exploring mathematics

Further adventures with numbers and such like.



The exam…well. From my own experience and an avid reading of the forum posts I’ll judge it fair. Most people, if not all, had time-issue problems, to be expected. For me there were a couple, or three, points of dodgyness—

  1. The number theory question: I’d expected Euclid’s algorithm, wrong, we had Fermat and his ‘wee’ theorum
  2. We had a proof by induction in the body of the exam; and not one involving a sum
  3. The part II questions were significantly different from what I’d expected

That said, some of the questions were easier than I thought that they were going to be. Or I thought that they were. As I posted in the chat forum, just after an exam is the worst time to judge how you’ve done, and as the memory fades…? A group of nutters have decided that once the paper is published we are going to provide solutions [yes, I’m on board], so if I can remember my answers, for once, I may be able to make a reasonable estimate of my grade is before the results are in.

and what result will that be?

I’ve identified a few flaws, don’t know how many marks will be lost, and I expect that usual tax on sloppiness, stupidity and plain bad penpersonship. Nothing henious. But twenty-five minutes to go, go-faster juice running out, I didn’t have the bottle to tackle the calculus question that I’d decided upon aforehand. So, as I’d already done the question on Group Theory, I was left with conic-chomping or an iteration question. Iteration question it was, panic in my soul; something about my answers screamed wrong! I’ve since sketched the beast but I’m still not calmed—that said Chris F. [a calculus genius] thinks the same about how he did with Q15 [the calculus question], so I’m in exhaulted company. Exams are sods.

I’m hopeful of a grade two.

the end

Is here for another course—I’m reluctant to let this one go; I’ve had too much fun, met too many great people and learned such a lot about maths [and myself]. But all good things come to and end, or they aren’t good things. And them good folks: I’ll meet again, somewhere, sometime. So

svn commit ms221 -m "last blog post"



the day before tomorrow

At about this time tomorrow I’ll be twitching and gibbering under my breath [as a result of too much ersatz red bull] and MS221 will be over. Which will be a relief and a sadness at the same time. I’ve enjoyed this course muchly but I have been getting that, “when will this all be over?”, feeling that comes towards the end of a course—all you want is the exam to be out of the way [and the next course to start].

After yesterday’s botched-job revision I decided that I’d tackle the one past paper that I have. I didn’t do it under exam conditions and I only took vague timings so it wasn’t a scientific exercise. That said things went mostly much as I thought that they would:

  • I’m very sloppy, a result of trying to be too fast
  • For most questions I know what it is that I want to do, or a look at the handbook reminds me
  • There are a few areas where I forsee problems—I don’t know what I’m doing or I’m too slow

Too slow and too fast? Tricky one to deal with that. The temptation will be to the rush the questions where I know what I’m doing to give me more time to tackle the questions where I’m going to take longer or where I’m less sure of my technique. However I think that this may be getting things upside down—I should spend more time on the questions that I can do, to ensure maximum marks, and less time on the questions where I’m going to lose marks whatever.

My intention is to answer the questions where I’m confident first; taking my time and being careful. Then I’ll tackle the ones which I know that I’ll have problems with. I’ve made such plans before and utterly failed to carry them out, but an attempt must be made…


The forums are busy, last-minute panic is on display. For a lot of people this will be their first exam in a long-long time. I feel most for non-British students who, not only pay much more than we do, but may have to fly [or whatever] to their exam centre. I just have to wander down the road and I’d like to complain about that. But then they [who exactly?] do say that “there’s always someone worse off than yourself”—but by using Fermat’s ‘infinate descent’ method this is clearly not so!

So fellow MS221ers, when your tomorrow comes have a good one, be lucky, have fun.

I’ll try to write something tomorrow night about the exam and the unconsidered course review should be up in about a week.


a tradition

Every so often I [live] blog my TMA woes, so today I thought that it might be fun[?] to blog my revision woes.

Let me set the scene—it’s Sunday morning, I’m at work [be-there work rather than work-work], I have a building full of builders and bag full of maths books & videos. Perfect revision territory! So here goes…

I decide that I’ll have a fag before getting started.
I think that I’ll start off with some of the algebra workout videos…
Bugger! I realize that I haven’t brought my handbook to work with me. Possibly this is a useful reminder for the exam? Or just the type of stupidity that I’m known for? A dip into the forums before I start exercise book A? Methinks a dip into the forums.
Desperately seeking displacement I decide that if I’m going to do this live I might as well put it online live. So here goes…
Videos watched, time to whip out the pen and scratch some symbols onto the mountain of graph paper.
Oh dear! I’m hoping that it’s just because I don’t have the handbook that I’m having problems. I suspect that it isn’t. I thought that I was happy with unit 1 but I called the auxiliary equation the characteristic, and I completely forgot how to deal with repeated roots. Time for a reflective fag [and perhaps some intravenous Red Bull?].
Spent some time in the M257 forums worrying about whether a String is an Array of chars. Onto conics…
The thought occurs that I’m an arse, this is not an original thought—everybody that I bump into thinks it sooner or later, but two days of revision for a thirty-point course? It takes a special type of moron to be so hubristic.
Don’t have a calculator with me either. This is a school so I should be able to find one somewhere but I’m not going to—I’m in the mood to punish myself…
I really miss the handbook, I hadn’t realized quite what a prop that it has become. Without it conics are a problem, I can’t remember the definitions. With it I think that they may be a breeze. Perhaps. One of my worries was that I was bad at conics: not so—it’s a mechanical thing in the end, perfect for the exam [although I won’t be rotating any!].
Fag, and then another video.
Interesting. I watched the video about transformations and it, well made me think. I knew that a lot of what we were doing was all-of-a-piece, but bits of it hadn’t sunk in. For any linear transformation we can write the [2 * 2] matrix as (what happens to (1,0) what happens to (0,1)). I’d watched this video before but this hadn’t sunk in. Trig. identities…
I’m losing the will to think, so I’m going to watch a few videos and hope that a second wind is in the offing…
At the risk of getting sacked for speaking out of turn may I give a big shout to the diddies who run my council’s computer system. Just because anti-virus software is important [it isn’t—don’t run as admin] doesn’t mean that it needs 100% CPU priority, and it doesn’t need to phone-home every hour. Nice to hang everyones’ machine for ten minutes every hour…
Why am I getting annoyed that they’re using a crappy [Pental] pen in the videos?
I realize that I’ve come to work without a piece [something to eat] and that nine hours is a long time. Still, we have eigenvectors on the menu…
RealPlayer stops responding—the swine, and I have to kill the process. Worry is eating at me—I’ve left this revision business way too late. I need to focus; what am I bad at? Surely not everything?
Much paper in the bin, no further forward. I’m going to watch the videos for blocks C & D [which I haven’t watched before] in an effort to cheer myself up. They won’t—just another avenue of misery opening up…
The etymology is uncertain, so I can’t say pardon my French, but fuck Taylor Polynomials. The man may have been a genius but if we ever discover a way to re-animate corpses he’ll rise from his grave to be greeted by a punch in the face from me. [Or perhaps I should approximate around £100 of coin in a sock and whack him with that?]
Shite! Shite! I’ve just taken a toddle round my school—I’d say bomb site but that doesn’t do it justice. We’re taking a bomb site with all the mess and none of the damage. The cleaning I’ve organized is way too lite. After the exam I’m going to have to get ‘on the tools’ myself. Life is such a joy!
Hateful exposure of flaws—13 - 4 is not 8!
Two coffees haven’t done the wake-up trick so I’m going to watch the differentiation video. If I don’t ‘get’ that then I really am stuffed.
Whew! Didn’t have to watch it, I can do differentiation. Now, what about integration?
Workies away, all that’s left are a bunch of musicians in the annex. When I went to see them the school’s resident jackdaw crew hopped about and regarded me with a hopeful eye; poor beggars, it’s half-term—their regular supply of junk food will not be forthcoming. They will have to do their own shopping.
Gone and fled is the will. I’m hopelessly unprepared for this exam, but there ain’t a whole lot I can do about it now. So let’s be realistic—aim for a pass. Aim to stay awake [,although I’m now yearning for some bed-time].

That’s that.


guess what?

Yes that’s right, still no revision done. Circumstances have conspired [as is their wont] to prevent me getting down to any maths work.

Things came to a head when one of my minions threw an unannounced sicky; this left me working a straight fourteen hour shift. Something that causes a systemic wobbler. Oh, and I’m now on back-shift. So revision plans stymied.

But you have all weekend neil, I hear you cry—alas not so. My school is full, to the rafters, of work-people under a nine day, October break, time-crunch to get too much done—weekend work for all [including the neil]. Saturday and Sunday are out [mostly].

I’ve only myself to blame—such crises are always on the cards [for me]; I should have started revising sooner.


I won’t pretend that I planned that it should happen this way—I didn’t—but I’m not fashing myself too much that it may come down to me only having one day’s revision. My vague, plan would be too strong a word: intention[?], hope[?], for this course was always to ‘learn the maths’. Well, there can be few harder tests of my success at that than sitting an exam unrevised.

I have worked, pretty hard, for most of this course. True I’ve [now] forgotten a few things and I’m rusty at others. But if I can spend a couple of days messing around I feel confident that I can make a fair showing in the exam.


Everyone in the forums seem to be doing past papers like they are going out of fashion. What do they know that I don’t?


oh dear…

I spent the weekend trying to do some revision, the result? Not a lot was achieved. Much displacement activity occurred, one note pad was squiggled to its papery death and a few questions from exercise book A were attempted. But on any, sane, assessment I did bugger all. This is not good. Time to re-think the plan.

