M338, M336
topology and group theory

Wallpaper and tiles,
bagels and prêtzels
all with a helping of angst.

2012–10–18

finished

It was a driech, grizzly day in Edinburgh yesterday but there was a song in my heart and a spring in my step. True, I had to go back to work-work, and the exam didn’t go too well but at least M336 & M338 were over for the neil. This year has not been the greatest of my academic career.

M336 exam

I managed the seventy-five marks available for the groups and colouring questions; that is to say I wrote something down for all of them. I won’t get seventy-five marks. This took me all of the time, so I didn’t even get to glance at any of the geometry questions.

Past sins and stupidity arrived to haunt me. Because I’d only a week to revise, to revise work that I had a poor understanding of anyway, there was always going to be a large chance that I’d be stuck having to answer a question that I couldn’t really do. This proved to be the case. I had to attempt a question that I wasn't confident about because I couldn’t do most of my intended question. It was asking about stuff that I hadn’t more than skimmed.

The stupidity? I didn’t take a calculator—I’d left it at work as it wasn’t until last night that I realized that you were allowed to use one. This hurt me in the colouring question where mental arithmetic seemed to have left my head—I could not add and divide numbers to save myself.

Interestingly the colouring question involved reflectional symmetries, this isn't usually the case and seems to have thrown some people. I spotted this but managed to cock things up in other ways.

What mark will I get? Well even being the utter pessimist I can’t see how I can have failed but I’d be an optimist if I thought that I could get a grade three. I’ve just lost too many stupid marks. I’d have liked a three but a pass will do me jolly nicely.

review of the year…maths wise

Despite the acmé of my ambition being a grade two and a grade three there are some positives to take away from it:

• When I did study I was effective, I just didn’t study enough
• My revision [especially for the topology course] was better than I’ve ever managed before
• My planning for the exams was good
• My time management during the exams was excellent

My flaws? There were many but they mainly boiled down to two things:

• I often couldn’t force myself to work when there wasn’t a TMA in the offing
• When I realized that I wasn’t understanding something because I hadn’t understood the under-pinnings I didn’t go back and fix this lack

These are more or less the same problems that bedevilled me during M208. So a lack of progress.

A big, personal, flag-up that I’m in trouble is when I’m not even reading the forums, never mind contributing. I had nothing to say, I had nothing to contribute and I couldn’t even understand what the subject matter was most of the time.

We all have distinct learning styles, I’m beginning to learn mine. I think that I now see the way ahead. I take a great deal of comfort from the fact that this time last year I was desolate. This year, while I may not have done a well as I liked I didn’t just curl up and blubber.

As ever there are lessons to learn from what went wrong. My revision taught me a lot about what I might achieve if only I can force my mind to it.

• It’s important that I am working at something, even if not course related [I have a cunning plan for that]
• I need to do is far more exercises.

The second part of the above is particularly important. I practiced doing a lot of the second part questions, for both courses, during revision. I got fast at [and more important accurate] and confident about some of them. If I’d spent more of my time this year doing exercises I’d be in a far, far better place.

Next year I’m doing staggered courses: number theory and software development. I should be inside my comfort zone and time management should be less of an issue. We’ll see…

It’s that time again. During the next couple of days I’ll write my course reviews. Meanwhile the number theory blog is up and running. So, last blog post…

$ hg commit

2012–10–14

exam…again

I have a single unit book, of the units that I intend to revise, left to work through. I’m work-working tomorrow night, I’ll do it then. Tuesday I have a day off, I’ll work through some questions in the exercise books; the exercise books that have been untouched for the duration of the course.

I’ve enjoyed my revision so far, which reinforces my belief that the geometry has been the sticking point of my mind. This course has been one long missed opportunity for me.

I see how groups and geometry go together, my problem is that I don’t get geometry and I don’t care that I don’t. Looking back I see how this myopia has made me miss many things. The big miss being the beauty of groups. There are some utterly stunning proofs and theorems involved here. This is maths in the raw, a wonderful, wonderful structure built on such-secure roots purely by the mental exercise of the thoughts of the great. I feel, rightly, small.

I’m annoyed with myself, which is good. It means that when I make my exam plan I will be realistic. I’m a minnow playing with giants, I will treat myself so.

2012–10–12

annoyed

Despite work-working or being asleep for most of today, I managed to get through three of the unit-texts for the groups course. Good. The downside is that my wife is pissed off with me—I’ve been mumbling maths, when she was trying to read a book. My wife is never shy or succinct when it comes to disapproving of my harmless tics. Nor are her tones dulcet in these cases. But I’m annoyed too.

What’s annoyed me is that, even at this stupid pace, I’m seeing [for the first time] the gaps in my understanding that have been tripping me up for so long now. Parts of the jigsaw have been found that never should have been lost. I just missed stuff because I was skimping.

I have excuses and culprits. I had to work hard at other things, the geometry wasted my time, the course was badly presented…mostly I blame me.

Ever since I decided that the lattices, friezes, et al were no longer welcome in my mind things have seemed to get so much easier. No longer do I have to try to bend my brain trying to understand something that I just don’t care about. I want to focus on what excites me.

Because I’ve been working really hard for a while now [on maths] I see that I haven’t ever been working hard [about anything] before. I suppose that this is what other people [educational professionals] call personal development. I have an insight into me that I didn’t have before.

Tonight I made a decision; I’m going to do a maths masters. And I’m going to do it as soon as I can. [Which is in about two years.]

I don’t really want too much from life, I just want to sit on a floor with a book or a game. I’m lazy. And because I’m averagely smart I’ve always been able to do so. I was proud of myself the other day, I tackled something really hard, topology, well. Well for me anyway. I realized that I am not complete, I will never be so.

I owe me this, this walking towards the event-horizon of non-understanding. I shall stretch my brain until it breaks. I’m going to learn until I die.

Funny, none of this seems to be a bad thing.

2012–10–11

groups−geometry

I had my first look at the specimen exam paper for the groups course today—things may not be as bad as I thought. By my reckoning, if a colouring problem comes up in part one and part two A, then there are seventy five marks on offer without me getting involved with tracing paper.

I’d like fifty-five of those marks, but being a realist forty marks will do me just fine. I just need to pass this one, that’s position A. Anything else is a bonus.

I managed to get through two units tonight. Granted they were muchly the same material that I studied for M208, still, I felt things were coming back to me. My hope is that the other group units will engender the same sense of, “ah, I remember that”.

This, my, revision has to be done quickly. We all know that quick is likely to be shoddy, what we might not all see is that quick may lead to bad judgement-calls. There’s a tiny bit of me that thinks of a grade 2. That bit of me is a moron.

I need to be absolutely realistic here—I need to pass. My suspicion is that I’ll do better than that but what I mustn’t do is to try for too much. Make sure that you get the forty marks neil.

2012–10–10

exam[1]

It was baltic as I headed off down to Gorgie for my exam, I was shivering having my last smoke outside the hall. When we finished the sun was shining, the sky was blue and it felt warm in the sunshine. Were my thoughts similar to the weather? Somewhat, I’ll explain what I mean by that later.

fair exam?

So far the forum isn’t overloaded with post-mortems, but taking into account what’s there, and from the discussion that my group of mathos had in the pub afterwards I’m going to say, mostly fair. Everyone felt that some questions were awful and some were easy. These questions were not a connected set—we each had our stinkers, stinkers which others felt that they’d aced [more-or-less]. Topology is like that—we each get different parts of it, it’s the rare person who gets all of it.

My mathos, to a person, found that we couldn’t even get started on one question; nobody on the forum has even mentioned it so far. Maybe other tutor groups had tackled a question like it before?

So I suppose that it was a fair, if hard, exam. I think that when we signed up for this course we knew that the exam would be hard. That the course would be hard.

how did i do?

There are quite a few positives that I can take from this exam:

• For the first time, ever, I revised hard
• My time management during the exam was excellent
• I was able to follow the plan that I’d made—I tackled the questions out of order
• I felt that, when it came to the exam, I’d given it about my best shot

What about my mark? I’ll get a grade two, which was what I was aiming for.

so…

This is the last presentation of this course, which is a sin, for it’s pure maths pesonified—if you can do this one, you do them all. It’s the acmé of your OU maths career undergraduate wise.

In the Digger’s, after the game, we were all a wee bit hyper, we got into a pure/applied maths argument. [What must we have looked like?] So what?

It was an argument that we could have had last, or any other, year [we’ve been doing maths together for a while now] but after this course it was a so much more nuanced argument. We got to discussing Cauchy sequences. Chris explained that the Laplace transform Fourier series relied on these. [At least I took him to have said so.] We all knew what a Cauchy sequence was, why it differed from a null sequence, what a Lipschitz function is and how our intuitive understanding of a concept might lead us astray. We could talk as equals.

There was a moment, sitting with the autumn sun shining through the windows onto our pints, sitting with people who between them know maths, pure and applied, philosophy, music, computer science… when I felt that I was at a home, abroad.

The entry fee for such company is a whole load of hard work.

Now for the groups…

2012–10–09

near the end

It’s the night afore the exam. I’ve been working, I’d like to say most, but some is nearer the truth, of the day. I’ve been answering timed questions. A thing that I know others do but not something that I’ve ever done before. Why the change in my modus operandi?

There’s a particular problem with this course—some questions require a good deal of thinking-time before you can even see how you might answer them. I’m going to have to create that time. Which means being fast and accurate on the few questions that I can do.

So I’m going to have to force myself into doing something that I’ve regularly planned and never carried out.

You’re allowed to tackle questions in any order in a maths exam; every year I play with the idea that I might do so. And every year I don’t when I’m bum-on-seat in the exam hall. This year is going to have to be different. Tomorrow I’m going to work my way through the questions in the order of my competence.

So, you’ve read my mission statement. I’ll tell you how it went tomorrow…

2012–10–05

revision[2]

Well here it comes—the last weekend before the first exam. I’ve still got three units of the surfaces to get through but the time has come for me to get those hands busy.

