed simply "through" in certain cases) and more carefully learning block A, I'm beginning to really enjoy the point-set variety.

In Our Time

I've been listening to Radio 4 for more than 5 years now, and (despite loving I'm Sorry I Haven't a A Clue, Laura Solon's Talking and Not Talking and various other 6.30-slot comedies) my favourite program remains In Our Time with Melvyn Bragg. Little can make you feel as sophisticated and intelligent as listening to Baron Bragg and his distinguished academic guests discussing the fall of Carthage, the Observatory at Jaipur, Schopenhauer, or some other deep topic.

Anyway, every now and then, we get treated to a maths topic for 45 minutes, usually involving Ian Stewart and Marcus Du Sautoy. I've heard discussions on Godel, infinity, the Calculus, the Poincare Conjecture, pi and many more subjects In My Time :)

After what seems to have been forever (though I could easily have missed some without noticing), it was a mathsy topic again this morning, namely Game Theory. I'm not overly interested in Game Theory myself, but it was entertaining enough, and gave me something to listen to while doing the washing up and tidying the kitchen. Ian Stewart was there as anticipated, and was as brilliant as ever. I'm quite an Ian Stewart fan for what it's worth. I made the (blindingly obvious) prediction to Kim, that John Nash would get a mention, and lo, at 18 past 9, he did. Other stars included von Neumann, and a tramp.

If anyone's interested, a cut-down-to-thirty-minutes version is usually repeated at 9.30pm tonight. It's also available on the Radio 4 website, as are all the episodes of In Our Time since 1998. Actually, I got rather good at Minesweeper a few years ago when I played it to keep myself visually stimulated (I tend to drop off eventually if the only thing I am doing is listening to something) while going through all the science and maths ones that caught my eye... and there were quite a few. I'm not very cultured, so I didn't bother with the art, philosophy, religion, &c, but I do listen to them if they're "live."

More maths please Melvyn!

Well, I got my assignments back over the last few days, and I'm really happy with the outcome.

I dropped one point on the M336 TMA, which is actually rather annoying, because I just didn't copy out the whole of an answer from my rough version. It was a question asking what transformation you need to do to move one of the 'motifs' on a freize pattern, onto another. The answer, remaining as vague as feasible, was in two parts: the type of transformation and the point about which you apply it. When I copied out my answer (and I did have it on my draft, because I dug out the sheets to check and lo, the full answer was there), I seem to have stopped the sentence short without fully explaining the point where to apply it. I don't begrudge this costing a mark, because I accept it being a vital bit of information. Just annoyed at myself is all. Though what can you really expect, with the last-minute panic to finish, the all-nighters, and all the other (admittedly self-induced) obstacles. Rather, it's surprising I only dropped one point.

My tutor was very kind in her comments, and gave me some useful advice on what to put more effort into in that block, &ct. I've not met her yet, because I was too busy working on catching up with the material, that I had to skip the tutorial last month. Actually, I had to miss the tutorial for both courses as they were on the same day (they were, however, at different times, which was nice as it meant we can go to both). It was a shame to miss the tutorials, as I do like to go, even if it is a bit of a trek to Leeds, and the fact that I can never find Leeds Metropolitan University when I get there. The problem was, no matter how useful they would be, the 7 hours I spent going to them would not get me any further through the study materials, which was my main concern at the time.

As for M338, well, it was nowhere near as bad as I expected, in fact, I just about pipped into the 80s! Not quite distinction territory, but easily high enough to put me in a good mood all day after I opened the envelope (...Kim opened it actually, as I usually make her check the results, when I'm worried about it). I tend to expect the worst about most things, but this time, I really went overboard! I mean, I was even trying to work out what I needed to do, to make up for it, if I only got 50!

In his comments, my tutor said it is a really tough TMA and that I should be pleased with myself for doing as well as I did. Of course, it's his job to encourage, but regardless of motivation, it made me feel good about myself. I kind of figured, if I managed to do okay under the conditions I was in at the time, I can assume that I might have done very well otherwise. Either way, he did warn us back at the start of the course, that Block A is hardest, whereas Block B is easy, and Block C is just "hard."

For what it's worth, I'm really enjoying the surfaces unit, B1. In fact, I will hopefully get through most of the last part this afternoon/evening. It certainly is a chance to breathe after the ultra-dense Block A. In fact, I am going to go and work on it now. I've already spent enough of the day watching snooker, reading (Rendezvous with Rama by Arthur C. Clarke - very cool), and general pottering around on the Internet. It's time to get productive, I reckon.

By the way, for anyone that didn't catch it, Dara O'Briain's School of Hard Sums, that I mentioned last time, was fairly entertaining. Not ground-breaking TV or anything, but hey, it was worthy enough of watching again tomorrow at least. Warning though, the puzzles aren't particularly hard (and I mean, for "normal" people as well as us mathsy types), but titling inaccuracies aside, it was an enjoyable enough 40 minutes, and I have little else on at eight on a Monday.

School of Hard Sums

Hello again,

Just a quickie for anyone who's interested, and doesn't know already.
The practically ubiquitous TV panel show comedy bloke, Dara O'Briain has a new programme tomorrow night on Dave: School of Hard Sums.
http://uktv.co.uk/dave/series/tvseries/257755
I heard him being interviewed about it on Radio 4 t'other day, and it sounded quite interesting.
And look, there's half of Melvyn Bragg's In Our Time maths brigade, Marcus Du Sautoy too...
Note how the set looks like it's right out of an OU video :)

Neil

Edit: Sorry, I just thought. As wrong as I no doubt am, it's wrong of me to give my answer. Deleted.