Despite doing very little I’ve noticed several things…

  • My knowledge of the course material is actually not too bad
  • I have a tendency to go off-task
  • Apart from a few areas, a quick squint at the handbook and a wee bit of thought are usually enough for me to make some sort of stab at most questions

So, taking into account the above, the first thing that I need to do is identify the areas where I’m weakest and work on those. That probably isn’t as easy as it sounds—how do I know where I’m weak if I’m not going to work my way through the entire course? [And that ain’t going to happen!] So I’m going to make the assumption that I’m weakest in the earlier material and the stuff that I found boring. That’s quite a list! Perhaps I should list the things that I feel confident about? So, in no particular order—

  • Sequences
  • Conics—sort of…
  • Differentiation
  • Integration
  • Complex numbers—although I could do with a wee bit of practice
  • Number theory—again some practice
  • Groups
  • Proof & reasoning

Put like this things don’t seem too bad. It still leaves a whole shed-load of work to be getting on with, but at least it gives me a target to fail to achieve.


Is going to be my biggest enemy—it always is with OU exams. [My sloppiness will be time’s willing ally in this war of course.] Flicking through the handbook and struggling to dredge up something, that I might once have known, from the bowels of my head are going to waste vital seconds. Vital seconds that will add up to vital minutes over the piece. Not much that I can do about that unless I’m going to put in much more work than I’m going to. What I can do is to make sure that I don’t rush things.

That’s the other side to, our mutual enemy, time—trying to be too fast. Fear of time is setting us up for sloppy to swoop. I have a half-formed plan to avoid this—one that won’t work. There’s no requirement to tackle the questions in any particular order; I could do the questions that I know that I can do well, at a measured pace, before I move onto the questions that I know I’m going to struggle with. This plan will not work—such plans are not do-able in an actual exam.

Perhaps you’re differently built from me and can stick to the plan—but for me when you turn over that paper and the adrenaline peaks everything goes out the window. I might be able to leave any questions that I’m starting to waste time on, but that’s about the full extent of the control that I’ll have. So I’m planning to lose marks in places.

Anyhoo, off for an evening of trigometrical identities, functions and matrix/iteration diddling. Or more likely time-wasting in the forums or a lie on the couch…

What happened was that I wrote this, made some [of my own–I can’t eat the real ones] baked beans and got drunk. Did I mention that I’m a hopeless student? Surely I must have?


time to panic?

Probably, I still haven’t done any revision. I’d hoped that last Saturday’s day-school would stimulate me into doing some revision—it didn’t.

That’s not to say I didn’t enjoy the tutorial—I did; I enjoyed it immensely. [It might have been better if I hadn’t staggered in half an hour late.] I’ve loved this course and one of the best things about it have been the tutorials. They’ve been informative, fun and I’ve met a lot of lovely people. I’ll probably shed a tear on the night of the exam at the thought that I may not see some of them again. Some will be doing M208 next year, so hopefully some of us will study together again, but, life being life, I’m bound to lose touch with a few. One of the great things about being an OU student is meeting the like-minded—indeed one of the on-going themes in the café has been our inability to talk maths with anyone except our course-mates—it hurts to lose anyone who can talk maths. But my tutor-group-mates aren’t folk that I’d voluntarily lose even if they thought 4 was prime.

One person I definitely do intend to meet again is my tutor, Alan. I’ve liked all my OU tutors [so far], but Alan has been a particular favourite—a natural teacher, a wonderful mathematician and a gem of a man. Fortunately he tutors a couple of courses that I’d already decided upon, however I’d have considered something like, say topology, if this hadn’t been the case.

I’m making the assumption that because I haven’t moved I’ll be assigned to him again, which isn’t always so. But he will be running a tutorial somewhere in Edinburgh to which I can go. You can always tag along to another tutor’s tutorials, and tutorials are what are most important to me in a tutor—I very rarely ask my tutor questions.

so revision…

I’ve never really got revision, because I’m feckless and demand instant gratification? Perhaps. But knowing why I don’t like/can’t get down too revision is of little help at this point—what I need is a plan and a kick up-the-arse.

Most people, that I’ve talked to or who’ve posted in the course forums, seem to be working the past papers, possibly in exam-condition fashion. I can’t do that. My plan was to work my way through the course units, but when I try my brain glazes over and I just doodle in the margins. My last hope is that the, saved for this point, exercise books will ride to the rescue. At the very least they may give me an idea of where I’m very weak.

There are a couple of problems—work [work] and M257. Since my last piece of lachrymose trash I’ve made an effort to buckle down and get things done at work. Which I’ve, sort-off, managed, but job [coupled with shift-change] stress has left me pooped and too whacked when I get home to do any serious maths. M257 is another problem—the forums are very busy and there’s much fun to be had in being online pratt. Actually it’s a wee bit more serious than that—at bottom I love to programme, and M257 is, to its non-existent finger tips, a course about [serious] programming for [in my case script-kiddy] programmers. Discipline, not a strong point with the neil, is required here [and now]. I’m not doing any work, so stop trying to start religious arguments—at least until you’ve done your MS221 exam neil.

So I’ve settled on spending this weekend working the maths. It’s a pity that you can’t get odds on my failure at William Hill’s isn’t it?


not revising

And not doing much else besides. I had planned a weekend of maths/java/lego seriousness but I spent most of it watching old detective series and re-reading the Oxford History of England [Anglo-Saxon] for the umpteenth time. To be honest I’m feeling a wee bit burnt-out. This happens, of course, but it’s damn inconvenient that it should happen now.

Still, I’ve been here before—it not yet time to panic. The first thing to do is make a list of the difficulties—

  1. I’m now fifty–yikes!
  2. Work [work] has become a real nightmare—I don’t get time to do jobs because other jobs are constantly being added to my burdens. The classic context switch problem.
  3. I can’t seem to force myself to do any maths revision.
  4. M257 and lego have arrived on the scene to steal my mental-focus.
  5. It was only this weekend that I realized just how worn-out I’ve been/am.

Not much can be done about one, two I’ll have to deal with at work—I can’t let it interfere with my me-time, three and four are self-discipline problems. Which leaves five.

I guess that I’ve been background-ill for over a year, but until the last couple of weeks I hadn’t realized it. I’d put being flat and brittle down to various factors: stress, over-work, depression, drink; all plausible but probably not the real issue. I now suspect that my body was being treasonous.

Which shouldn’t have been a problem if I’d been on guard—I should have been watching my body and my mind. I knew that doing a degree, working and trying to have a life was going to be tough. In my arrogance I assumed that I was going to breeze through it.

I’ve been caught out by depression in the past, it was only my wife who saved me, I’ve now been caught out again. This time I didn’t notice that I was beginning to find it hard to concentrate, I was sleeping too much, I was frittering and footering. It wasn’t every day, it wasn’t every week but it was enough that I should have noticed.


Now that I’m aff the wheat I’m feeling a lot better in myself—I’ve got more energy and I’m feeling a lot more focused. Which is why I’m going to spend the rest of the week doing bugger-all. I need a rest. I’ve a day-school on Saturday, that’ll get me back into maths in plenty of time for the exam.

One of the hardest things to do on an OU course is to stop and allow yourself time for reflexion, especially when you’re only a couple of weeks away from an exam. Which makes it all the more imoprtant that you know how to do it when you have to. And I have to.


no more beer…

I had an endoscopy last week, the full results aren’t in yet, but it looks like I’m a Coeliac—so no more beer. Jings! As I said, the results aren’t actually in, so I’m in the position of the person whose credit card is going to be cancelled soon—there’s a huge temptation make the most of it while you’ve got it. A temptation that I’ll probably succumb to.

The endoscopy itself was fair to middling unpleasant. The worst part came afterwards; ‘some stomach discomfort’ was promised, what wasn’t mooted was that, due to the air they’ve pumped into you, an enormous bout of flatulence is on-the-cards half an hour after the event. Don’t be on a crowded bus at that point; I was, it wasn’t fun.

To be honest I’m a wee bit relieved that there is something wrong with me, I now weight under eight stone and I’m constantly tired. I’ll gladly give up wheat[beer?] to change that.

block d

While I was waiting the three-and-one-half hours to have a tube stuck down my throat I did some of TMA04. I soon tired of that, so I sat back, watched the world go by and pondered upon block D. There’s been an ongoing thread in the chat forum about this—quite a few folk seem to be having difficulties/disliking this block. What do I think?

I don’t think that the block is more difficult than the others, it’s just that we’ve changed a mathematical gear. The other blocks all build on materials that we’ve worked on before; a lot of block D will be new to many people. And new is often daunting.

The only thing completely new to me was number theory. I did a lot of logic during M263, I did complex numbers at school and I’ve worked at groups on my own—so I should have been alright? Yes, sort of…

I’ve enjoyed block D great deal, in a sense it’s ‘my type of maths’, but I had to work a lot harder than I thought that I was going to. Some of the new stuff flummoxed me, some of the known stuff was presented in a different way, things came hard in places. [Some things are still hard.] This didn’t stop me enjoying the block.

New maths, or old maths that comes at you from a different angle is always going to require work, and lead to some swim—don’t panic, work your way through. If you don’t want to learn hard things, new things, or work, I’d suggest not doing any maths.

For those of you unfamiliar with my computer-course blogs, swim: the feeling of at-seaness when learning a programming language

Which leads me to another theme of the thread…

there are different types of mathematician

Are there? We might consider the essential divide to be the pure maths/applied maths dichotomy [we’ll leave statistics aside, to me they seem to be something else again]—useful maths and maths that, while beautiful and elegant, isn’t going to change the world. [To mis-represent it boldly.] But is this divide real?