Tonight it’s the PTA wine tasting, so I’m marooned in my school. Still this is be-at work rather than work-work so I can do some maths. I have my marked TMAs, some brand new whiteboard markers and a wall covered with emergency glazing film. All that I need for some proper get-the-hands-working revision.

Well not quite, I need some seriously loud music and like the diddy that I am I didn’t bring a CD into work with me. It’ll have to be youTube then.

thoughts

Time to start having the I think.

What have I done this year? I made the mistake of tackling two level three maths courses.

Well, I’ll say mistake, I could probably have made it work. I think that the mistake, if there was one, lay in the courses that I chose.

Topology has been hard, very hard but I’ve loved it. It has given me a huge confidence boost. I don’t feel that there’s anything pure maths [I’m never going to grokk integrals] that I can’t understand given enough time and effort. I’m not saying that I’m ever going to produce anything of my own but I can plod along in the footsteps of others.

The groups? I’ve not spent enough time on these. There have been some truly beautiful results [I’m thinking in particular of Sylow’s theorems] that I just haven’t had time to appreciate.

Geometry? Ahh, the filthy geometry. I’m not sure what went wrong there—probably me. I just never got it. Which is strange because I don’t think that it was too hard. In the end I think that I just didn’t care enough to put in the work that I needed for me to get it.

I think that much of the problem was that I didn’t have an option to switch the gears of my head. So far I’ve always had a maths course alongside a computing one—if I didn’t feel like working at one I could work at the other. This year I’ve done almost nada programming wise, every time I opened up netBeans I felt like I was skiving. If I didn’t feel like doing topology, what did I have? Bloody geometry. So I did nothing far too often.

I’m not sure that I can say that I failed this year, perhaps I didn’t do as well as I might have. Still, failure is only failure if you fail to learn a lesson—next year I’m doing number theory and some object-oriented stuff. I foresee fun.

2012–10–01

revision

I’m on back-shift this week, revision is going to be hard, if not impossible. Today I’ve managed about an hour’s worth. As the week drags on revision-time is likely to get less. So I need to get smarter as I’m not going to be working harder.

I need to focus on two areas: block two [surfaces] and fractals; there are lots of marks to be gained there. Not exactly easy marks but…

I didn’t much like block two and I haven’t even worked my way through the entire fractal unit. I should do these before I do anything else.

I have an odd confidence about this exam, for some reason I think that I can do well. I suppose that comes down to the fact that I am working. Being immersed in the stuff you feel that you understand. I might not actually understand but I feel that I have a shot at this one.

I’m deliberately ignoring the groups course, indeed there’s a wee bit of me that thinks I should just fail. Alas I can’t—that would mean that I would need to do another course between now and the end of the year-after-next to get a degree. But all I need is forty percent. Unless I fall asleep that should be do-able. And if I do a good topology exam that will fire me up to achieve something.

I’m in an interestingly different position from the one where I was last year. This year, for at least one course, I’m on top of the material. For the other…

Looking back at what I was thinking this time last year I can see a difference, this year I’m focused, chipper and not prone to laxity. Things may go badly wrong but my attitude is right.

Last year I fell into a kind of despair, I’ll be fucked if I let that happen this year.

2012–09–29

last tutorial

It’s my last topology tutorial today, the exam revision one. For various, mostly work-related, reasons I haven’t got to many tutorials this year. Which is a pain.

Apart from the advantages of having maths explained to you the big miss is chatting to your mates. Normal people really don’t want to talk about topology, or groups, or geometry I find. I don’t know what you think about but I often finding myself saying things like, “…of course an intersection of open sets is open, it follows from tee two …” at inappropriate moments. It’s great to able to talk openly about maths.

The topology revision is going well. Well…in the sense that I’m working. I’m probably a wee bit too much in love with topology to be an effective revisor. I’ll do OK in the exam but I won’t shine, I’ll get lost in something.

I’ve learnt one thing about myself this year [this year being my current courses], I’m not very good at visualizing maths. This was a bit of a shock. Because I can draw well and I have a decent awareness of space I’d always pegged myself as a see-er. Not so.

The geometry has been awful, I feel like I’ve just been wasting my precious time, and I distinctly didn’t get the surfaces stuff for the toplogy. I feel much more comfortable when I’m manipulating symbols. This needs to be thought about, it has a bearing on my future studies.

Speaking of future studies, the books for the number theory course are sitting on the floor beside my bed. I’m resisting looking at them, from the brief glance I took I can see that I’m going to be fascinated. I’m reminded of the building blocks of software—one of my favourite courses.

Sometime soon I’m going to have to decide which computer course I’m going to do alongside M363. I’m almost certainly going to go for the AI course but if I really need a distinction I may go for the the database course, even though this is a shameful cop-out.

After that? When I have my degree? I’ve more-or-less decided that I need a treat. I’m going to do a single maths course, complex analysis. It may strike you as odd that I consider this a treat. But to have only one course that I can pass and fail as I like feels like my reward for all this struggle and strife that I’ve been through.

For sure I’m so not the boy I was when I first started down this road.

2012–09–22

exam time

The final TMA winged it’s way home yesterday. As predicted I did rubbish. I’d only attempted two questions, out of four, one I did well the other? Well let’s just say that it wasn’t well handled. Still I managed, with substitution to get over the seventy percent hurdle; I have something to aim at.

Which leaves me in a bit of a quandary, should I try to revise for both courses? My gut feeling is no. The topology exam is on October 10^th, the groups the 17^th. I could concentrate on topology and try to do a weeks intensive cramming for the groups?

It doesn’t sound like a proper approach does it? Or does it?

Most of my problems this year come down to me having to rush things, I tackle questions without a proper understanding of the principles involved, I end up just parroting the methods ⇒ lost marks. When it comes to maths, if you don't understand the principles it’s often hard to even begin to think about how to tackle a problem if it’s put to you in a way you haven’t seen before.

For example, in the second topology TMA there was a question which all of my tutor group decided was evil. [It involved the continuity of a function between two topological spaces.] Last night I was working my way through a unit text when I had a sudden flash—I’d been so fixated on the function that I hadn’t considered the inverse image of the function. The question still wasn’t easy, but I saw the way I should have tackled it.

But perhaps there’s something bigger to be considered here. Why am I doing all this learning? To learn, or to get good marks?

It’s October, the blogs a full of eager new learners. Their enthusiasm to learn is infectious and salutary. I’ve begun to lose sight of the bigger picture—I want to understand this stuff. And I think that, with topology I’m getting there.

For once, I’m revising and learning as I go. I can’t let the fact that this may stuff-up what degree I get matter. Eighteen heavy days of topology it is, the groups can look after themselves. [I don’t even plan to look at the geometry.]

2012–09–12

the car crash

I’ve just posted off my final TMA for the groups course. I only attempted half of it, and I didn’t do the half that I attempted well. Frankly it’s the worst piece of OU work that I’ve ever submitted. I had to write a note of apology to my tutor.

I’ll get the required twenty marks, the ones that will give me an OCAS of above seventy but I feel—soiled.

All maths builds upon what you already know, there are alarming gaps in what I know. Last night I thought I saw two different prime decompositions of an integer. I knew that this couldn’t be [I’ve worked my way through that proof] but because I can’t do basic arithmetric…

It’s been like this all the way through the topology and the groups courses—I’ve skimped the time and effort that would be involved in actually grokking them. Too often I’m flailing around for a solution, which I know is there, because I didn’t really understand some of the groundwork.

I’m utterly sick of myself. With my lack of effort, of application, of organization, of will. It’s not as if this dropped on my head like a load of seagull shit—unexpectedly; I knew what I was in for. I deliberately signed up for this. Why didn’t I do better?

Who cares? Regrets hardly matter now—time to save what I can.

• I can still get a one for the topology course, I’ll concentrate my revision on that
• I can still get a two for the groups, I’ll worry about that later
• Remember this time last year? When you just stopped? Don’t do that

Failure happens, by all means beat yourself up about it. Once. After that? Just work out what went wrong and resolve to do better in future. Then do your best with what you have left to work with. To do otherwise would be layering idiocy upon stupidity.

2012–09–06

a mistake that I made earlier

I was working my way through the final unit of the groups stream for the groups course, when the chickens came home intending to have a kip. I’ve cocked this up. I knew at the time I signed up that doing two third-level maths courses at the same time was serious mental, did I let that put me off?

The unit, GR6 to give its full title, involved us classifying all the groups of order twelve, a real exercise in using all that we’ve learned. I loved it. I loved it despite having to thumb the handbook hard to see what results we were using. I wanted to know so much more. For I could see vistas more.

I’ve hated this course [M336], or, more exactly, I’ve hated the geometry rubbish. Mostly. Some bits of it were interesting but geometry and me will part ways after this. When I look back through the group stuff I realize that if this had been a course about groups alone I would be loving it.

With effort and will I’m sure that I could have done myself justice. But they weren’t onboard. I bit off more than I can chew. Either the groups course or the topology course would have been fine if I’d been doing a computer course; both together? This has been too hard.

That’s not to say that I’m dispirited. I’m not stupid—I knew that I would make mistakes and would have problems. The only stupid thing would be to get this wrong again. Which I will.

But, hey, that’s me and why I love me.

2012–09–01

tma away

The last TMA for the topology course is currently in the bowels of her Majesty’s postal system, I trust her not to screw up. As I may have.

My mate Chris often blogs his take on the TMA questions, which is always a worthwhile read. He described this one as, [not a direct quote] … conceptually … the hardest … that I’ve ever done …. I think I agree. Which poses an important question, why do we agree? We’re very different mathematicians.

I ran a unit test on myself. I opened unit book C1 at…p12 consider theorem 2.2 [this was a random choice] (I hope the CSS works for the following)

Let (X,ΤX) and (Y,ΤY) be topological spaces, Let X be connected, and let f:X → Y Let f be a (ΤX, ΤY)-continuous [function]. Then f(X) is connected.