The best laid plans, eh

Hi

Sorry for being so rubbish at writing in my blog lately. Actually, this is a symptom of a much wider issue I'm going through of being rubbish at doing anything.

Whether it's been work, study, or just life in general. I've had almost zero motivation and very little capacity to stick at something for any useful period of time. Well, that's not totally true I guess, my capacity to get through Twin Peaks on DVD recently has been admirable, but that's hardly productive...

2012 has been tainted by a general malaise so far, and the worst effect it has had is on my studying. Although I've been equally unmotivated with work, I'm still meeting all my deadlines, being too responsible to do otherwise, and too courteous to refuse work when allocated to me. So despite the many times I've not even got started until 4pm, or when I've had three days to do a job but not started until the final day, work has been mostly unaffected.

I've been looking forward to M338 since before I even started MST121, so it's quite upsetting to be so far behind so soon. I even bought the first three units back in December so I could get started... only I didn't. So where exactly am I? Well, I finished my first TMA, more or less on time, and got 90-odd. I was not expecting there to be a TMA based on the first unit of the course only, so it was lucky that my tutor who, coincidentally is not only from Portsmouth as I am, but did his undergraduate degree at Sheffield Uni, like me... (I wonder if it was at the same time because he looks fairly young; I should ask!), emailed to remind us. The comments on it were very encouraging. However, I had to then switch to M336 to catch up for a while, and somewhere along the way I got to last week, at which point the situation was thus:

M336 TMA due 12th April - relevant units complete
M338 TMA due 13th April - only Unit A2 complete (with the TMA based on A2 - A4)

Well, I got a good start on the M336 TMA over the weekend, but had to put it aside for a bit to finish a big job (it was legal, a contract, and a right pain to complete - involving an all-nighter from Monday, until the deadline at 9am Tuesday). I finally finished the work itself on that TMA sometime Tuesday afternoon/evening. But as I was so knackered from the all-nighter right before, I opted to quit for the day and go to bed early, at ten. Wednesday morning, after driving Kim to uni (it's the holidays but she wanted to go in and do some work), I wrote up the M336 TMA in neat. Of course that took hours, as it always does for me, and I got it to the Post Office at about 2.45 on the 11th. Pretty sure it arrived on time though; it usually does.

So then I found myself faced with M338 TMA02, at around 3pm the day before I had to send it, and only a third of the material covered. Not good! Rather than just dive into it head first, I thought I'd speed read those two units before starting. So from 4 to 6, I blitzed my way through A3 on Topological Spaces, and after dinner, from about 7 to 9 on A4, Closed Sets. I can't deny that I took very little of it in... but I was up for a challenge.

It took me from 9.30 until about 12.30 to do the stuff on A2, Metric Spaces, but I'm fairly confident of that part. In fact, I was pretty pleased with myself over how I cracked the question on proving the third metric space axiom is satisfied by the "vine-picker's metric", though I suspect I went the long way round. By now, putting aside the prospect of another all-nighter so soon, I was feeling pretty good. I figured, well it took me three hours to do the part I knew. Maybe it'll only take twice that to do the rest, so six hours on A3 and six on A4. Actually, fast forward a bit and I found myself only 15 points from the end (though with a 9-pointer skipped), at 5.30am. So I actually went to bed for two hours! Finished those fifteen points by about 10am. Took me just over four hours to write up. Leaving me at 2.30 with the question I'd skipped left to try and do, and hopefully get to the Post Office at 4-ish.

Unfortunately, by this point, I could barely hold a pen and write, let alone be capable of abstract thought. A few false starts, then I just decided to get it to sent.

I'm not expecting a very good result. But, I think, perhaps, that this might have been the kick up the bum I needed. I actually came this close to picking up my text books again later that evening, despite the epic burn-out of the week so far. I talked myself out if it and opted to just lay on the sofa that evening with B'elanna our dog, watching Vinnie Jones as a butcher killing people on the underground (in Midnight Meat Train, based on a Clive Barker short story). Not bad actually, but the makers need to realise that CGI gore looks silly; the flying eyeball put me in mind of the health meter on the first few series of the (excellent) kid's show Knightmare.

My aim for catching up is to continue working through the material from where I actually should be by now, and working on getting through the previous stuff at the same time. I do not think it's in my interests to catch up first, as from experience, I know I'll just end up a unit or two behind throughout. Meanwhile, I think I'm still on schedule with M336, and with some luck, I reckon I can keep it that way.

I'm sure either you've given up reading by now, or would like me to finish soon. So I shall.
Hopefully, by the next time I post, I'll be up-to-date on everything, getting great results back, and just generally having a good time. I doubt things will change quite that quickly, but I reckon I'm over the hill now and will start sorting out, whatever it is that's been going wrong... watch this space!

Neil

Edit: Mentioning Knightmare above made me think.... do you guys remember The Adventure Game in the early 80s, set on the planet Arg? That must've been the highlight of my week when I was little....

Edit 2: The attentive will note that I've been discussing M336, not S282 Astronomy. Well spotted. Actually, I changed my choice within a week or so, due to concerns over the transitional fee rules.