I’d say not. For one thing you just can’t ever say what’s useful and what isn’t. The machine that you’re reading this on wouldn’t exist without pure maths. For another I don’t think people fall quite so neatly into the pure/applied camps—I like calculus, groups, proof, series…there’s no rhyme or reason to it. Finally applied maths is beautiful and elegant too.

If there are different types of mathematician then I suspect that what type you are depends on where you’re approaching maths from. I came to maths from computing, what’s going to interest me maths-wise are the things that I can apply to computing. Not always, calculus isn’t something that programmers often dabble in, but mostly.

There is another side to the question—someone, Liga I think [apologies if I’m wrong and apologies if I’m right—I’m going to twist your words], said that she preferred the maths where she could manipulate the symbols, the mechanics of maths so to speak. This struck a chord, I’m the same—happy to while away the hours learning Euclid’s algorithm. I’m less happy trying to following a proof—or trying to create one of my own.

My happiness, however, doesn’t mean a thing. Some of the things that I am good at I didn’t ‘get’ at first, I still have to think hard about, I still don’t enjoy, but I do do them well.

I’m going to try a metaphor here, a rally-driving metaphor—I don’t drive, I don’t know anything about rally-driving, it is more than conceivable that I’m talking cack but…

And argument by metaphor is something that we know spawns falsehood, isn’t it my fellow MS221ers?

With rally-driving, as with maths, we want to get from point A to point B, we have a map and a car [a skill-set and a developed intuition]. The driver and the navigator have two very different skills, skills that come together to get us from A to B very fast. I’m willing to punt that individually both team members are better at navigating and at driving than ninety-nine per cent of the rest of the human race. To be great they need to be very good at what the other does. That doesn’t mean that they are going to swap places.

There aren’t types of mathematicians, there are only mathematicians who are better at some aspects of maths than they are at others.


flagrant stupidity

This is a part two of the last post, decided upon after a night’s brooding.

I’ve been reading Deutscher’s Trotsky assortment and it may have skewing my thinking; I’ve decided to revise but not to—neither peace nor war. This is mad, but not quite so mad as it appears at first blush. Let me explain…

I’m doing this degree for me—it won’t change what I do to earn my monthly envelope, I can suit myself; MS221 doesn’t count to my degree classification; it’s more important, to me, that I learn maths technique than it is to pass an exam. So…I’m going to work at the course materials instead of trying to pass the exam.

Every so often I read this tripe that I write, it’s one of the reasons that I write it, and, in the reading, I’m beginning to get a sense of what it is that I’m trying to achieve—for wont of a better triple of words: a better me. All the UTF-8 letters in the world after my name won’t make me smarter—I don’t need a piece of paper to make me clever, I’m not one of Dorothy’s chumps. [July Garland reference!]

All very lovely and laudible but there are a couple of problems: I want that distinction and I may be rationalizing away my own sloth. I know myself, I can always explain, after the fact, my actions; that wasn’t why I did them things, but to others I appear rational. Am I there again?

I guess what I’m trying to say is that I need to ‘know my stuff’. It occurs that this might be harder than focused revision. I’ll tell myself that when I’m lying on the couch doing bugger all, shall I?

Think on neil…but for now off to hack JavaScript and enter one of my, other, worlds.



I haven’t done any maths at all since last weekend. I’ve been busy at work and hacking JavaScript so I haven’t had time. This now has to change—the exam is only eight, short, weeks away. I need a revision schedule—a plan.

And there, straight away, I have a problem. I haven’t done a maths exam in over thirty years and I’m certain sure that I didn’t revise for that one. [At least I hope I didn’t given the woeful mark I achieved.] So I’m unsure how to revise. Could I learn something from the computer exams that I’ve taken? Well…yes, but it’s a negative something—I’m not going to do a single past paper under exam conditions.

From posts in the forums it seems that most of my fellow students [the ones who operate online, the lags so-to-speak; there will be a silent majority] are planning their revision around the past papers. They’re probably right and doubtless somewhere on the OU site there’s screeds of useful stuff about how to revise for an exam. The problem is me—I won’t be able to force myself to do it this way, or in any normal way.

There is a positive that I can learn from my computing exam experiences—if you know your stuff and you have an idea of…I’m going to say how the questions fall, you’ll do well. I’d better explain that question-fall bit.

In exams the same types of question appear year after year, you need to decide, aforehand, on which questions suit you. For example, in the one past paper that I have, there’s a question on rotating a conic and one on logic. Neither of these do I fancy under exam conditions. I can do them both but I’m too sloppy for the conic-diddling and I’ve come a cropper with logic before. [Actually this post seems to be a re-hash of that one!] Know yourself.

Which leaves me with know your stuff. How am I to achieve this? There I really am at a loss…


new term, new plans

For the majority of my life I’ve either been at school or I’ve been working in a school, so mid-August has always been an important time for me. The new school year—a clean-slate time, a time for looking forward, a time for a re-assessment of the past. So I thought that it might be a good time to give some consideration to my personal OU roadmap. There’s no real reason for me to do this now—I have another year of compulsory courses ahead of me. But it’s useful to know where you’re ultimately heading, and a bit of fun too!

I’d originally planned a Java-heavy computer road and I was in the air maths-wize: what will be will be. Over the summer there’s been a firming up in my mind of where I’m trying to go—in particular there’s dawned the realization that Java is not the way of my in-head warrior. So…


‘Less Java’ narrows my options. If I don’t want to write [too much] Java then I have to do M362 [Developing concurrent distributed systems]. Yes, it’s still Java but it has a more general usefulness than the other courses on offer.

My other level three computing course has to be M336 [Natural and artificial intelligence]. It’s something that has always fascinated me, it’s exactly the type of computing that I’m interested in and something that I can happily mess around with on my own.


Two years in I’m beginning to realize what areas maths I’m most interested in and I’m now, fairly settled on the courses that I want to take. I’ve already plumped for M208 [Pure mathematics]—I’ve decided that I’m the pure type rather than the applied.

If I’m headed down the AI path then MT365 [Graphs, networks and design] makes a lot of sense, as does M373 [Optimization]. What also colours my choice is that [as of this moment] they are both taken by tutors who I know and like!

Because I only did a single level one course I get an extra level three maths course [it could have been computing] and that would be M381 [Number theory and mathematical logic], I loved M263 [Building blocks of software] and always wanted to take it further, M381 is the closest [OU] thing to doing so.

M381 and M373 are presented every second year, which means that I have to be a wee bit careful with my planning—this is something that can be decided upon down-the-line.


This leaves me ten points short of a degree. I had thought that I’d signed up for T184 [Robotics & the meaning of life: a practical guide to things that think] but it seems that I was drunk when I did it—hasn’t happened. I still plan to sign up for this course at some point but, on reflection, it’s probably a good thing the I’m not starting it in October. Ten point courses are very intense—not something you want to be doing alongside even a twenty pointer. [As I type this the worm of self-doubt squirms at the root of my skull—when else will I have the time?]

There is, however, another option…

A211 [Philosophy and the human situation]

People whom I respect, for example Christopher F and Kay H [in system only] have done this course, Kay H has even out-and-out suggested that it’s a course for me. This, on it’s own, makes it a course worth considering. [One of the things that I have learnt is that you should always consider your fellow students’ views carefully, I’ve gotten much valuable advice over the years.] I’m tempted, sorely tempted, the subject interests me greatly—I read all the ‘philosophy’ blogs [actually I read all the OU blogs] and I can see where it might fit in to the plan ‘that-I-can’t-properly-articulate’ that I have for the future ‘place-that-I-where-to-be’. However, for now, I’m going to give it a miss because:

  • It’s a sixty-pointer—lots of time needed
  • It’s a bit pricey on my current budget
  • I’d, being realistic, have to cut back on my computer/maths courses to fit it into the schedule. Although I could do this [I’m under no time pressure to get a degree—I’m not going to use it for anything] I’d like to get the computing/maths under my belt so-to-speak.

I can always come back to it, or alter my schedule if circs. change, nothing is set in stone.

The above should really have been a stand-alone article [haven’t done one of those in a while] so to balance things up; some maths…


Oh yes, that time is nearer than we think fellow MS221ers! We have a TMA due at the end of September a, seemingly, comfortable distance hence, and then the exam itself in mid-October—plenty of time. Not so, two months are going to fly by. We need to get that TMA out of the way soon, and we need to start revising. I’ve been here before and I know of the things that will stick sticks between the spokes of our way-cycle; life will rear its ugly head from the waters. Every day missed now will be regretted with bitterness later. So I’ve decided that this weekend I’m going to do something that I don’t normally do—work a TMA using the books.

Since TT280 CMA01 I’ve tried to treat course-work as an exercise in seeing how I was doing rather than a revision tool, or a mark gaining exercise. Ok, this is a lie, I’ve often used them as a catch-up, but my intentions are good. I haven’t ever tried to work them, in the sense that I’ve never looked at the question, went to the relevant book/reference/webpage and monkey-parroted the thing. I may do this for my next TMA. Why am I doing this?

Well, I’m not finally decided on this evil but I feel that I’m not up to speed with this course. I feel behind, I feel that I’ll need to do a lot of hard, practical, hands-on, pencil-on-paper work to have a chance of doing well in the exam. So I don’t want to be wasting time doing a TMA.

Fortunately I write down my thoughts, and when you write down your thoughts they seem different and it enables you to say to yourself, “this is a stoopid plan”. I’ll stick to my way, TMA without the books then. More work, I suppose, but it makes much more sense.