Batcrap mad. Well, it isn’t but there’s rather a lot going on to even see what we are saying, and that’s before we even get around to proving it. I know what it means, it’s what comes next that disturbs me:

…Suppose that g:f(X) → {0,1} is (Τf(X), Τf(d0))-continuous then the composite g ° f:→ {0,1} is a (Τf(X), Τf(d0))-continuous function…

I won’t give the entire proof, it relies on another proof that:

A (Τ, Τ(d0))-continuous function, f ⇒ f:X → {0,1} is constant.

Many things can go wrong with your mind there. That {0,1} ain’t an interval, it’s a point-set with, let’s just say…interesting features. And d(0) is a strange metric.

At this point you ask yourself, What does connected mean again? How does this help? What is it for?

Since the start of this course I’ve been saying that seeing and intuition aren’t a help. [That’s not strictly true, as I was walking my way to work yesterday I tried to see why the Contraction-Mapping Theorem allowed us to find intervals containing zeros of functions—that worked. If I’d done it the day before yesterday I might not have lost some marks.] And, in general I still think that this is the case. I just can’t figure out why this is so difficult—it’s conceptually hard to understand why this is conceptually hard!

Where might this be useful? Well, say I took two sets of words, the words that Shakespeare used and those of Dylan Thomas and a string-metric. [Oh yes! There are such things try the Needleman-Wunsch algorithm]. I could define a couple of topological spaces, then I might find a function f:S → D (Τ,Τ)-continuous function that might say something interesting…?

It’s official, I am now batcrap mad.

2012–08–18

topology & solitaire[2]

I’ve been thinking about this a lot over the last week, mostly because it seems to be helping me study the topology. For example I’m trudging my way through sequences in topological spaces at the moment, if I ‘see’ a sequence as moves on a solitaire topology it keeps me interested. Can I use this? I ask myself. It keeps me from self-harming.

I’m not so far-gone as to think that I can do anything with this but it is interesting. I have some ideas, which probably need to be tackled using both maths and computing, which means time. Which I haven’t got, or rather cannot make. The current plan is that I’ll do it during M256—Software development with Java. For now, when I have any time to spare, I’ll write a few articles on what I already know about solitaire and the approach I’m going to attempt [I tried to do this a while ago but never got very far. And I talked rubbish].

What intrigues me is that when I look to topology to model solitaire I find that properties, such as path-connected, compact, (Τ,Τ0)-continuous functions, etc. chime with the way that I, heuristically, play the game. This is almost certainly coincidence but as a group approach hasn’t ever got me very far, the topological approach must be tried.

The sad thing is that the current version of my Solitaire Machine™ will need a re-built from the ground up. The analysis engine that I spent so much time on was based on my blinkered groups-based approach. This time I need to build the thing properly!

I’ve said that more than once before.

2012–08–17

reality check

It’s been a busy week, full of work-work, topology and work-conversations about our future plans. Autumn is the beginning of the year in a school, the plans are laid down then, August. And ignored come October. Still, one must try.

My plans get laid down in the summer holidays. We’re to get a new building soon and I’m determined that when we move into it I’ll have the staff trained to stick to the brand image. That we have a brand image would be a start. I’ve made sure that I’m involved in all the sub-groups that are going to decide upon these matters. I’ve been pro-active: I’ve ripped down about a hundred posters, no longer will I put up with the pen-scrawled or centred comic sans…

Today the head of the upper school came to me panicked, “where is the board? I need to put up a list of the study classes”. This board would be the piece of crap that she’s addicted to and spoils the effect of the front entrance that we spent four figures on and Danny and I sweated blood to achieve.

“That’s all on the plasma screen”, I replied with a wave of an arm in the plasma’s direction.

They won’t look at that!”

“Crivens Shiona”, [because I can’t swear at work I speak like Oor Wullie] “What are we here for? To teach these edjits to fend for themselves, no? You’re spoon feeding these tumshies. If they are too stupid to look at the plasma (that we installed at some expense) should we not just let them wander around suffering the agony of the cretin?” [I speak like that.]

She conceded that I had a point. Then she tried to go over my head, she went tattling to the head. I’d got their first and with Danny hovering menacingly around, my argument prevailed, she stutter-muttered her way along the corridor. The first of many wins for me, I hope.

So I’ve been concentrated more on my school than on my OU for a while, but your brain is always thinking. Especially when I’ve had a pretty-big dilemma to resolve for a couple of weeks now.

I’ve been busy not making the decision that I knew I was going to make —all I can expect to get from the groups course is a grade two, at best. I made that decision today—if I fail I don’t care.

As soon as I made this decision I felt like a weight had been lifted off me; lot’s of the time crunch has gone. I can concentrate on the topology course.

When I do have a spare moment for the groups course I can concentrate on the actual groups units and ignore all that crap about tilings, friezes, wallpapers, lattices, et al… My life has been blighted by this shite for too long. I’ll try to do the group parts well, which should get me a grade two for the, whatever it’s called, the bit your tutor marks? Oh, yes OCAS. If the assessment calculator can be trusted, which as it’s server-side I don’t, I need only forty-one for the final TMA to get above seventy. Then, after the topology exam, I can do some revision and, hopefully, get a grade three. Number theory is in the offing which should suit the jib of my brain, so if I don’t fail the groups course and get a grade two in topology I should be fine.

For a while now I’ve had the feeling that there’s something wrong with my head. I’m starting to see the world in an odd way—today I moved a math’s-cupboard that had some child’s take on the Escher’s Lizard, a transitive tiling, blue-tacked to its side, as I struggled under this burden I was fretting about which tiling it was [there are eighty odd]. I’m broken beyond repair. This stuff has somehow seeped into my head and I will never shake it out again.

2012–08–07

topology & solitaire

I was working my way through unit C1–Connectedness of the topology course [I know, I’m so behind], when I had the thought—could I do anything topological with solitaire?

My first acquaintence with group theory was solitaire related I never got very far. Either with the group theory or with a way to use it to play solitaire. Anyway. I’ve seen solitaire in group theory terms since then—I think that I once used the orbit-stabalizer theorem to get the wrong value for the number of possible positions. Wrong world-view. Groups just didn’t get me any further forward solitaire-wise. Actually that isn’t strictly true: as my group knowledge grows I’ve began to have insights into why groups don’t quite cut it for solitaire, and hence I get insights into solitaire. At, the very, least I see that the simplistic groups that I used to reproduced someone else’s arguments are good for little more than a single result. [Symmetries are important — I think — there are some reversals that I can’t seem to do without them. That might just me being a bad player.]

Skip on half a year and I have new tools to play with. If I consider a board as a set of points, could it be a topolgy? The immediate problem is that a single ‘marble’ isn’t the empty set, and a cleared board isn’t achievable…

I might get round that. But even if I do manage to achieve a solitaire board as a topology, why might this help? It might not. My suspicion is that it won’t. Perhaps I should say what I am trying to do and why pissing around with such matters?

What we seek is a Pagoda function [or a SAX count], a function that we can input a move into which will tell us, given the board condition, if the result is such that the outcome that we desire is still on the board. [See the triangle5 board analysed here. Can we generalize that triangle result?]

At this point you might be wondering why I don’t just write a computer programme to do my business for me, alas this is NP incomplete => an algorithm that runs in non-polynomial time exists not. If I could write such a programme I’d be feted beyond normal bounds and hosannahed.

This might be the deadest of dead ends but almost nobody has published anything about the subject. I know this because when I google 'peg solitaire' topology I’m in the top ten. Even before this post.

I’m bona fide mad amn’t I?

2012–08–06

crunch time

August—two course blocks to do, two TMAs to complete and two exams in two months time. Things are looking bleak.

I’m seriously behind for both courses but I can’t let this get me down. A lot of hard work will be required, which is maybe for the best.

This year my final TMA is due in mid-September [exactly the same as last year]. Last year it was a revision TMA and I just stopped after I’d completed it. I did have excuses but they were excuses—I could have worked. I doubt if I spent more than ten hours revising. I’d forgotten almost everything from the early blocks, the rest was just hazy. Hence the exam was borkked, big-style. As could have been predicted.

I’m not a complete idiot—I learned the lessons and made a plan to deal with this. True, I didn’t plan to be in quite this of a time-crunch. However I don’t think that it will hurt me too much. The panic of having to work hard on the TMAs will get me into the habit of regular maths-toil. Hopefully momentum will be acquired.

My plan?

• I haven’t looked at my marked TMAs. I intend to start my revision process by using these to identify where I’m weak[est]
• This time I have notebooks full of notes that I can annotate as I revise the units
• All the exercise books remain undone—if I don’t cheat I have a wealth of problems to cement my understanding
• None of the DVDs have been watched, no audio CD has been heard
• I have four tutorials [two for each course], tutorials I will get to. Last year I missed them, it cost me dear.

If I do want to take a shot at this I can—I have all the tools to hand. The question is how much do I want this? That’s one problem—the will.

The other problem, the big problem, the heffalump, is when I should I cut my losses? I only need 71% for the final topology TMA to give myself a shot of a distinction in the exam. However, thanks to a really bad first TMA for the groups course, things are a wee bit tighter there. [I won’t really know where I am until I get my mark back for the third groups TMA.]

I need at least one grade two, I reckon that the highest I can aim for is a grade one and a grade two. My suspicion is that the topology course is my best bet for a grade one. For some reason I like and get-on-with topology. [I reckon that this is down to an early-course decision to stop trying to see and a chucking of intuition out of a figurative window. A topology is a set of open sets—get used to that, everything else follows.]

At some point you have to stop aiming for the stars and start concentrating on getting to the moon. For me and maths that time ain’t just yet. But when that time comes I need to aware that it has arrived with its kitbags, and intends to stay. Otherwise I might not even achieve escape velocity.

I’ll sit the exams for both courses, one must have a priority of my time.

