Happy New Year, results and triangles

Hi fellow OU-ers

Happy New Year. I hope you all had a fun and productive time over the festive season. I managed the first of those at least, but I have been far from productive.

For that reason, I originally wrote right here about doing only a small post, as I need to get cracking on catching up with MT365 so I can address the TMA due on the 10th (or thereabouts). That never happened, as like always, I got a bit carried away, so I've changed it to what you're reading now. In fact, it was the worry about that happening and me spending ages typing that kept me putting off posting for so long. I don't know why though, since I really enjoy it. Either way though, I am very sorry about that.

So, pretty late I know, but here's how I did in 2012:
Topology - Grade 2
Groups and Geometry - Grade 2
Consistent, at least, but very disappointed about the Groups result. I honestly felt that I had all but aced the exam... apparently not. Topology I should be pleased with, as many of us know how awful it was; there was no way my performance in the exam would be distinction-level. So that didn't upset me at all. But that bloody Groups one did. Looking back, I can only assume I lost most marks on the Part 2 questions.

Work-wise, I have had a very busy time since the exams. This is usually great for me, as I tend to need to make more money to counter the lost work while revising, and to prepare for the fast-approaching tax bill at the end of January (for which I've usually failed to put away adequately in advance). And with no studying until the courses start up again in February, in previous years, everything has been hunky dory.

Not so with the change to the autumn start. So not only do I have to contend with no break between courses, but also with too much work to keep up with my course. Very not good! I am so glad I've just got the 30 points this year, or I'd be in really bad shape.

Still, it got me a slightly brag-worthy achievement, before Christmas. For whatever reason, MT365 has a few CMAs thrown in with the TMAs. The first one was due on the 19th of December. By the time I got to the 19th (and I'd at least quadruple checked that the deadline was... how to put this.... er, "twenty four O'clock" on the 19th, and not "zero O'clock"), I had finished just one of the four books it was based on, and about 15 pages of the second. And for reasons I've still yet to fully fathom, I didn't actually get started until gone 3pm on that day. However, I finished it with an hour to go, and managed 93%. However, it was both fairly easy and multiple choice, so do not misunderstand my point, I'm not claiming to be a graphs genius. But it is fun to tell people :)

I was hoping to do some major catching up over Christmas, but I had a lot on in the end, and I'm still quite a way behind. After I've written this, the rest of the day will be for studying. Alas each of the other days until this deadline has to be shared with a fair (but not excessive at least) amount of work for deadlines on the 7th and 10th.

Kim got the result for her Masters by the way. She got a distinction which was just the best news. She's now officially a Master in Human Osteology and Paleopathology (or "bone-ology" as I oh-so-wittily refer to it).

What else is new? Oh yes, I got a second tattoo. I decided to (bad pun alert) complement my Sierpinski Triangle tattoo, with a tattoo of the complement of the Sierpinski Triangle. It's on the other arm, and I think looks pretty good. Despite the more ink it actually took less time, and so cost less. It was my Christmas present from my parents.

If that wasn't enough, my Mum also bought me a nice large 3D-printed Sierpinski Tetrahedron, from the very excellent Shapeways website (where Kim got me my Klein bottle from last year). I'll just get the camera out and take a picture...one sec.

Pretty cool, huh? I put the ruler in for a bit of perspective in terms of size. You may be able to pick out the scale on the ruler, at least in the larger version. If not, it's a 30cm ruler, and it comes to just short of the 18cm point. The hardest thing about this picture, was choosing which angle to take it from. It's just so amazing in any orientation, in my opinion.

Well, I think I shall leave it there and get on with some studying. Sorry again for taking so long to post.
I hope that what little there has been of 2013 has treated you well so far.

Neil H

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