I hate it when I make sense to myself!


an unfortunate series of errors

I got my TMA back the other day, on the whole I’m pleased with it, as usual there was sloppiness, but there was one piece of stupidity that deserves a mention. [The question was about the area under a graph] Here’s what happened—

  1. I did the question; I wasn’t happy with my answer, looking at graph it didn’t look right—but I couldn’t see my mistake
  2. So I decided to check my answer using MathCad
  3. I was wrong so, knowing this, I worked through the question again and got the right answer

All to the good? Not quite. I made two mistakes in my final solution, two mistakes that cancelled each other out, and because I had the right answer I didn’t check my working. Lost marks.

The moral is—don’t use MathCad to check your TMAs, or worse use MathCad to find the right answer before you begin them. If you know the right answer you’ll, at some point, get to it in the wrong way. Remember that half the marks are for the working and that we’re still learning here folks.

Don’t use MathCad! For anything. Ever.


magic squares

For some reason—I think that I may have caught sight of a wild one recently—I got inordinately interested in these over the weekend. You know the ones—where all the rows/columns/diagonals add up to the same number. Somewhat like this…

a magic square
2 7 6
9 5 1
4 3 8

So when I wasn’t up to my eyes into javaScript annoyances I was scratching away at magic squares. On Sunday night I had that Eureka moment—I had an algorithm, for odd squares only, but still … I gayly posted news of my success to the chat section of the MS221 forums. [Those that know me will already be already sniffing the ozone-stench of Hubris here.] I retired to bed, pondering the wee bit of mopping up left to do, a happy man. One bit of the mopping up was to write a programme to create magic squares.

On Monday I got up, on Wednesday I write this—I still amn’t even near to a working programme—something that I felt would be easy. Hubris hurts you where you are most vulnerable, and, for me, that’s computing and a specific language—I can’t reproduce my method in JavaScript! I beginning to wonder if my algorithm actually works.


I do have/had a method [the aforesaid algorithm] that I don’t have difficulties expounding to my fellow human beings [although this is not a thing that I’ve tried]. And I did tackle the programming in my ‘old’ half-assed fashion.

This doesn’t excuse me, in fact it’s part of the indictment. I’m still sloppy—

  • I didn’t document what I did
  • I didn’t fully understand it myself before I tried to take it further
  • I’m, still the programmer I was, not the one that I want to be

Don’t, Don’t and Don’t neil.

But there’s a smile on my face and there are thoughts in my brain—failure always encompasses the roots of success [a complex number thing?]. I’ll survive—{the best one]


red letter day

Why is it called a red letter day? Something to do with the Church I suppose. Anyway, whatever the origin, I had one yesterday. I got a distinction for M255 and my new computer arrived. Which left me with a wee problem—I thought that I deserved a drinkee but drunk is a bad place to be when you’re breaking in a new laptop—you run the risk of creating an expensive beer-soaked door-stop. [Yes, I had the drink.]

For someone who spends a lot of my time messing around in the [software] guts of the things I’m worryingly inept when it comes to computers, I’m not sure if I even like them. I pretend to myself that I’m a computer scientist—I treat computers like astronomers treat their telescopes. Self-serving clap-trap.

So I wasn’t looking forward to getting it up-and-running. However it wasn’t too bad, setting-up took me about fifteen minutes and getting online was a breeze. At which point I put the thing away and had a think about what software I needed for my new hardware.

Every computer I’ve ever had dealings with has ended up with a dog’s dinner of seldom-used applications—this time I’m going to get it right! No rubbish. So here’s the basic list [so far]—

That’s the very basics. Time to add some side dishes—

  • Dia, not something that I use a lot but useful for UML and network diagrams
  • Opera, Safari and Chrome. I don’t do much web [design] work any more but I suppose that I should have the essentials. I should also get the javascript/HTML/CSS debuggers [Dragonfly et al]
  • Wireshark, I don’t need a packet analyser but it’s fun and comes in handy on occasion
  • XML Notepad—it’s free and does the job
  • A Haskell compiler—I’ve rather dropped learning Haskell but I feel that it’s time to get going again
  • Inkscape, I haven’t opened this in ages but it great for creating SVG files

I think that’s enough to be going on with…

some maths…

I’ve been having a second go at unit D2—number theory. I worked my way through it some weeks ago but apparently not a lot [possibly not jot one] of it has stuck to the inside of my head. Certainly I haven’t developed any great feel for it; maybe because much of it is new to me, maybe because I’m trying to go at it too fast.

New maths stuff is always fraught. I’ve read a few threads in the course forums where people are complaining about the course materials/are having difficulties, mostly with block C [calculus]. Personally I rather like the course materials but I will admit that there are places where they ‘jump’. This is unsettling, especially when it involves maths that’s new to you. When you bump into one of these jumps there’s a temptation to skip past, planning to come back later.

I’ve done this myself—it’s wrong. Maths builds on known foundations, if you don’t understand these foundations you’re building on sand. Try to work at it until you do get it. If you’ve torn out your entire head of hair and you still don’t understand ask a question in the forums, eMail your tutor. Repeat as necessary until it does click, then it’s time to move on.

This isn’t quite what’s happened to me with D1. But as I was working my way through section three is began to dawn on me that, while I could manipulate the numbers, sort-of follow the proofs and do the activities I wasn’t grokking it. A quick peak at the TMA confirmed my suspicion—I couldn’t begin do the questions. So time to go back to the start and work harder.

how long will this take?

Who knows? If there’s one thing that I’ve learnt during my OU years it’s that the course schedule is a tissue of nonsense—if it says a week it can take you two hours or a month, or any time in-between. If you’re doing an OU course throw away your life—it won’t be wanted for a while.



For the neil…

  • Stop writing this blog in a flopping drunken state
  • Get your TMAs in early. This last-minute submission routine isn’t something that you want to get used to.
  • Read less Nietzsche and more Orwell—your style is getting florid

As ever these will be honoured in the breach.


I think that I’ve signed up for T184, I’m always unsure when I register online. So that makes this year’s/next year’s courses T184, M208 and M257. That should suffice? Actually it should more than suffice.

The rationale behind this is that—I don’t much like Java, I love maths and I’m interested in artificial intellegence. So the plan is to go down the AI maths/computing line. However, there’s still time to back out.

Now all I have to worry about is whether I can scrimp together the cash to buy the Lego™ Mindstorms kit. I do fancy a ROBOGATOR…


back to reality

Acch, jings and uther Scottish half-swear words. Holiday is over, work is back and a mountain [of tasks] have, again, shooggled themselves into my gravity well. Such is to be expected I suppose.

Looking on the bright side the anderson-house is de-cluttered and cleansed, on the dark side garden-anderson is awash with the dead and the things that shouldn’t be allowed to live. I brood upon it as I sip my morning coffee and squint my eyes out of the filthy windows. And then I turn to something else, I lack the plethora of mâchetés required to grapple with the thing, so I pick up my course books…

the busted TMA

I need to post this off tomorrow; I started it on Friday. Not good, bad in fact. In the full knowledge that I’ve said the same about every single piece of work that I’ve ever submitted, this is the worst thing that I’ve ever done [OU-wize]. Frankly it’s a horrid piece of jobbery. So why am I submitting it?

In part to teach myself a lesson. In part because I don’t have any more time. In part because I don’t be seeming to be having much fun.

there comes a time

In every course there will come an occasion where you have to ‘work through’ the ennui, to walk the hard road, to remember the will to learn. Such a place is easy to see.

But there is another place that we go to…when you lose the will to teach. Tell would be a better word—I tried to explain number theory to my mum the other day. When that goes you, do indeed, have a problem.

But, I want to tell, I want to explain and I desperately want to understand. So my life, is, my life. Am I wrong in hating that?


holiday time…

Is nearly here. I finish up on Friday for two weeks—oh joy. While I’m not against holidays I usually don’t enjoy mine much. Partly because of all the ‘catch-up’ house-type work that I have to do [this time we are decorating], and partly because it takes me a week-or-so to wind down into a mental condition where I can enjoy myself. By which time work-loom is on hand to blight my happiness.

Normally I try to take a break from the computer and lay off the coursework when I’m on holiday. This time I have a TMA coming due which is going to make that problematic. I’ve done most of the non-MathCad stuff, except for the Taylor rubbish, so it shouldn’t take me too long to get it finished. I could do it over the next couple of nights, but I have a tutorial on Saturday and I’d like to get that under my belt before I commit to submit. So I guess that I’ll have to do some OU work just this once.

Enough with the personal rubbish neil, get back to the maths…


Seems, to me, to be vital for a mathematician, so I’ve been working on my technique. Specifically I’ve been working on my integration. My differentiation is fine[-ish] but, while I seem to remember doing a lot of it, I never really grokked integration at school. So time to break out the ancient maths texts and do the work.

Mostly I use the ‘old books’ for their exercises [although in the case of integration you can make up your own examples—differentiate to check your answer], but you often find that their methodology is slightly different. Which is to the good—tools for the toolbox.

For this course we aren’t going to be presented with an integral without one clue as to the method that we need to use to solve it [inspection, by parts, substitution]. It won’t always be thus so, so while I had the yen to work, I decided that I’d go that step beyond.

I spent ten hours, a whole ream of paper and whittled two pencils down to their nub’s. I was happy—I could look at an integrand [is that right?], decide on the correct method and slay the thing. Job done?

reality check

And then Christopher F. posted a Cambridge University question [PDF–53KB] (number eight) that he’d found. I wasn’t up to it. I moaned, as is my wont, but I’m eternally glad that he did post it. It was a punch to the face of my comfort-zone arrogance.

The comfort-zone is a bad place to be, avoid it, shun it, push past it, don’t go there. Without a sense of danger/inadequacy you’re liable to get thus punched. Don’t—be aware that you aren’t that good.