In part this post is a reaction to my mate Chris’s woes, This week is last-week-of summer holiday here in Edinburgh, as a janny that weekend is never your own. I will be at that tutorial to talk him out of it. The other part is to make my internal narrative external. I find it hard to argue against myself inside-my-head. When I put it online I can usually spot the flaws.

2012–07–30

paloma time

I, more or less, finished my TMA for the groups course today—I’ve solved all the problems and I have ninety-five per cent of a fair copy done. Two days early! We’ll see how good it is, I suspect that glaring flaws may have crept into the crevices.

The lattices and wallpapers were, frankly, skimped; I just can’t be bothered anymore, I’m tired and I just want it all to go away.

I’m already half-decided that all I’m after here [groups-wise] is a grade two, so seventy odd will do me, which is about what I’ll get. After this course acetates will never darken my doors again, and there will be a bonfire, of the books that have blighted my life, in the garden some evening. With strong-spirits, fire, wrongness and dancing.

I feel sorry for the groups, which I like, and have ignored because I’m having so many problems with the bloodiness of geometry. I will work on them again, on my lonesome. But forever I will have a certain shudder when we meet, “you aren’t going to ask me about the translational symmetries of a frieze are you?”

Still Paloma has calmed my soul and I’m starting to think about topology, where I don’t have to see [I seem to remember that at some point I suggested here that I could see; a sad chortle would escape me if you suggested that I could do such a thing now].

I haven’t looked at the next block of the groups course yet, but every fibre of my soul knows that I’m perched upon the maw of a personal hell.

Business as usual then…

2012–07–29

technique, insight and truth

I’m sitting on the floor drinking half-and-half red wine and San Pelegrano doing my TMA for the groups course. I have two days left before it is due, I have one and one half units yet to read and the same amount of questions to do. Much of a muchness when it comes to me and TMAs for this course.

Thoughts are pricking my back-brain re my uselessness. Unusually such thoughts don’t centre upon my idelness or my inability to understand the material. This morning I was working through something group, I began to see that I had choices—not usual. Apart from one question in the topology course, most TMA questions are ‘straight’, they are based on the texts. Today I saw two ways to do something.

Non-mathos just won’t get why this such is a massive break-through for me.

I’ve battered on, at length, about the importance of a good technique. I’m right of course, but that isn’t the whole story. You do need an insight. Insights are hard and aren’t handed out to everyone, however hard you work. My insight may be wrong. Probably is.

This doesn’t get me any closer to truth. My Solitare machine may be the acmé of rubbish but it still saves my games, there are two reversals that I’m missing. I spend too much time on solitaire. Actually I don’t spend enough.

Truth is a strange bugger. Slippery and odd, and my strange-strange blue-blue eyes will never witness it. Alas.

2012–07–22

fun question

Every so often a TMA throws you a fun question [an example of which was question three of M257] such things are to be relished. M336—has thrown one up.

This is a live TMA so I’m going to be circumspect, but I think that I can project the general-gist. Let’s look at the following tables:

When I’m, sober, I’ll fix this table horror. I need to dive into a CSS file.

You are only allowed to swop rows and columns. Can table 1 be morphed into table 2? The answer is yes, the how is the problem. Crap like this is what I signed on for. I can’t give you the answer, because I don’t know it. But I know how it looks and where it lives. How?

Because I’m a game player—I see this stuff. I can see that it can be done, I can’t explain how, I skipped the bit of the unit text which proved this but I knew this anyway. I’ll have fun trying to do it for myself. More importantly I will begin to understand something that I can use elsewhere.

<snip />

It was windy out, so my wife and I decided that we needed to to get out in the night and take a walk along the canal. We saw bats and heard the trees. Things of wonder, things that will will live in my head and support me through the week of trial to come.

There’s a joy in everything if you know the right way to look at things.

so stupid am i

As I stated the problem, it’s impossible, without cheating. Row and column operations preserve parity. I don’t want to go into details but, I will say that if what you want is a reflection [reflections change parity] then you shouldn’t be messing around with rotations. I spent hours on this dead end before I realized this.

2012–07–21

matrices

Say I held a series maths parties at various locales around this planet of ours, where maths things got together over a drink [nibbles are available]. These are themed parties of course, so we wouldn’t want the Differentials to turn up at the Groups’s party. Whom might we expect to attend these bashes? Who would almost always turn up? How would they get on? Would there be fighting?

I suppose that we should distinguish between the gangsters and the loners—those that come alone and those that have to come together. There’s a wee bit of wiggle in that statement is there not? At least when it comes to maths—I can have a Set of functions, does in make sense to have a function of sets? A function operating on a set or a list of sets, or a set of sets, or some other collection of collections. See the problem?

We should remember that π is the type of guy who’s head is likely to appear between your knees, and lick your thigh, when you’re having a dump.

We always have to invite the numbers—the integers, and the reals [et al], who will strut their stuff on the dance floor and get between each other; Archimedes might nod over his Retsina in a corner muttering their denseness but they are the heart and soul of the party. Complex numbers, being punks, will pogo.

Then there are the proles, the work-a-day, The matrices. these won’t be invited to classy bashes but without them we have nothing usually.

…

A couple of years ago I spent a christmas holiday two weeks learning how to diddle matrices. Best two weeks of effort that I’ve ever spent.

2012–07–18

wallflower

Did you know that there are only seventeen types of wallpaper? And now that you do know do you care? Apparently people do/did, because I’m currently working my way through an entire unit devoted to proving this fact. A quick google also suggests that some of the mathematical greats were interested. I’m not. As far as I’m concerned wallpaper can detach itself from the wall it is currently hanging off, re-roll itself and piss-off back to from whence wherever it came from.

On principle I avoid interior decoration, or the discussion thereof, I pretend to be phobic when my wife brings the subject up; but that bastard-wallpaper in the kitchen [type p2mg if you are interested] now has to go. There’s a real chance that I might become a huger bore than I already am, about wallpaper. This is not good however one looks at it. Especially if you are me. Still this is missing the big picture.

Today I read this screed of repetitive rubbish in full for the first time in ages. I re-read it because last night’s post got me thinking—should I just give up on the groups course? [That would be to the extent of just going for a basic pass.] Which would hurt me only in my pride—I’m doing enough level-three courses such that it won’t effect my degree classification. It doesn’t really matter in the greater sense.

I’m trapped in a hell of my own choosing. Worse, today I had a thought about what ℜ^z might be when z < 0.

2012–07–17

m336

The least said about that last post the better. I’d like it to be gone hence to nada but that’s against the rules that I impose upon myself. So stay it shall, please ignore it.

Again I’ve got myself into that situation—too little time, too much work. For a, supposedly, clever man I’m an awful clot. Fortunately this is a two-week panic rather than the more-usual two-day desperation. Doesn’t help much, if I’m being honest. Inside my head the adverb utterly is again being used alongside stupid and a swear-word regarding said me.

The one bright spot is that tonight, when panic was rife, I managed to complete nearly a quarter of the TMA. This should be balanced against the fact that, again, I have three units to complete in less weeks.

I’m tempted to just write-off the groups course—I won’t but I’m so tempted. I’m tempted because I’m pretending that it is stopping me working more effectively elsewhere. Which is an utter fucking lie. It’s me that’s hindering whatever progress that my brain might be up for.

I spent the last few weeks steeping in my pit, reading history books, feeling sorry for myself and reading my own dog-food.

My take on me? I come across negative. I don’t mean to be—most people that I meet in the real world are annoyed about…that isn’t true either. It’s another lie. Let’s just say that I rarely lack a reason to explain, and exploit, my sloth-tendencies. Catholics have confessors, I only have me. If I’m not horribly-hard on myself I’ll do diddly. I wasn’t always so; and guess what? I did diddly then.

Just a depressed bore? Probably.

Still, today we re-arranged the office so that I have a huge wall-space to scrawl-upon, so that I feel that like I’m a proper mathematician; I’m going to search up Amy, play it loud; have a wee drink and regard my scrachings. There’s a joy to be had in this studying lark.

I suppose that I should own my inner-idiot, but you can’t have it all. Sometimes you just have to smile at yourself.

2012–06–30

epsilon delta

I really, really, shouldn’t be writing this. An idiot’s guide to wrong.

Everyone struggles with the ε–δ definition of continuity, so I’m going to relate my woes and insights re the beast. What do you mean?, “what do I mean?”

Continuous

That a graph, of a function, can be drawn without taking the pencil off the paper, on the domain of the function.

Which will do for now. Notice the bit that I emphasized. Let’s take a perfectly normal function like 1|x, pretty obvious that it is discontinuous at 0 isn’t it? Alas not so, the domain of 1|x is {R - 0}, so 1|x is continuous on its domain. Head hurts? Leave now, things are going to get worse.

Good, we’ve dropped the lite-weights. The problem is that we don’t have a way of defining what we mean by continuous. Enter some eminant Germans who say that if we can get as close as we want to something and yet can always get closer then we have continuous. This is an odd concept, shouldn’t we get there sometime? But that’s the point—whatever the input to the function, we can always find an input that will be closer to the point which we want to be at. If the function is continuous there must be points in-between. [NOTHING has been defined here.]

When we were first introduced to ε–δ it was all, “I give you “ε you must give me a smaller δ”. I well remember the tutorial when I saw the wrong. The function is the thing to look at. Never assume that δ must be less than ε. Maths is a shitland of horror.

We need to ensure that for any number, [here we are talking real] that for any ε we have a δ. So we need to define ε in terms of δ. And we should realize that we are dealing with mods here; everything is positive. It’s not about my ability to find a smaller number, it’s about my inability to to develop an algorithybm.

We come to life with an attitude. We are nearly always wrong. -headfed

2012–06–24

minimality conditions

I’m really struggling with the groups course. This is because I’m not enjoying the subject matter—I’m OK with the groups but the lattices/friezes/wallpapers etc. just put me right-off. So much so that I can’t settle into a work régime—I sit down, get out the books, start reading and give up. Part of the problem is that because that I don’t like the subject-matter I’ve skimped when it came to learning the basics. So now not only do I not like it, it’s now much harder to do.

I know the solution, but I don’t want to apply it. I need to go back to the beginning and own this stuff. I’m always moaning on about my inability to do just this it seems. Usually I’m right about my laziness being a factor, however there’s new problem here—I don’t really wan’t to own this stuff. I just don’t care. I’ll muddle through I suppose, I usually do, but I see a bigger problem—what am I going to do next?

Come October my last maths module [M381–Number Theory] trockles onto my stage. After that it’s three computing modules and the degree. What then?

You think about these things, I’d planned either a maths MSc or a trip back to applied maths. The programming stream doesn’t appeal: I don’t want to build enterprise solutions to problems that I’m not interested in. Up until now I’ve loved the maths that I’ve done, suddenly I’m wary.

I could, I suppose, just study the things that interest me by myself. Chortle. Without the structure of the bits-of-paper and the OU I’d do less than just piss-around. Without my maths-mates and my tutor I’ll waste the rest of my existence.

I’m not where I want to be yet, but I do know that if I’m going to get there the OU, and the people who I’ve met on the journey, will be the major part of my process.

2012–06–16

cheating

There’s almost always a way to cheat at anything, probably many ways. This must be a particular problem when it comes to distance learning, and indeed it seems to be.

That particular way of cheating should be easy to catch: looking at the marks you’d quickly spot a series of anomalous patterns. In fact it’s so easy to spot that I wouldn’t even consider doing it that way.

Cheating, and stealing I suppose, have always fascinated me. I’m not [really] tempted to do it myself, but I always think about how it might be done.

In part this is down to the job I do: one of my main responsibilities is to ensure that millions of pounds worth of things don’t get chorried and that over a thousand humans don’t get hurt. [It’s always a wee bit gobsmacking to realize the I (me!) am responsible for that.]

It’s also because I’m a programmer and webmaster; you have to think of what Dr. Evil and her pals might do that would leave you bare-bottom naked in the room of blame. You have to be able to think like the bad guys.

Good security is always a trade off—I could make a plan to cope with my school being attacked by tanks and rocket-launcher welding mad-people. Should I? Seems a wee bit excessive. Bad security is all about doing things so that you can be seen to have done something when the bad thing happens. I see my job as to making sure that most of the bad things, that might happen, don’t. Others don’t see it that way.

It’s always the details that trip you up.

When I attended an actual bricks-and-mortar university I did a maths course. Every couple of weeks we had to submit an assignment. To submit this we had to pop our work into our tutor’s pigeon-hole. The pigeon-hole was in a public area. Can you spot the flaw?

Correct; swots would submit early and idle-losers like myself could man-in-the-middle—i.e. pick up somebody else’s assignment, photocopy it, return it to pigeon-hole and use it as a crib. I didn’t do this, the idle was strong in me then.

There’s a large part of me that, while I respect the cleverness of it, just doesn’t get cheating. There’s an effort involved that might be better spent in actually doing what you were supposed to.

Take the above example: I’d have had to taken some trouble to ensure that I put my mark onto the assignment. What do I mean by mark? That’s complex to explain, but you already understand it.

I have two maths books that I’ve been working through for a couple of years now [and for the rest of my existence]: Halmos’s Niáve set theory, and Hardy’s Pure maths. Both books positively drip personality. Outsiders might see maths as something that it isn’t: devoid of humanity. Which couldn’t be further from the truth.

I suppose that I’m still that wee boy saying to my maw, “look how well I done!”. Look how well I cheated would not have gone down quite as well.

2012–06–12

where am i?

Yet again rushing to complete a TMA is the answer. And, yet again with a unit left undone.

I’d planned that I would work at it last weekend, but guess what? Yes, that’s right: no work got done. I spent my time piddling around at I know not what. Again I’ll get away with this [I hope]; forty per cent of the marks are for something not conceptually difficult, which I have done some work on and which is almost self-checking.

At least for this set of TMAs I have put some effort in. Actually, and more to the point, is that I’ve put a lot more effort into attempting to understand the units. Which isn’t the same thing and is the reason why the TMAs have gone better.

What’s tripped me up is that life gets in the way—when I need to work the hardest I always seem to be at my lowest. No, what’s tripped me up is that I don’t actually understand the units.

Maths is no longer coming easily to me. When I signed up I knew that this moment would come, but on-the-road I seem to have forgotten this fact. It’s not that I can’t understand—it’s that I need to work much-much harder for an understanding. And by understanding I don’t just mean getting good marks. Sometime I’m going to want to use all this stuff. It has to be part of me.

The problem with maths is that you have to be right, and that you can be. For example my marked TMA for the groups course dropped through the letter-box today—I got a mark that most students would probably bite someone’s extremity off for, [for once I’ll tell you, ninety-five per cent], I won’t say that I was disappointed but I was miffed about the silly slips that I’d made. With maths it is perfectly possible to get full marks, and to do it regularly.

In my heart I know that I don’t understand and need to work harder; it’s just that my head is having issues.

2012–06–06

yet another TMA post

I posted off the TMA for the groups course today, still with the feeling that it wasn’t right. Now I have about a week to do the topology TMA. I still have about a unit and a half left to read but I amn’t panicking just yet. I can throw a lot of time at it this weekend.

Part of the reason that I’m not as far forward, as I would like, with the topology is that I got interested in something group. True, it’s something that will be explained in block three, but for the first time in ages I enjoyed myself messing around with maths. That’s what I’ve been missing—a bit of fun.

It’s a wee bit more than that; I’m not certain-sure how I ended up doing all this maths stuff but part of the reason must have been about me solving problems. When I look back on the maths courses that I’ve taken they are all of a type—proof-heavy and applied-lite. I don’t want to know things just for the sake of knowing them—I want to know things so that I can do stuff. True, that stuff is mainly computing, still…

I won’t ever do anything truely original, that wasn’t the point really. I do want the tools to be able to mess around properly. And while I’m aquiring said tools I should be messing around. Otherwise I won’t learn how to mess around properly.

2012–06–02

nice

I have a fair copy TMA for the groups course ready for the off. I’m not happy with it. It won’t be the disaster that the last one was, but it still isn’t right.

There are places where I’m sure that there’s a shorter, more elegant, solution. Actually I don’t care about shorter, I do care about elegance.

I may be beating myself up unnecessarily here—elegance is something that you achieve when you’ve mastered something, you don’t get it out of the box. Then again, I may be right—because what I’m producing isn’t aesthetically pleasing [I’m a Hardy fellow-traveller] I know that there’s still much road for me to travel.

I’m getting ratty with myself when it comes to the groups; for once I am putting the work in, but I know that I’m not grokking it properly. I can do all the technical stuff but I can’t put things together. If you framed a question in way that I hadn’t seen before I’d be lost.

My problem is that I don’t have a proper understanding of the basic material. Time after time I had to look up something that I should know—what does isomorphic mean? [The equivalent of not seeing that 2 × 3 & 12 ÷ 2 are the same thing.] There’s a nice distinction between doing the work required to pass a maths course and actually understanding the maths involved. I’m on the wrong side of that distinction.

I was wracking my brain for a suitable metaphor for what, I think, is wrong with me. It came to me when I was looking at the higher computer paper. [I won’t rant about it this year…] There was a question about a binary, a two’s-compliment was required I think. My first thought was, “what’s the point of that? Who uses binary operations now?” My second thought was, “me.” I don’t use them often but there are some places where they shine. Take a minute to think about an algorithm to decide whether a given integer is odd. Not exactly easy is it? Here’s how to do it in JavaScript:

function even(num){ var even = num & 1; if (even === 1){ return false; } return true; } document.write(even(23333)); //false

The & is the bitwise AND operator.

I suppose I spent a couple of days studying binary operations, I use them rarely, but having them in my toolkit makes a big difference sometimes. That’s where I want to be with maths. And when it comes to groups [and the filthy tilings] that’s exactly the place where I’m not.

There’s a sticking point here—to get to where I want to be I’ll have to do a lot of uncongenial work. Work outside of an, already busy, schedule. But sod it neil, do you always want to suffer the nagging sense that there’s something ugly about your solutions? You want them accurate and elegant, you want them nice in all the senses don’t you?

2012–05–16

working…

Hard for once. I’m not sure where I am with regard to the course schedules, but I feel like I’m beginning to catch up. There are still problems, particularly with the groups course. These difficulties are mostly down to me having been lazy in the past methinks.

So the plan is to get the TMAs done and in early so that I can spend some time [re]learning the basics. Then it’ll be time for me to learn what I’m supposed to be learning now. There’s a problem with stuff going in you see.

I think that the problem lies in the proofs. I was reading Duncan’s blog the other day—he seems to be having a different M208 experience from me—but I think that he’s spot-on regarding the proofs. You really do have to do them, and I haven’t been.

This week I’m on back-shift, and I know, from long experience that I can’t do any proper [OU] work on back-shift. What I can do however is piddle around with my own maths stuff. So that’s what I’ve been doing—trying to create my own proofs for some wee bits & pieces. To no great effect alas, but actually managing to create a proof wasn’t my primary motivation.

Reading other peoples’ proofs is one thing, trying to create you own is a different matter. It’s like a lot of things: music, writing, rocket science—you really have to try doing it for yourself. I know that it won’t come easily, it may not even come at all, but it has to be tried.

Probably the piddling around will be of more help to me in the near future. For too long now the only maths I’ve been doing is course maths. Sometimes you need an unrelated [related] problem to allow things to gel. I know that I’d never do a computing course without giving myself a project to ignore and fail to complete. The point isn’t to create anything, it’s about trying make something where what you are learning may give you new options.

I still don’t have the basic skills to tackle anything non-trivial maths-wise, but that shouldn’t stop me trying.