I spend a lot of my time on the web apps survivors’ conferences asking stupid questions of people who I’m not fit to walk with; why do I do it? To keep them straight—if they can explain it to an idiot like me they might be on to something…

Ask, people, the right questions. [That’s a wee bit harder than it seems!] And ask these question of yourself first!

I do need a holiday, don’t I.



I had a stress dream last night, not one of my normal stress dreams, but it clearly was a stress dream. My hair was falling out and I was beginning to look a lot like Gollum [I was naked and I was watching myself]. This isn’t a good sign, it means I’m stressing about something new, possibly my health.

For those of you who don’t follow my M255 blog [you scunners!] I’ll explain—I recently found out that I’d lost a bit of weight and was forced to go to the doctor’s for some tests to see if I needed any running repairs. [Read part the first of the saga.]

Well, apparently, I’m, weakly coeliac and have, raised random glucose levels. This shouldn’t bother me; my wee brother is strong with the coeliac force and I can cope with being a diabetic [it’ll probably do me some good]. What would have worried me is if my liver had been shot and I had to give up booze. So I shouldn’t be stressing, maybe it’s something else? I’ll keep an eye on it.

my normal stress dreams

I have two, both work related—

  1. I’m working in a school and I discover a swimming pool that I hadn’t known about. [It’s always somewhere in the dark, dark, bowels of the building.]
  2. I’m trying to lock up a school but people won’t leave and even if they do they get back inside somehow.

One means work undone and two means too much work to do. The distinction is subtle perhaps, as one can lead to two or vice versa, but I know what they mean to me.

I’d better explain why these thing should be so stressful that I have bad dreams about them—

  • Pools take a lot of looking after, leaving them for even a couple of days [if they are being used] isn’t something that you can do. And getting a knackered pool back into condition is a horrid task. Boilers, even coal ones, are a doddle in comparison—if they don’t work people are cold and can go home, they don’t hurt people on the whole. However, in principle, you can kill people with a badly maintained pool. [That said coal, or oil, boilers are not something to be taken on lightly—there are numerous ways that they can kill you.]
  • Schools are big buildings with many doors, locking them up is a pain. The only way that you can insure that you do it right is to have a routine. Couple this with the fact that people don’t want to leave—I’ll only be five more minutes, and you have problems. If you break your routine false memory syndrome will kick in. [I’ve locked up my present building five thousand times or so—it’s difficult to tell if what I remember doing five minutes ago actually happened, or if I’m remembering something that I did last week.]


While I’m not in mid-season form, as Bertie Wooster might say, I’m getting back into it. Taylor polynomials will never be my favourite friends and it took me much longer than usual to work my way through their unit book, but I did finally manage it.

The temptation now is to make my way through block D. A temptation which I’m determined not to succumb to. I need to put in many hours at the paper-face to ensure that Taylor Polynomials, integration and differentiation are second-nature. I was forced to do this at school and I still benefit from it—I can integrate nearly everything that I’ve bumped into, so far, on this course.

This won’t be fun, but it has to be done methinks. Another thing that won’t be fun is the MathCad work that I need to do for the next TMA. Yes, MathCad hasn’t changed.


taylor polynomials and an old flame

I’m still struggling away with these, I’m not having fun. I see what they’re for, I see how they work, it’s just that I don’t like them. My main reason for this distaste is that they are approximations, not pure enough for [precious, little,] me. I have another reason for disliking them—MathCad is a great help in studying them!

When MathCad and I first met I was taken with its graphing abilities, but, as our acquaintance grew, I lost sight of its graphical attractions. I began to concentrate on its flaws [flaws to my mind anyway]. We parted, I have TMA visiting rights, but we don’t talk much anymore. But there came a point, as I was thrashing around trying to visualize/sketch polynomial approximation functions, when I had a thought, a sneaking thought, maybe not even my thought. Whatever, someone, perhaps Gollum, tapped me on the shoulder and said—you could use MathCad.

So I opened up the beast. It was a wee bit like meeting, on a sunny street, an ex; an ex who’d been, callously, dumped for…erm…being mentally incompatible[?]. You remember that initial attraction, you wonder if they’d changed for the better since you’d spurned them, you visit what-if and what-might-be. You notice how lovely they look.

Right, I’m dumping this metaphor, I’m dumping it now!

I suppose that I’ve always known that there was a place for MathCad in my maths. [Why do I camelCase this? Its makers don’t.] But I’ve resisted—it annoys me, I dislike using it, I don’t like doing maths on a computer. That me, me, me is a dead giveaway—it’s my fault.

So, for now, MathCad and I are an item again.


a slight difficulty

You can’t like all maths and I don’t think that I like Taylor series much. It might be that I don’t understand them. Every so often a subject comes up that I don’t get, a subject where I don’t have that, ‘I understand’ click moment. So I have a decision to make, do I—

  1. Work at it until understanding dawns?
  2. Just leave it?

Two above is an option. It doesn’t even have to hurt mark-wise, I’ve noticed that you can often do maths that you don’t fully understand. It might not even hurt in the long-term, coming back to something later often works.

I’ve decided that for Taylor series I’ll adopt option one. So now the question is what should I do to promote understanding? Actually the question is—what is my problem with Taylor series?

I haven’t finished working my way through the unit book yet, I’m on section two, out of four [there are five sections but I never do the computing one]. What’s worrying me is that I’m having problems in the area where I’m usually strong—doing the calculations. I’ve worked my way through the activities, I’ve worked my way through the exercises, I still have to look up the methods and I’m still not getting many right answers.

That’s where the problem lies—I need to feel comfortable with the calculations. All that’s needed there is some hard work. So what I have to do is to throw aside the book for now and work at it on my own for a while. So that’s what on the math’s agenda for the next few days.

why i write these blogs

There are many reasons but the above is an example of one of the most important ones. I had a vague feeling that something was aglay, but I couldn’t put my [mental] finger on what it was. I struggled [more than usual] writing the above precisely because I didn’t know what the problem was. And you know what? The very act of trying to put into words what I was feeling helped me to understand what my problem was.

Because I was struggling ‘working the symbols’ I wasn’t happy. Which led me into thinking that I wasn’t understanding [the usual issue].

Even if you don’t ‘keep’ a blog it’s often worth the effort to attempt to write down [thinking about it won’t help] what the problem is. Sneak up on problems by varying the medium/senses that you use to tackle them.


limbering up again

Over the last few nights I’ve been forcing myself to do some maths. This, forcing myself, was the right thing to do—I’m getting back up to speed, maths-wise and my appetite for maths has returned. I’ll have to think about forcing myself to work more often.

I’ve been working my way through block three [calculus, more or less] doing the activities as I go along. I’m following my usual maths methods [which you will find somewhere on this page]. What I won’t be doing is using a computer—I don’t even read the computing book, I only crack open MathCad to do the TMA. Computers and learning maths don’t mix in my humble.

I may be wrong, it might just be me, but I don’t think that a computer can help you learn maths. Help you do maths yes, but learn? That said I’m a confirmed Luddite when it comes to maths, Jim of Mathematics => A Blog uses all kinds of tools to do his maths and it doesn’t seem to do him any harm. But he’s a software engineer!

I worry about computers and learning in general, it’s all the rage—distance learning, the information superhighway, virtual learning environments. I’m not so sure that it isn’t all a bunch of crap. My suspicion is that any, perceived, benefits are due to improved communication.

If you think about the parts of the web that really work [in the sense that heaps of people use them]—twitter, facebook, wikipedia—they’re all about the ability to, easily, communicate information to anywhere/anyone in the world quickly. This works in a learning environment too. If I have a maths problem I can post a question in the forums, I can contact my tutor, I can search the web. This is a major boon, but it comes at a cost—how do I judge the information thus gleaned? That’s where my internal bullshit detector comes into play, and I can’t develop that using computer.

Don’t get me wrong, I love computers, they are useful, wonderful things. But they can’t do everything. I’ll further qualify that with: even what they can do well isn’t done because people won’t use computers that way. I’d better explain that using…

a case study

My work have recently signed up to a Scotland-wide VLE [actually it’s more than that but…], I have issues with it, but I’ll do my best to make a success of it. As a school we probably have a real chance to make this work—we have excellent computing/IT teachers who are willing to go the extra mile, we have enthusiastic teachers, we, thanks, in part, to my cajolery and tantrums, have a web culture [staff realize that our web site is their responsibility], we have a management who won’t put road blocks in our way, we have a we culture. I still predict failure.

Why? Because even if we [those that want this to work] maintain our enthusiasm I’m not sure that we’ll be able to enthuse the kids, or convince the staff that this will make things better for them. Pupils will get bored with us trying to be ‘cool’ and staff will see hurdles.

People like, and use, computers but they aren’t interested in making their lives easier thusly. Have you ever met anybody that uses Excel in the way that Joel meant it to be used? I’ve met one—and he has the mark of me upon him, most people use it as a formatting tool—a tool to make lists.

Computers have a humped graph—to achieve long-term gain you need to put in short-term effort. Humans aren’t built to do this. It doesn’t matter if you’re the type of human who bought life insurance and started a pension scheme at twenty-two, you won’t be able to use a computer in an efficient fashion unless you have a Zen-like discipline.

I don’t, which is why I don’t use computers for important things like maths.


strange times

I’m in a new place and I’m not sure if it’s a wrong one—I’ve just finished one course and I can’t seem to muster up much energy for the other course. The other course would be this course—exploring maths, MS221. For the last month or so it’s been all public void doM255() and I can’t seem to get my head back into maths mode.

According to the course calendar I’m actually behind, somewhere that I haven’t been for a long time. I’m not too worried—with a fair wind and an unclouded mind I should be able to catch up. But it feels like too much effort.