If you can choose a problem related to what you are studying, you’ll get the side-benefit of having to learn the course material to solve your problem. Such problems are quite difficult to find—they tend to occur in the course texts. [I have my solitaire!]

So the plan outlined in paragraph two above has to be altered to make time for me to mess around. Jolly good.

2012–04–28

stuck inside my head with the group theory blues again

The first set of TMAs are done, gone and back for both courses. The results?—mixed. The groups one was a predictable disaster—you can’t expect to do well if you don’t do the work, do the thing fuelled by much way too much red bull and only give yourself a couple of days to complete the process. The topology one? Not too bad, at least I knew where I was struggling.

My problem is with the groups course, which isn’t the one that I expected to be struggling with. The wonderous surprises of life…

The other day I was lying steeping in the bath pondering why this was so, my conclusions—I haven’t worked hard enough. Stunning eh? What I mean, however, is that I didn’t work hard enough starting with M208. Nothing comes naturally. I can parrot things but if you gave me a question without a hint as to the how of tackling it I’d be stuffed.

When I’m working my way through something group I keep having to remind myself of results/theorems that should be second nature. I lack basic technique. You can’t build a maths understanding on shoogly foundations.

My problem is spot-lighted when I have to do something where I have done the work. This week I’ve been doing colourings [How many distinguishable ways can you colour a cube with x colours etc.]. Now, for various reasons, I needed this for my solitaire thingee, so I’d actually created an algorithm for this [though you had to know what you were doing to supply the params]. Hence, although I didn’t do things the way that they do them in the unit text, I wasn’t lost. I may even have come to some of the conclusions independently—it’s difficult to remember. This is where I want to be with the rest of the course.

There aren’t any short-cuts here—I just have to work hard. And by work hard I mean get the paper and pencil out and do some scrawling, fiddle the symbols—develop a tacit understanding.

For example, last night I needed to use the binomial theorem for some stuff; it took me about an hour of messing around to see what I needed to do. I should have put that hour in during MS221. It’s done now, but my past lazinesses are coming back, like holiday acquaintances, to haunt me. For the sake of the future me I have to tackle this now.

Fortunately I seem to have found a study-rhythm again, I want to be doing stuff for, what feels like, the first time in ages. True, that stuff is programming or topology, but after nearly six years at this OU lark I do have a wee bit of study-discipline.

All that said, this weekend I’m going to give myself a break, I’ll make myself a curry, get drunk, go to bed early, and do some topology. Pukka!

Before I posted this, and possibly skewed the results, I googled 'group theory blues'. This, I think is the most fitting. Still Bob is always better, just replace Memphis with group theory, Texas medicine with topology and railroad gin by programming.

2012–04–16

the groups course

For the last few days I’ve been playing catch-up with the groups, doing the units that I should have finished weeks ago. As I work my way through them I become more-and-more despondent with my TMA effort. Silly mistakes, dodgy proofs and outright misunderstandings are all abounding. I dread the thwunk! of the arrival of it marked through the letter-box.

Putting all that to one side, I have a question: what exactly is it, about this course, that makes it feel so odd to me? I still don’t have a full answer, but I have a few pointers as to where that answer may be skulking.

This course was written a long time ago [in an OU sense]—I know that because the PDFs aren’t real PDFs, they’re scans. Why does age matter?

Courses change, as does the way that they are presented. All of the maths courses that I’ve studied so far have followed a similar format—the structure, the language used and methodology are similar. Before the groups course I hadn’t really noticed this, now it stands out a mile.

This course was created before the pow-wow that normalized the maths syllabus was held. Which is a part of its oddness methinks. But it’s more than just that…

With the M336 units I feel like I’m reading a maths book, a certain kind of maths book anyway. Actually that’s another issue, the units aren’t like any maths book, never mind OU text, that I’ve ever read. There’s something … almost … discursive about them. They all have authors.

Perhaps that’s it: that this is a course build by collating the efforts of a group of individuals? Looking back at my notes I can see that I’ve written down the same theorem multiple times, although to be fair the contexts have always been different.

Am I studying an anthology?

I’ll suspend judgement until I’ve completed block two, or at least caught up.

2012–04–12

standard form

I managed to get my TMAs away in time, just. I’m not very confident of any good results. The topology one shouldn’t be too awful, but the groups one unravels in my mind on an hourly basis. I’m beginning to think that it might become my worst TMA ever.

Aside from the fact that I was rushing, didn’t understand what I should already have known and hadn’t done the work my main problem was—the standard form. The standard form is a notation that ensures that if a thing is the same as another thing then the notation makes sure that they look the same. What, in computer terms, I call normalized [warning: this is my in-head word for it, it has a very specific meaning in some contexts.] It goes like this for affine transformations…

t[a]λ[θ]

λ being either at rotation [r] or a reflection[q] and [a] being a 2*1 vector. I got this [although in my TMA I used the explicit form a couple of times—marks dripping away…] Where I started to have problems was when we came to a standard form for groups. Consider this…

D6 = <r, rns, n = 0, 1, … , 5: r6 = s2 = e, sr = r5s >

Not quite so obvious eh? It took quite a while for the penny to drop; if I’d been reading the fora, as I’m supposed to, this would have happened a great deal sooner, lesson there. As I thrashed my way to the end of my TMA I began to appreciate how wonderful the notation was. To late to do any TMA good, but hopefully something that will help me for the rest of the course.

The beauty is that you can manipulate the group algebraically so that you can see that sr4ss = sr4 = r-4s = r2s ≠ r5 (using various identities and inverses). This is a huge advance—no longer do we have to diddle with bits of paper and diagrams. [Well…I still check my answers that way!] I’m still not wholly comfortable with it, but I see possibilities…

I was, becoming, worried about the way that the groups course had been going for me—I seemed to have lost my appetite for something that I love. People have been been posting in the fora about their woes with the thing; treacle and other non-runny substances feature heavily in their similies. I’m with them—there’s something odd about the groups course as a maths course. I haven’t go a handle on what the this is yet. I will do

But last night I found myself doing something that I haven’t done in ages—trying to solve a problem that didn’t attract marks:

For D₈, find the number of sub groups of order four.

I came up with a geometrical way of looking at this, and being an edjit of type-one I posted this way to a forum. The cold light of sobriety threw shadows and caused doubt. I still think that I’m onto something, and, as, in the background I sense an algorithm or, more likely, a heuristic, it’s probably worth a night or two’s effort. Tonight I’m going to apply the standard notation to the bits of paper that lie scattered on the floor that are driving my wife to despair. [It’s only a matter of time before I’m allowed a slaked-lime board in the living room. She can only take so much…]

Having fun again!

D₆ is the Dihedral group of symmetries of a regular hexagon.

2012–03–31

notes

This week has been all topology. I’m still very behind but I’m catching up—I should have the topology TMA complete sometime early next week. Then it’s on to the groups. The first groups TMA is due in by the twelfth and three and a half units are still undone. Gulp.

I tell myself that, worst-comes-to-worst, I can work the TMA. Something I dislike but is nearly alway do-able.

Work: in the context of a TMA, means to find problems/worked examples in the unit texts that are similar in form to questions being asked. To parrot answers without any understanding.

There are obvious problems with this methodology [if you can dignify such shameful behaviour thusly], especially as this is the first TMA—however much you promise yourself that you will go back and do the block properly, you won’t. Or at least I won’t.

I did this for a couple of M208 blocks last year and it really hurt me, both at exam time and when doing the later blocks. [Interestingly although I do mention this in my blog, I don’t make it explicit what I’d done.]

Actually, writing this has made it clear that I am going to have to do this. I might as well be honest with myself and start doing it early. I remember the hopeless-flailing-panic of having to do it on the day before the TMA was due. I never want to suffer that again.

As of this moment I won’t be reduced to such desperate methods for the topology course—so I should take an extra couple of days to complete the block properly. I should try to avoid having two borked courses on the go at the same time.

topology

Strangely, I think that this course is going rather well, for the first time since M221 I feel on top of a maths course. All the continuity business, that we did during M208, has finally sunk in, I like metrics and already see how I might use them in my on-going solitaire project, I’m comfortable with everything that we’re doing. I understand the what, the how and the why of what we are up to. I think that I even have an inkling about where we are headed. All-in-all I’m pretty happy. Maybe that should worry me?

I’m sure that much of this is down to the fact that I’ve changed the way that I’m tackling the units—I’m making notes as I go along. I’d never considered making notes for a maths course until someone [I’ve, shamefully, forgotten who, but thank you someone] on the course forum said that they did it. I decided to give it a go; it seems to have worked.

If for nothing else it’s good practice at writing the symbols—one of the odd things about maths is that you have to be familiar with the Greek alphabet. Write ξ [xi] anyone?

It also seems to help stuff get into the meatware. Just reading a theorem isn’t good enough, writing it down fixes it in your mind. I’ve also taken to writing down any theorems, then, before reading the proof, attempting to find a proof for myself. My strike-rate is woeful, I’d be lying if I claimed even one-in-ten. But often I have the right idea, with work it should come.

next course

Despite my current troubles I’ve just signed up to number theory and software development for next year. [Thankfully an October/February split.] Now it’s back to topology for the rest of the weekend.

2012–03–23

getting back…and problems

Because I’m, again, marooned, in my other building, on a Friday night where I can’t post to my nonsense I will format this as if I was posting there; and fix it tomorrow. [2012–03–23]

Tonight we have the PTA race-night. Which is OK as they are all getting drunk and I condone that type of behavior. They, do, tend to interrupt a janny trying to focus on his maths and there are, what might be their, strange yoofs gathering outside. Still, I’m always up for nonsense…and the quashing thereof.

how’s maths?

Slowly-slowly this week I’ve been ramping my maths back up to speed.

I’ve been on back-shift: but every day I’ve tried to do a wee-bit before, during and after work. Some days it hasn’t panned out. Most days I’ve gone to bed with a fear in my heart.

I made a decision last week—one that I think was the right one—to just do something. I think that it’s paid off. Here is the balance sheet:

• Woefully behind at work: disciplinary action hovers over my bonce for my massive undone
• I have a tutorial tomorrow, the venue has been changed, I might not even be able to find the place—never mind do the maths involved.
• I looked at the course-fora for the first time in ages today, I didn’t have the bottle to open up a single post, never mind to make a reply.
• I’m a whole four weeks behind with the groups course. For the first time ever I can’t read Nilo’s stuff, because it’s like a blade turned into my failure. [Not his fault—mine.]
• I’m still behind on the topology course
• The end of the financial year is coming up, there is everything that I haven’t done for this.

still…

Been here before, will be here again, blogged it. I’m alive, I have food, drink and drink-drink and a better life that 99% of the people on this planet have ever had…

The problem is, that, often, in your day-to-day the above doesn’t make you feel better. When you have been massively blessed: to be thwarted, or asked to pay, or even slightly indisposed; seems to be an imposition of the worst kind. Someone else than you must foot the blame.

Others have more, others falsely out-shine…, others—cheats & scoundrels all, do better than you unjustly. Just others.

Tonight I found the first diagram in the topology units that actually reduced my understanding of a concept. [Although these diagrams have been on a cusp for a while.] Something that I’d predicted.

I don’t care about others. Any more. From now on it’s just me who I have to blame.

2012–03–19

hopeless

On back-shift again. I’m trying to get something, anything, done, but the two hours of topology that I did this morning while waiting for the gas-engineer was probably a wasted two hours.

My despare isn’t total, but it’s getting there. Tonight I brought my group books to work, not opened. I know that I can’t do OU-work at work. Still I persist in lugging unopened books back-and-forth on a semi-regular basis.

I’m just annoyed.

Yesterday I went to my Mum and Dad’s to borrow some money off the cheque that Scottish Power has eventually had sent. They had sherry in the dinky high-end shot glasses that they have, I had a claret, I think. My Mum and Dad have got old.

They are still H & H [Hale and hearty] but I’ve began to believe that they are mortal.

We had a conversation about maths, a sure sign that Mum isn’t well, this wasn’t something that she would have allowed when she was on the ball. Then we walked round the garden. The grasses look great; Dad and I had a conversation about why their tulips were so far ahead of ours.

This week, Thursday, my mother goes in for her second cancer operation in three weeks. I’m screaming inside and feeling like a louse because we said that outside the four of us and the sisses this wasn’t to be shared.

I was always the weak one.

2012–03–16

catching up

This week I’ve been playing this game. I get home, eat a couple of bowls of rice & beans and get out the maths books. The plan is to complete block one of the topology course, get the TMA done and then tackle the groups course. This isn’t a great plan but it’s the only one that I’ve got.

Yesterday I realized that through a series of mis-judgements I’ve ended up in this strange place—doing two level three maths courses, having my life ruled by TMA deadlines, being always surrounded by paper and thinking about numbers… How did that happen? I don’t remember this being part of my life plan. I don’t remember any conscious decision being made.

This came to my attention because I was at the chess club, explaining pawn endings to some of the kids. These would seem simple to the uninitiated, but there are a lot of subtleties involved: opposition, triangulation, zugzwang etc. I began to explain that, for a king, a straight line isn’t always the shortest distance. Pretty quickly I began to talk metrics—as the crow flies, as the wolf runs…

I’m not unhappy, but I am not the same person that I was six years ago, I’m not sure that I’m a better one, I’m just changed. Maths has clamped a rigour on my soul; there are things that I can [want] no-longer be slap-dash at. I didn’t mean to end up here. Be aware, folks, that if you take one step upon this road of ours it may lead you to a destination that you didn’t expect.

2012–03–10

way behind…

I’m very behind now. I’m beginning to realize how badly I’m missing a computer course.

For the last few years I’ve been doing a computer course alongside my maths one. Which meant that if [when] I got bored/stuck with one, I could just switch over to the other one until my appetite returned. The only time that this didn’t work was with M208 when M257 finished. Which was an omen that I should’ve heeded.

I thought that I’d be alright—I could do the same with two maths courses—if I had trouble with groups I could do topology and vice-versa. Well it hasn’t worked out like that. All this week I’ve been trying to force myself to do some math—any maths. It hasn’t been working; I sit down, get out the books, make a few notes, do an exercise or two…after about half-an-hour I give up—nothing is going in.

So why isn’t the plan working? I think that there are a few things:

1. Computing and maths use, however slightly, different parts of my mind; topology and groups are too samey
2. The October–February break in my studies has hurt me [as I thought that it might] I’ve lost my mettle
3. I’m trying to force myself to finish something that I’m not having fun with

Number three above is the key problem I think, perhaps with a smidgeon of one thrown in.

I’m stuck on a part of the groups course which, while not difficult, is something that isn’t my cup of tea but does involve work. I should just do something else, either some non-course computing or topology. But my mind resists:

• If I do any computing, it’ll be programming—it will feel too much like fun. I’ll feel guilty
• Because I got ahead with the topology course I’ll [again] feel guilty if I devote any more time to it

There we have the answer—good old protestant-work-ethic guilt.

So this weekend I’m going to make a last effort to get over this hump. If I don’t manage that then I’m going to forge ahead with topology. At least that way I’ll be getting something done.

update 2012–03–12

This post was meant to go up on Saturday, but I was suffering from computer connectivity woes.

I went home on Saturday, watched the rugby, ate eight bowls of rice and went to my bed at ten o'clock. I woke after three in the afternoon on Sunday. I guess that I must have been tired.

If you surmised, from the above, that nil work was done award yourself a coconut. So plan B—get torn into the topology…

2012–02–23

falling behind

For the past couple of weeks I’ve managed little maths-wise. I think that I may be officially behind the schedule. I did manage to get the first topology TMA away.

I’m never sure about TMAs—when I think I’ve done a good one I haven’t, and sometimes [not always] what I thought was a rushed shambolic attempt earns me good marks. This is a worry.

The worry is that, if I was on top of my maths, I’d have a fair idea of how good what I was producing was. And would know why my TMA was rubbish; if it was.

We’re not allowed to talk about TMAs or the marks that we receive for them, but there was a question in the last one that I think I can use as an example without citing it directly.

I had a fair idea of what I wanted to do, I had a clear idea of what I wanted to prove. I think that I managed, but there’s a nagging feeling that I didn’t cover-all-the-bases, I skimped, I think, on parts of my argument. There were a couple of places where I knew that what I was saying was true, but my arguments weren’t convincing me of this truth. Even the sentences that I’ve used to describe my woes are wandering waffle.

Maths may require an attitude of mind that I just don’t have. No, that’s not quite right: proper maths may be beyond me, but maths, for the rest of my life, will always be with me.

Computers, programming is just a stuff that I do. Whether I’m bad at it or not doesn’t matter. Maths gives my mind another attitude. I might never understand even the basics but it’s something that changes the way that I look at life and who I am. And as I’ve never been too happy with me…

2012–02–13

nothing done…

…this weekend. Well, I did manage to catch up on my sleep and I had a new idea in my endless, obsessive quest to crack peg-solitaire. [I also did some Voynich catching up too, but the least said about that…] So almost, but not quite entirely, a wasted couple of days in the life of me, as a savant.

The little maths that I did do involved unit 2 of the topology course—metric spaces. Already I’m almost too taken with topology, I’m neglecting the groups. I wrote a rambling post on the OU supplied blogs on the subject but I’m pretty certain that I didn’t make much sense. I probably won’t make much more sense here either, but hey.

This is the narrative:

Maths for me, so far, has always been about completing the course-work; it’s never been about me foraging the wide-world of maths in general; I have the books but all I look at them for is exercises. I took up maths again because I couldn’t understand the computer science without it.

I didn’t expect maths to be much more than a type of mental body-building—something that I’d have to do to be better at my chosen mind-athletic event. But maths, like body-building [apparently!?] sucks you in.

First it was groups. As soon as I began to understand what was going on I was hooked; I began to see linkages. Vague sure but… for a long time that was enough for me, then came M208, and group actions. I saw that hadn’t appreciated groups, in a practical sense, before; sure, I’d seen the beauty but…the raw power? Hadn’t seen that coming.

Next we have Topology. Unit 1: continuity again. I have to say that I’ve never had too many problems with the ε–δ definition of continuity [what I do have problems with are the black-arts of symbol-mashing that are required for the proving of. Territory, I suppose.]

Then came unit 2, distance stalked in, Euclidean, so what. Cantor distance: I was smitten. Suddenly I could see the point, suddenly…… Calm down neo, you don’t know nothing yet.

That’s what love does. A certain kind anyway. You never see the shackles until they are firmly on, and when you do see them you realize that you want to flaunt them as ornaments.

You may wish to know what my new idea about peg-solitaire was? I’ve tried distance functions before [to plug into algorithms], but I hadn’t realized that they’d all been Euclidean. Now I have other distance functions to consider.

I need to write some more stuff about solitaire soon. When I have considered.

2012–02–04

first tutorial

This afternoon. It’ll be a bit of a rush getting there as I’m working until 12:30. And the weather is looking gray and sinister—snow might be on the cards, just what we need!

Today is officially the first day of both courses, but I’d be surprised if a single student hasn’t already started weeks ago. The fora, while not exactly on fire, have certainly been fairly busy. Which is good.

The note taking for the groups course seems to be going well. However, It’s still early days—I’m about half way through the first unit. I rather like tilings, I’ve already managed to get the fact that there are only eleven kinds of Archimedean tilings into a couple of conversations. One conversation was with a couple of maths teachers, who were surprised by this fact, which surprised me.

In S1/2 [Secondary years one and two] the kids create lots of tiling-type drawings on graph [or hex] paper which get stuck up on the corridor walls if they do it well—maths teachers should know all about tilings[?] Turns out not. Well, that ain’t strictly so, they just haven’t ever had to rigorously define what they mean by a tiling.