For the last couple of nights I’ve been trying to work my way through C1—differentiation. It’s been hard, to force myself that is. [The maths is a wee bit tricky in places but nothing that I shouldn’t be able to handle.] I’m tempted to follow my usual methodology and just leave it until I feel like doing maths. But I think that this may be one of those times when I should force myself.

Why do I feel that? I’m not entirely sure, but I’ve a nagging feeling that if I don’t weeks, or months, will slip past in idleness. The hope is that if I force myself I’ll begin to enjoy it again.


What doesn’t help is that this is a rotten time for me at work. Summer holidays are coming up and others are planning mountains of tasks for me. As usual the assumption is that if it’s easy for them to say it’s easy for me to do—we can move room 2–09 to 0–01. That we would be me.

I’m being harsh there, it’s a tortuous process for them to decide what to say. They have many meetings before they make an off-the-cuff decision at the last minute. Fortunately as I’m handed the job of implementing these decisions unsupervised what they decide isn’t always that important.

More maths tonight then.


there are times…

When I wonder why I put myself through this self-imposed hell. How did I come to this pass? Here’s the [potted] history…

It was the mid-nineties and I was having my first brush with serious, pill-required, depression when pokémon cards hit the playground [I was working in a primary school]. It was a game! I spent playtime swapping cards with the kids, I started a club, I was obsessed. I paused to wonder if one of those funny looking iMacs could connect to that internet thingee that I’d heard about…

Of course there was a wealth of pokémon stuff there and I grew to love those ‘inside-out’ iMacs. So much so that I bought a MacUser magazine. Which had an article about using AppleScript to talk to your Mac…

By now I was off the pills and I decided on a change of job—to a Windows environment, which I hated, but which had this database called Access that looked useful…

Skip on a couple of years and I needed to share my many databases, how do you make webpages? I found out, I volunteered to curate my school’s web site

It’s now 2006 and I’m beginning to realize that, although I can use an XSD file to create a web form on-the-fly, I haven’t a scoobie what I’m really doing. At which point some serendipitous browsing brought me to the Open University web site, and tt280…

I was coming to the end of the webapps. and planning what to do next [only the death of one of us will separate the OU and me]. Obviously computing but…

Something was missing. Computing seemed too inside my comfort zone, and it was beginning to dawn on me that I wasn’t that type of geek—the one that builds things—I can, but it isn’t my main interest. I got into conversation with a fellow webapper cried Paul who had a degree in Maths and Computer science who wrote, possibly, the most important sentence that I’ll ever read in my life…

Third level maths is always hard but it helps you understand some of the more ‘esoteric’ blogs.

I don’t know if you’ve ever played ker-plunk, but that sentence was the removal of the right cocktail stick—all the marbles tumbled. I knew what it was that I wanted to do…

So I’m in a self-imposed hell of work/deadlines/work.

…but there are times…

When you come home, see that envelope, rip it open, do the dance, punch the thin air, and get, that most unlikely of things—100% for a Maths TMA. Such things are to be treasured and hugged to one’s heart.

We, I, forget sometimes what a special thing it is that we [OUers], are doing—juggling it all: life, work, drunkenness, the OU . We forget what we are getting out of it: the joy and the better I. I had a conversation the other day, someone asked me something—once-upon-a-time I’d have rattled off some crap, but I couldn’t, I had to think. I’m better.

We won’t earn a fortune—we aren’t that Type, but we will, when we face our God, be able to say I didn’t waste my time. We are the blessed and the OU is blessed.


the books arrive

The books for blocks three and four arrived last Friday afternoon. So I spent a fair bit of the weekend perusing them. Not what I should have been doing. What I should have been doing is the MathCad stuff for TMA02, but I’ve developed something of a phobia re the thing—I can’t even force myself to open it up. Not good.


I’ve been looking forwards to these units, they’re about the maths that I particularly like:

  • Calculus—which I love, a semi-routine task that requires intuition and a certain creativity.
  • Taylor polynomials—which interest me and are something I’ve never got my head around due to not working at them.
  • Complex numbers—I can take or leave these.
  • Number theory—yum, yum.
  • Groups—ibid.
  • Proof—the heart of mathematics and a fascination to me. I don’t suppose that I’ll ever create an original myself but I’d love to be able to re-create others’ work. Or, in some cases, understand.

I like/love all maths [strange, a couple of years ago I didn’t realize this] but what’s approaching excites me; by the pricking of my thumbs something wonderful this way comes.

So I should be overjoyed, enthused and raring for the off? Alas not. I’m not sure what’s wrong with me but I’m finding it difficult to focus. I can force myself to work but when I do I don’t have the feeling that it’s going in. This isn’t something that I’m used to—I often lose interest but when I do work I do feel that I’m learning.

Should I be worried? I honestly don’t know—it might be just one of those things. I’ve got a tutorial this weekend and they always spark me up. If this one doesn’t I’ll know that I’ve got a problem.



I’m in a strange, unfamiliar place, one course [M255] is approaching its end and another [this one MS221] is only half way through. How should I be managing my time? Obviously revision for the M255 exam takes precedence, but exactly how much precedence should it take?

Here’s how things stand—

  • For M255 I have an, almost completed, TMA due in the next week or so, and then the exam in mid June.
  • For MS221 I have a TMA due in mid June and the block three and four unit books will arrive in mid May.

The basic problem is that I’m going to have to force myself big-time to buckle down to revision, the slightest temptation to not do it is going to throw me off course. Then there’s the fact that TMA02 for this course has a large MathCad component, something else that I’ll instinctively avoid. What I should do is the following:

  1. Submit TMA04 for M255
  2. Submit TMA02 for this course
  3. Revise for the M255 exam

But I won’t. I’ll succumb to the temptations. The temptation to laziness and the temptation to [non-MathCad] maths.

mmmmmmm, maths

Said in a Homer Simpson fashion.

I was lazy this weekend, I spent most of my time messing around with graph theory, determinants and solitaire. Nothing on-task. Perhaps not wildly off-task but not actually course work. I did stuff that I enjoyed—I could have done some real work, but I didn’t—I wanted to play. And into that mental attitude will fall the block three and four unit books.

I’m fucked.


not doing any maths

Well not much. I don’t suppose that I’ll ever be in the position of not doing any maths ever again. I think that I quite like that.

Life is a funny beast—in the summer of 2006 I didn’t have any idea that I’d ever do any maths ever again. I didn’t even think about maths. I built rotten databases, wrote bloated code and designed terrible websites and I was beginning to realize that that was what I was doing. In September I signed up for tt280.

So little step by wee step I’ve ended up here—doing a degree, doing [and loving] maths, thirsting for knowledge, straining my mind. Sometimes it’s hard; sometimes you feel like giving up; often I’m tired, harassed and desperate. But some mornings I think about getting out that book on Laplace Transforms that I don’t understand and spending an afternoon wrestling with it. Such mornings are to be treasured and make it all worthwhile.



My marked TMA dropped through the letter box on Saturday morning, that was fast! Considering that I only submitted it on Tuesday and that it had to make a round-trip to Walton Hall it is in fact seriously fast. All tutors are wonderful but mine is particularly so.

I was pleasantly surprised by my mark, I expected to drop serious marks for the MathCad stuff as well as the usual sloppiness tax, but it wasn’t too bad, in fact you might say good—I got ninety-nine percent. I don’t usually flaunt my marks but ninety-nine percent…

Enthused by success I decided to spend the weekend tackling block two once again, this time with a particular focus on doing the next TMA. This is part of my usual approach which goes somewhat like this:

  1. Work through all the unit books in a block doing all the activities. [I don’t do this for my computer courses!]
  2. Work through the block again and do the exercises.
  3. First attempt at the TMA—work through the block again doing the TMA questions as they appear.
  4. Work through the [block] exercise book.
  5. Complete the TMA.

So I was at stage three above.

Interesting, I made a similar dis-similar list below. Have I changed my methods? Not really, it’s just that I don’t work to a strict system so what I think that I do can change depending on when I think it.

I had a pleasant weekend scrawling maths onto mountains of paper, the TMA [non-MathCad portion thereof] has been half completed and I even managed a bit of gardening. All good.


On Sunday evening as I lay back on the couch with my first beer to watch Doctor Who for the third time [it’s the only BBC programme that makes me think that paying the license fee is worthwhile, so I like to get my money’s worth] I realized that I had a couple of important decisions to make:

  1. This is the last point that I can, realistically, swap horses and opt for a computing only degree. Should I drop the maths?
  2. Am I seriously going to not request a replacement MathCad disc?

One isn’t an issue, for all kinds of reasons I want to carry my maths forward. I could change to a computing only course but I’d have less fun, wouldn’t learn what I want to learn and I wouldn’t be pushing myself out of my comfort zone. This degree is for me, my brain, my itch and maths is part of that. I’ve signed up for M208.

Two is difficult. I know that I’m right, for me, to try to learn how to use MathCad properly my way but…the mark that I lost was because I didn’t use the supplied worksheet. I can cope with losing marks if, if, I learn how to use MathCad as a result. But will I?

I can’t believe that I’m still bloody agonizing about this—just order the effing disk neil. But, but… I’ll give it one more TMA.


I finally caved and ordered a new disc.


[future] good intentions

I finally managed to submit my TMA the day before the cut-off date, which given that I have to use snail-mail was effectively the cut-off date. This was not good. So I’ve resolved, in future, to do the following:

  1. Get started on the TMA as soon as possible—this can’t possibly hurt.
  2. Do the MathCad stuff first. It’s the part I hate and the part that I find the most difficult, ergo it’s the part that should be tackled first. Doing something you dislike under a time-crunch is a recipe for unpleasant-feeling failure.
  3. Prepare a fair copy, of any finalized work, early. Three and a half hours of writing the whole thing is a pain on the pen-callous. [That said it is good practice for the exam, pen-wise.]