Because I’m doing topology and a tile is defined as a: closed topological disc, my mind started asking questions and having ideas. Are affine transformations an example of the continuous deformation that we seem to be thinking about in topology? Which led me to the definition of an affine transformation and a thought, the matrice has to be invertable—what happens when it isn’t?

I’ll let you fret about that for yourselves… Time for me to get my ε–δ–diddling head on.

2012–01–31

more plans…

I started reading the first unit of the Groups course lying in my bath this morning. I like a wee bit of maths with my bath. As I was towelling myself down I began to see a wee problem—I’m going to have to rigorously separate the topology and groups courses inside my head; otherwise they’ll bleed into each other and confuse me.

You’d think that after nearly six years of OU studies that I’d know what works for me, learning-wise, by now—not so alas. My big worry is that I went wrong last year, and I’m seeing the symptoms of the same malaise.

My problem, with M208, was the exam—the TMAs were fine, mostly. I can see this happening again. I can work my way through the books, I [suspect that I] can do the TMAs, what I didn’t do last year, and I must do this year, was to work at the exercises. And not just the ones that we’ve been given, I must make up my own.

When I was at school we spent hour after hour and exercise after exercise when we were learning the calculus. Such an effort may not be required for every part of my current courses; but there are certainly going to be places where I could develop a proper feel for the concept better by doing, rather than by just reading.

I think that this learning-paradigm will be more suited to the topology course. I may need to adopt a slightly different tack for the groups course.

There I’m going to try something even further off-the-wall—making notes. A post in the café by Duncan E gave me the idea. He’s doing M255 and asked about our attitudes to taking notes. Which brought back to me my M255 notes, probably the only comprehensive notes that I’ve ever made. They, the notes, served me well. Perhaps it’s time to try the same thing again?

The spin-off is that I’ll be working in different ways at different courses, so I should be able to keep them apart in my mind.

2012–01–28

plans…

That will gang aglay [Burn’s night quotette]. As ever.

This week, when I haven’t been work-working, lying in my pit moaning, or [playing at] studying unit A1 of the topology course, I’ve been thinking. Thinking about how I’m going to tackle my next nine months of maths.

The only, reasonable, plan that I’ve developed is to stop all this bloody planning. Too much of my time is consumed by thinking about what I should do, instead of just doing—something. I seem to remember adopting this non-plan plan before. Expect more plans soon.

topology

Interesting stuff.

This, being maths, we approach it carefully. The first unit refreshes our [M208] knowledge of continuity in ℝ² and then, begins, to extend this knowledge into ℝⁿ [n ∈ ℕ]. We also make a start on what we mean by distance.

I haven’t looked at the second unit yet, but from its title, Metric Spaces, I’m going to assume two things: it’s about spaces where distance more-or-less means what we assume that it means, and that there are other spaces where distance is strange[r].

Although distance isn’t exactly natural on anything that isn’t a[n endless] flat plane. I remember my old boss being bamboozled by me telling him aeroplanes flew over the arctic to, charge you for more miles; because you could see on a map that this wasn’t the shortest route.

I’ll admit to being quite taken with topology. And, despite all that ‘not planning’ guff above I’ve made a resolution—learn to work the symbols. I’ve a sneaking suspicion that being able to see things may be a trap. Which leads me to…

groups and geometry

Shamefully ignored. Serves it right for not having a soon-due TMA. I’ve had a quick peruse, seems easy enough but then…am I going to be relying on my knowledge of Islamic Art?

Nilo is onboard for this one—I look forward to seeing how differently we view the beast that is M336.

I’ve deliberately deep-linked to something that is course-relevant and to which I might not agree with Nilo upon. Why would you invent a notation that is so ugly, [I agree there] are you just trying to confuse the issue? Are our tutors capriciously torturing us? There must be a reason for such strained syntax?

Possibly not, but… on the topology course fora there’s an on-going discussion about why we might write:

|f|(x) = |f(x)|

Instead of

g(x) = |x|

Admittedly it’s me that’s doing most of the fretting, still—when you see a new notation, is it a new idea? Or are you not in full possession of the facts? Maybe, somewhere down the road the strange-stupid thing that you did now will turn out to be a blessing?

It doesn’t work that way with maths [they essentially have a time-machine when it comes to us under-grads], perhaps it will with life.

Whatever. Time for a large coffee with five sugars and a ladle of carnation milk. I’m so sad and I’m so happy. I’ve taken to the Klein bottle.

2012–01–21

winding up

Both brown-boxes of goodness have now arrived [although there’s a second posting for both courses], the dates for the first tutorials are arranged and I now have two personal online-calendars.

I don’t know how others organize themselves when they start a new course, I always feel that I should be making lists, setting targets and planning milestones. None of which I ever do. It’s not that I can’t—it’s just that I won’t. I have a congenital aversion to planning. If there’s one thing that all this OU stuff has taught me about me it’s that I’m not fit for a proper job.

initial thoughts

topology

I’m spending my time on this one. Disorganized as I am, I know what dates are, and the TMAs for this one fall due before the TMAs for the groups course. I also suspect that it may be a wee bit trickier.

The first unit is part re-hash of the first analysis block of M208, and part extension of same into more dimensions. I’m taking my time—the temptation is to rush ahead to the new stuff. After all I know all about the ε–δ definition of continuity don’t I? Aye right! In fact it isn’t certain that I truly grokk the sequential definition of continuity—I think I get it, but I ha’ ma doots.

I’m fairly certain that time spent now—on the basics—will be time well spent.

groups

Haven’t really looked at this one yet. What I have noticed is that there are a lot of friends onboard. We are graced with the presence of Nilo, there are a load of last year’s M208 lags and Liga is already getting stuck into unit three and asking difficult questions already!

Maybe I’m fooling myself about this one—I’ve alway felt comfortable with groups, and yet in every exam I, royally, stuff up the group questions. Is it because I can see what’s going on that I get sloppy? Or is it that I see wrongly? Or do I just not understand?

This course should sort out whether groups and I have a future together.

long-term

I have one more maths course to take, number theory, then it’s on with computing. For me, this year is a bit of a time-out. Wait, I’m doing two third-level maths courses and I’m treating it like a trip to Disneyland? It’s this type of stupidity that allows me to sit here, in serious pain, with what is clearly a cracked-rib and pretend that all I need is, “a wee bit of a sleep.”

I’m an arse of monumental proportions.

2012–01–16

the books arrive!

Albeit only the ones for the groups course, and it may not even be books; it only says DVD, CDs and something called the tiling pack in the description. I don’t know what this means yet because I’m at work and I only have the tricksy-online parcel-tracker’s promise that they’ve actually arrived.

This arrival, the fact that my tutor mailed me today with the dates of the first tutorials and the topology course-site going live are harbingers—my maths has gotten serious again.

How am I preparing for this? I spent [some of] the weekend working my way through part of the first unit of the topology course [I was a bad-boy and printed it off]. Distance and continuity. I’ve been here before—I was, quite, pleased with what came back to me. Which is no reason not to worry.

Still last year’s fiasco should serve me well as a font of lessons; I did much wrong and, much wrong was done to me and my plans by my life. This year, I have these resolves:

• To work when I can, not, only, when I want to
• To work on my technique from the off, no skipping to the answers anymore, do the questions until your brain hurts and bleeds
• No more working the TMAs, treat them as exams. Get bad marks, begin the panic early
• Dig deeper—skipping the proofs isn’t an option any more—understanding from do isn't the same as do from understanding
• Attend all my tutorials

Most of these, resolutions[?], will be broken serially, except for the last. The last is a must.

I missed the last three tutorials for M208; what I would’ve learned at these was an important miss, sure, but who I would have been with was a more important loss.

I’d began to feel alone with my maths, I missed talking to the like-madded, I missed the utter-pleasure of being with people who shared my joy. Because I had nobody to talk about maths with my will was sapped, probably all I needed was a couple of hours in the pub with a math-minded-looney.

Won’t happen again [will], [still] your course-mates are your most important resource. This year I will be trying to get to the pub more.

2012–01–10

start…

I’ve decided that it would be pointless to keep separate blogs for these courses—if only because I’d get mixed up in my own head and mis-post in a fashion that might confuse. [Get me.]

At some point recently the Topology site went live. I don’t know when, because I wasn’t really watching; that’s a problem. My enthuse has lost its -iasm. [Which reminds me, I need to get my OUSBA repayments planned.]

me & maths

Since the M208 debâcle, I’ve been, not exactly avoiding, but let’s just say less-than-happy about, and not doing much, maths. There’s a brittleness when we meet, like meeting an old flame. It’s not that I don’t love my maths any more—I do—it’s more that I’ve had my confidence knocked. It’s easy to love something that you’re good at. If you aren’t so good at it…?

I have an entirely different attitude when it comes to programming/coding/[whatever]; there I know that I’m going to fail often and big-time. I could code-up the equivalent of a feral-Terminator that ate up half the world, the next day I’d still get up and try again without one whit of woe. Why don’t I feel the same way about maths?

I’ve had three months to think about this, and I may have come to a conclusion—I’m not actually that good at maths.

ermm?

You forget the reasons why the you-then placed the you-now into your current predicament. I could have done a computing only degree, I’d be doing well—it would still be a hassle, but a hassle well inside my comfort-zone. What’s the point of that?

I started this degree as a challenge to me, now I seem to be blubbing because, “it’s too hard”. I meant this to be too hard for me.

I hate the me-then, but he was right. I’m stuck doing two three-level maths courses that may well cause my brain to overload. I want to curl up in my bed at-night and read a book, [that I’ve read three times before], I want to have no-pressure, no-deadlines, I want to do what I know that I can do well.

There is no real life in that! Bring on the big-maths...

&…

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‘Other thoughts’ are articles about non-OU matters, mostly web and computer related, but there will be some mathematics stuff at some stage. My OU thoughts [degree/tt] are tangential semi-blogs about my current course[s].

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