As with all my good intentions it will probably come to naught But the plan is, over the next couple of weekends, to put TMA 2 to bed. So time to open MathCad.


TMA panic over?

Not quite. I’ve got something MathCad that I can submit, it won’t earn me [m]any marks but at least I tried. I’ve finished and eyeball-checked the rough draught; I’ve yet to pen the fair copy and do the MathCad/calculator check, but the worst is over. The thing won’t be submitted tomorrow, the plan, now, is Saturday. But unless something terrible happens, I suppose that the is panic over.

Are there any lessons to be learnt from this proto-débâcle? For me, and for my approach to this course, I think that there are. But I ha’ ma doobts about any universal relevance:—

  • I’m right about trying to learn MathCad without input. It may be old kit but, from a couple of comments on the Moodle forum, it seems to work in a similar fashion to other, newer, maths applications. If it works in the same, basic, way then it’s worth learning. Learn the form not the details.
  • This course is about learning some basic techniques. To solve real problems you need a toolkit, an understanding and an intuition. I could earn more marks by ‘working’ the unit books while doing a TMA—but that isn’t right for me—I need to test my technique/skills.
  • I got away with this panic by having done most of the work ages ago, and by developing my maths muscles by hard work. Exercise after exercise is what’s required, when I’m in the mood [or when I’m not but can force myself] I should be doing them.

I guess what I’m saying is that, in the end, for this course, the marks don’t matter as much in the end as what I’ve learnt. And here we have a problem—we judge what we’ve learnt by the marks that we get.

But I know what I should do…it’s, as always, the doing that matters.


Fear not my fellow MS221ers I’m wrong here.

snuck up on

I was lying in bed this morning thinking about how things were going course-wise when I had a sudden thought—this coming weekend is Easter. When is my TMA due? A quick calculation revealed the sad truth, Tuesday 7th, so I need to post it off by Thursday. Aaaargh, I’m in an unexpected time crunch.

I’ve done most of the questions [except for the MathCad ones] so things aren’t all that bleak. All I have to do is write a fair copy, some bits-and-bobs, the MathCad and some checking. As I type that my heart sinks slightly—there’s still a bit to do, even if things go smoothly. I don’t like this.

It doesn’t help that I’m on backshift and without my math’s head. By which I mean [about the math’s head] that, as of the present moment, I don’t have any great appetite for doing maths. This happens to me on a regular basis—I go through phases where I lose interest in maths, in computing, in cheese. Not something to worry about normally but a damn nuisance at this point.

So I’m stuck with the prospect of spending the next three mornings forcing myself to complete my TMA.

Avoid thinking that the thoughts that you think in bed are set in stone. The 7th of April is Wednesday! So I have the weekend to complete my TMA. But I’m still going to force myself to finish and submit it by Thursday as a punishment.


fun with mathcad

I’ll apologize in advance for the jumbled logic of this post—my thoughts on MathCad are [hopefully] still in the process of gelling. This post was written as a desperate effort to make some kind of sense of my thoughts.

When I’ve had time I’ve been messing around with MathCad this week. So what’s the current state of my thinking re the thing?

  • There’s a keyboard shortcut for everything and it helps if you know and use them. [MathCad may not be pre-mouse but I have the strong sense that its original incarnation was meant for keyboard input alone.]
  • My estimate of twenty hours to learn how to use it was out by a factor of about twenty. This is industrial level software—serious people do serious things with it.
  • The help system/resource center[sic] is woeful. [The course worksheets are slightly better but not by much.]
  • I was right to think that the only way to learn MathCad [for me] was to ignore the worksheets and try to do things for myself. I’m now treating it like I’d treat a new programming language, which helps. [It is programmable!]
  • Without the course disc I’m going to lose lot’s of marks. For example TMA one has a two-mark question which requires you to rotate a conic. Altering the supplied worksheet would probably take about two minutes, I’ve spent three hours on it so far.
  • I’m not having fun.

All of the above leaves me in a hard place—do I push on, or do I request the disc and give up trying to do the right thing? For me this is an either or, without the spur of marks I won’t try to learn to use MathCad properly—I’m too lazy and as I said above I’m not having fun.

There’s a real problem here; I appreciate the power of MathCad, I see [in a very general way] why it behaves slightly oddly, I’d like to learn how to use it properly, but it isn’t something that I enjoy. Or something that I foresee using for something. The problem is me, the way I think/am—I’m happy to learn Haskell for no other reason than curiosity and I’m happy to learn, say, python because I can see that it might be useful sometime. MathCad ticks neither of these boxes. It’s a philosophy thing.

maths on the computer

I’m always fascinated by Jim of Mathematics Diary [yes I know he calls it something different now]. He uses a battery of applications to study his maths; he engages all his senses to learn, for example he watches videos etc, I can barely be bothered to watch the course videos. We’re polar opposites when it comes to maths.

So what? Well I think that there’s something important to note here. Jim’s complaint about MathCad is that it’s old kit, not that it’s hard to use; my complaint[s] are all about the way that it doesn’t work for me. I’m happier with a pencil, my head and some paper. I don’t want to do maths on a computer.

At this point neil is struck by a body-blow to the head—there’s better gear out there! I’m trying to learn MathCad because I thought that it was state-of-the-art. If it isn’t…?

A simple bugger will suffice. I don’t want to use a computer to do my maths and the thing that I’m trying to learn isn’t even the best…

Time to order that disc.



I’ve not been doing any maths for the last week or so—computing TMA being to the fore. But it is now time to deal with my first TMA for MS221. Which meant that I had to open MathCad yesterday. As expected this was not a pleasant experience.

Being a diddy I threw away the MathCad installation disc after MST121 and I hadn’t installed the MS221 course materials, which puts me in some difficulty. Of course I could just ask for a new disc, but I don’t want to. Which, on the face of it, seems a wee bit thrawn, and perhaps is. But I have a plan.

I don’t like MathCad [I’ve yet to meet someone who does] but if I have to use it I should be able to use it well [it’s a geek thing]. And the only way I’m going to be able to do that is to use it in anger. I suppose that most people when doing a TMA open up the supplied file and alter it as appropriate. I know that’s what I did during MST121. That ain’t good enough. I have some experience of this computer crap and I know that the only way to learn how to use an app. is to use it, and use every bit of it. That sounds obvious, but it’s surprising how often people don’t do that. They use a tiny subset of an app.’s functions. Badly.

Let’s take—for example—Word; everybody uses it [I don’t unless I absolutely have to] and nobody knows how to. I won’t go into any great detail but if you haven’t set up document templates, customized your toolbars, created some macros and edited your auto-complete then you haven’t even started! I can use it, and I can use it because I spent a lot of time learning how to. That’s what I need to do with MathCad, altering worksheets isn’t going to do the trick.

At this point you’re probably thinking that I could just do the exercises, couple of things wrong with that:

  • I don’t do exercises
  • It’s still just altering worksheets. You can’t learn how to use an application unless you create things for yourself—it’s a tacit thing.

dangerous territory

I expect that you’ve spotted the danger in this—I could lose a lot of marks. There’s fifteen on offer for TMA one and a, whopping, thirty for TMA two. Still I’m willing to risk it. After all this course doesn’t count for my degree classification.

How does this square with my philosophy of doing a degree to learn, rather than to use it to earn cash? Well, we all want to do well, but my main motivation for getting a good degree is that it will allow me to do post-grad courses. I may not want to, but I’d like the option.

how long will this take?

Too long when I don’t want to be doing it. But learning how to use an application takes time and effort—I’m guessing around twenty hours. I can hear your scream, but that’s what it takes I’m afraid.

the problem with mathcad

The classic answer is that it’s, un-intuitive. The computer [crap] part of me understands a wee bit why this is so, but that helps not one jot. It does seem to work differently from the way other applications work—but the do other applications do maths?

I’ve thought quite a bit about this and I can’t decide what the problem actually is. Which is interesting in itself—if you can’t pinpoint what’s wrong is there a problem? In the end it may all come down to that it doesn’t work like a word-processor and it doesn’t work like maths.

Time to get down to it I suppose—uurrrgh!


on holiday…

I’ve been on holiday for the last couple of weeks, from work, from the OU and from the computer. But that hasn’t stopped me from doing some maths! But not OU maths.

I had a tutorial on the first Saturday of my break [my tutor is the man from the videos and is truly excellent]. I came away from it with three things:

  1. To prove an equality work on one side, reducing an equation to 3 = 3 isn’t what is being sought.
  2. Show all the steps in your working.
  3. I’m a sloppy sod who’s trying to work too fast with a too shallow understanding when it comes to maths.

Three seemed to be something that I could work on. So I dug out one of my more elementary text books [get them in second-hand bookshops] and worked my way through some of the basics. I’d love to report that hours of diligent toil have left me with the mental equivalent of a six-pack, alas not so. I did not stick to my task.

However I think that it’s the way to go. It’s all to easy to get carried away with the “new stuff”—but don’t neglect what you’ve already learnt. I spent hours as a child [under the lash of Ms. Harkness’s tongue] doing exercise after exercise—it’s only now that I’m grateful.

So, in future I’m going to force myself to do an “old” exercise every time I do the, more exciting, “new stuff”. I’ll let you know how that [didn’t] go.


rushing ahead

The course hasn’t officially started yet and I’m already working my way through unit three [Functions From Geometry]. I just can’t seem to stop myself. Which begs the question—if I enjoy doing maths so much why amn’t I always doing it? The answer, I think, lies in the quality of the OU materials.

I have other maths books, but they either assume knowledge that I don’t have or they’re designed to used in conjunction with a real, live, teacher. They’re often badly written too. The OU texts on the other hand are beautifully written [I love the wee historical asides], aimed squarely at someone with my level of knowledge [give or take] and they’re meant to used solo. This makes learning from them less frustrating and far more fun.

That isn’t the whole story. I have a tutor and an online forum that I can turn to for help if I get stuck—I’m not on my own. I generally forget that this is a major factor; the ability to ask, virtually 24–7, questions gives you a mental safety net. So you don’t put up internal barriers to learning.

I often come across people who, can’t do maths [by with they usually mean arithmetic], they can. It’s just that they’ve erected the aforesaid mental barriers big-time—it looks hard ergo I can’t do it. It’s, all to, easy to do this at any level. If you think that something is impossible then it will be. If you think that you can do everything you may be wrong but, at least, you give yourself a shot at it.

I suspect that generations have been denied mathematics by the early combination of non-intuitive text books and an uninspiring teacher. [Or permutations thereof.]

talking of non-intuitive…

I opened up MathCad the other day, entered in a sequence, failed to plot a graph and closed the beast in disgust. I’ll either have to take the time to learn how to use the thing properly, or just accept that I’m going to lose a lot of marks because the only time I open it up is to do a TMA question. I want to do the latter but I’m trying to talk myself into the former.

However, I’ll stick with pencil and paper for this weekend!


getting started

The course proper starts on 2009–02–13, perhaps an inauspicious date, but it feels like we’ve kicked-off already. So, instead of doing any work, I thought that I’d jot down my initial thoughts.

The course looks very interesting, the title says it all—Exploring Mathematics. I don’t think that we’re going to be too concerned with any practical applications of what we learn.

I rather like that. When I started MST121 I [thought I] liked that we applied what we were learning to ‘real-life’ situations. However, as the course wore on I became less and less interested in the applied bits—and I really hated the statistics. I suppose that there are different types of mathematician—I enjoy pure maths, I like algebra, I don’t much like geometry… I think that this course is going to suit me.

Presently I’m working my way through units one and two—sequences and conics. Why two units at once? I’m not sure, sometimes I fancy one, sometimes the other. I plan to have a first go at unit three this weekend.

I did a lot of work on sequences during M263, so I’m in familiar territory, but the conics are completely new. I think that I’m getting along well enough [apart from a worrying sloppiness with my algebra] but it’s early doors.

moodle & elluminate

The course web site is live and there are new toys to play with—Moodle and Elluminate. Moodle is a fairly bog-standard online forum [well it looks like that at first glance] so I’m not over-excited. Elluminate is a Live![sic] online tutorial application which, In order to fully participate in […] you will need a headset with a microphone. Jings! I won’t be using that.

I know that the OU is planning to replace First Class with some Google app-in-the-cloud, is this it? Probably not. I suppose I should try it for a while before damning it out right. But it’s not in my nature.

In fact, when I think about it, I’m a bit of a technophobe—I use computers but I’m not much interested in them, or all the wonderful things that the can do. Oh, and I hate MathCad!


some early thoughts

Now that I’ve had a chance to look at the units I’m looking forward to this course even more I was. From the course description I’d a good idea of the ground that we’re going to cover, but seeing the units has sharpened my appetite.

I loved MST121 but, in a sense, I was covering old ground. Old ground that I had an incomplete knowledge of and a patchy understanding of what I did know, but old ground none-the-less.

Not so with this course—even the first couple of units have introduced me to techniques and concepts that I hadn’t come across before. I’m sorely tempted to rush ahead to the end of block two [there are two mailing for this course]. I know that it’s wrong but…

No Neil! Stick to the plan. What plan…?


I’m not sure how others tackle their maths courses but here’s my way of doing things:

  1. Initial run through. I read a whole block’s worth of units, doing the activities.
  2. Second run. I go through the block again [this time doing the DVD an audio portions—if I can be bothered] and do some explorations of my own.
  3. I do the exercises in the unit books—looking for weaknesses that I can swot up on.
  4. I do the exercises in the exercise books.
  5. I do a first-run at the TMA

At which point I’ve run out of [answered] questions time to hit the second-hand book shops. And time to play around with my new knowledge/skills—has it all gone in?

This served me well[–ish] during MST121, but will it still serve this time?


the books are here!

One of the great moments on any OU course is when the books finally arrive. I say finally because, as you can track their progress or lack thereof online, the process can seem to take forever. Take for instance the the odyssey that my materials underwent—you may imagine my feelings as I saw them heading the wrong way! Anyway, they arrived on Friday afternoon.

As I was signing for them the delivery guy said a strange thing, I guess it’s the start of the season again. What? Then I realized what this meant—people all over Edinburgh, Britain, the World[?] were receiving their books, and they were feeling like I was.

Despite the fact that I was entertaining the Mother-In-Law [note the capitalization] I skipped into the front room and ripped open the box. It’s a drug-like rush—there is no smell like that of new books, and there’s no sight quite like the beauty of course units nestling pristine in their box. For the next eight months these books will be my companions—they’ll end up as a tattered palimpsest ruined, like a much loved teddy-bear, by too much love.

Once the initial high had levelled off somewhat, and I’d exhausted myself flicking through the units, I sat back [with a beer] and had a wee think about what it was that I was feeling. There was the normal pre-course excitement; that clean-sheet feeling, the eager anticipation, the hopes of perfection, but there was something more—a feeling of being part of a giant family.

Sometime I forget what a special organization the OU is—it gives an aged jaded-janny like myself reasonably-priced access to a higher education. Not only that is it does its job well—every interaction I’ve ever had with the OU has left me feeling that people care, they’ll go out of their way to make things better for you. This is not the normal way of things. And there’s nothing else like it in the world, something for Britain to be proud of.

Of course like everything else that Britain can be proud of it will be destroyed [take the NHS]. Destroyed, because it goes against the mantra that the Rich should be able to purchase unfair advantages for them and theirs and the rest of us should know their place.

But for now I’m glad to be part of the family.


It seems that I wasn’t the only one keenly awaiting the books, there was a long thread discussing same in the OUSA MS221 conference.


nearly time…

According to the course web site the materials [i.e. books] are due to be despatched by the 22nd. I can hardly wait—time to get my revision started methinks.


infinity and beyond…

Stupidly I got myself sucked in to an online argument about countable sets [a subject which I don’t understand]. At best you could say that my contribution allowed the knowledgable to ‘explain the concepts’, at worst you could say that I made an arse of myself.

Not that I mind making an arse of myself if it helps me [or others] understand—worse would be to say nothing and remain in darkness. However this time I may have gone too far, I actually thought that I understood what I was talking about. Clearly this was not so.

Still, lesson learnt: learn—so added to my christmas math’s homework are infinite sets and Cantor’s theorum—I’m printing off multiple PDFs as I type.

groups [and solitaire], again

Still working on this one. I’ve been [slowly] building my ultimate Java solitaire machine™ for a while now and, in about two years, it will start producing erroneous results. So for the mean-time I’ve been trying to tackle the problem using only my mind. You know how that’s going, don’t you.

I suppose that I’m being a purist about this, I could buy what seems to be the book about it, but where would be the fun in that?

I will warn you that I have a long, obtuse and possibly wrong article about the entire subject planned for the new year.

proper work

Fortunately the world isn’t composed of cretinous, dilettanty shilly-shalliers like me. There are people out there who do useful things. And MathsJax is certainly a useful thing. An open source AJAX solution to displaying maths formulas, it’s pressing all my buttons.

I haven’t had a play yet but if it does what it says on the tin it will be making its appearance here in the near future.

So off to collect my reams of paper, do some first last-minute shopping and then off to contemplate the infinite on the couch—have a nice one!


as usual, wrong

I was wrong in my last post [quelle surprise!]. But, for now, I won’t be explaining the where, and the why I was wrong until I’ve done a wee bit more work on group theory.

I’ve been doing quite a lot of this [group theory] over the last couple of weeks—for me it’s the new calculus. I enjoy messing around with it [while drinking beer—the ultimate recreational mathematics], so there’s a chance I might get quite good at it. I noticed something like this during MST121—I got good marks for calculus because I liked it and thus I spent a lot of time working on it. This is a potential problem—I should be spending more time playing around with, say, vectors where I’m weak.

However, for now, I’ll let myself off, it’s not as if I have a course, so I can suit myself, can’t I?

Anyhoo, once I’ve got my head around permutations and parity I’ll get back to you about the solitaire.



Mathematics Diary finally prodded me out of my maths inaction and got me started on group theory with a side dish of modular arithmetic. Pretty interesting stuff.

For reasons that I won’t go into I’ve always been into solitaire [they’re sad ones] so I was interested in this proof that there are only five positions where a single peg can finish. All well and good, but it occurred to me to ask what happened if you removed a peg other than the central one so that you have a different starting position. There should still only be the same five finishing positions, shouldn’t there? Erm, one problem—I can play to a single peg finish in another location.

So what’s wrong? I think that the problem lies in the symmetry argument for not being able to, for instance, finish in a corner position. I found another proof that uses a slightly different board which has both 90° and 180° rotational symmetry which the first board doesn’t.

However, I may be missing something, so I’ve printed off some complicated looking PDFs for weekend perusal—I’ll get back to you.


all set

This course doesn’t start until February 2010 by which time I will have forgotten everything that I learnt during MST121. I really missed a trick in not doing this course alongside MST121, but then I didn’t have the wonga at the time. Alas it isn’t always easy being poor.

I won’t be posting much here until the course books arrive [sometime in 2010 according to the course web site], so I wouldn’t visit again until then if I were you.