The Hiatus is Over

Hi all!

Gosh, I really have been away for a long time. I knew I'd left it a while since last posting, but only just now realised that it was way back on 4th July that I last wrote anything.

Many things have happened in the meantime, the most significant of which is that I got married on 12th August. It was a great day except for the New Forest weather which tried to ruin things right around the time the photos were to be taken. Some of you may appreciate that me and Kim have Mobius wedding rings. While it doesn't do it justice, I've added a picture of mine below (please excuse the state of my fingers, I had a fight with a ferret a couple of weeks ago...)

My M381 TMA was, unfortunately, due around this time. My tutor was kind enough to give me an extension because of the wedding, which certainly helped matters, as I had a few large projects to get finished in my work as well. The M337 TMA was due a few weeks earlier, but again, poor timing on my behalf meant I spend the whole weekend preceding, camping with my brother and a few friends. So I had to get that one out over an intensive all-nighter after getting back. Fortunately, I got good marks on both of these.

In September, we went to New Orleans for a week for our honeymoon. Again, TMA deadlines almost perfectly coincided with our departure, and as you probably know, there is no scope for extension on the final assignments. I managed to complete my M337 TMA in Portsmouth after driving our dog there so my parents could doggy sit while we were away; I only got about two hours sleep though because I spent the whole time trying to get my head around conformal mappings and fluid flows (the Mandelbrot set questions were easier at least), which made the prospect of a four hour drive back a little worrying. Alas, this left me little time to finish my final TMA for M381; I was actually working on it at the airport on the morning we left, but had to post it more than 2/3 unfinished. I thought it would be better at least, to send something, however short, than to skip it altogether. I was quite upset at having to do this, but tried to put it out of my mind, and focus on the fun and exciting (but hot and expensive) week ahead. I was under the slightly deluded impression that I'd be able to study while out there, so I took practically all my textbooks with me, as well as past papers and previous TMAs. Ultimately this just added about 15kg to our luggage for nothing, as I did not one minute of study.

After getting back, it was time to begin thinking about the exams. I am rather annoyed at myself in this regard as I put it off and put it off, and started much later than I should have done. The exams themselves were very hard, though I doubt starting my revision earlier would have changed that too much.

The M337 exam started out okay, but I was behind schedule by the time I got to Part 2, and when faced with the optional questions, quickly realised that I was only really qualified for one of them. You'll have to forgive me because I cannot remember now which that was. My second choice was on generalised circles and Mobius transformations, and I doubt I got many points on that one at all. I left it thinking that I'd probably got a Grade 2, but would not be overly surprised by a Grade 3. A twinkle of hope for a Distinction arose in my mind a few times over the ensuing month and a half but I made a point of quickly extinguishing that each time, as it would only lead to tears.

The M381 exam started out badly and then got worse, or at least that's how it felt. I probably did better than I felt I was doing at the time, when in the throes of mid-exam despair. I got off to a bad start when I took almost half an hour over a question involving a proof by induction. The problem was that I knew I could do it. I knew that if I fiddled long enough I could get the two sides of the induction step to match and therefore complete the proof, so I kept on going until I did. Not the most efficient way of tackling an exam, that's for sure. By the time I'd finished, I had only done eight questions, and since they take your best nine answers across the two topics, that did not bode well either. I can't really recall much of the content; probably a psychological defence mechanism. But I do remember my final question being one where an incomplete formal proof is given and you have to fill in which assumptions (or was it the rules, or both, I'm not sure?) were in use at each step. By the time I got to that point, I had about two minutes left. I tried to to ignore the time and tackle it normally, as I was quite good at this when I did similar questins before. But in the end I had to quickly scrawl out some answers in the hopes I'd score some points by luck, or indeed by hoping my subconscious would do the work for me. Anyway, I left that exam very very depressed. I've not had an exam go so badly since my module on Modern Japanese History in my 2nd year at Sheffield University... at least I didn't leave the M381 exam half-way through knowing that even what I did write was little better than gibberish! So I was hoping for a Grade 2, but expecting a Grade 3 (remember also, I'd only done a small part of the final TMA, and as useful as the substitution rule is, it can't fully counteract something like that!).

Anyway, as some of you must know, the results came out on the night of the 30th. That's almost two weeks earlier than my M208 one last year! I was relieved to find that I'd managed a Grade 2 in both cases. I'm in shock regarding the result of M381, and I keep checking back to make sure they haven't changed their minds on me. I like to think they're not allowed to do that, but I still worry.

I've just signed up, over the phone, for M338 Topology, and as a bit of a diversion (as well as a step back, hopefully, in difficulty) S282 Astronomy. I may even be tempted to get out my telescopes over the winter to get me in the mood; there's already been some very starry nights here. I expect Topology to make M337 and M381 look like child's play, but I've been looking forward to the course itself for a long time, as the topic really interests me. Hopefully that, along with the (presumable) lack of weddings and honeymoons next summer, will help me to do well in it.

I hope everyone else who was awaiting results, has got what they hoped for!
If I don't post again in the meantime, have a great Christmas.

Neil

Patterns of study

I had not thought this through beforehand, but somewhere along the line I fell into the pattern of completing a whole unit of one of my courses at a time. No one day one one course, the next day the other, then repeat, nor a bit of each course every day. Nope, I work right through one unit of a course for however many days it takes, then work right through the corresponding unit in the other course (though that's not strictly true, as I'm not at the stage of "corresponding units" any more; not since I cut my losses on M381 and accepted that I'd be behind until the end, but you get the idea).

Pro: I get to keep my mind on one area of maths, e.g. Complex Analysis, for a few days without disrupting my flow by having to get my head around Church's Thesis slap-bang in the middle. Then, within Complex Analysis itself, I get to cover an entire unit, which basically equates into a single topic, residues, Laurent series, or whatever, to its conclusion before switching to something completely different. And these courses are different! Psychologically, this way also helps me feel like I'm getting somewhere, you know? Because I can tick off another completed unit fairly quickly. I'm well aware that this is silly, because technically, I should progress at the same pace either way, but it feels effective at least. A schedule placebo of sorts.

Con: I am prone to not remembering diddly when I get back to one course after maybe a week on the other one. This is worse with M381 because of the fact it alternates Logic / Number Theory / Logic.. It could be three weeks by the time I get back to number theory after our last encounter. That can't be too helpful for driving the material home, can it? Would I have had to look up Euclid's Lemma what seems like a hundred times already, if I were chip-chip-chipping away at M381 every day? Who knows?

Anyway, why am I telling you this? I don't know. It just strikes me as curious, that beavering away in the solitude of our homes, we've probably all fallen into patterns of study quite unique to ourselves. I assume they vary wildly. I'd certainly not be surprised to find that any of my fellow OU students are doing a couple of hours of each course per day. But it doesn't work for me. I'm fairly sure that I started off with the intention of doing it that way. And I didn't make a conscious effort to stop either; but it clearly happened at some point.

Until this year, I'd not had two courses at the same time, so I've never had to tackle differing topics concurrently. I opted to do MST121 and MS221 with an overlap, starting one in the autumn and the other in February, but it wasn't quite the same. Not only were there long periods of one course only, but they also complemented each other in terms of content. Then of course, M208 was a 60-pointer, so it was not an issue there either. In fact, that's the one thing I find attractive about the upcoming level 3 pure maths course; at least in terms of scheduling, there'll be no need to work out how to go about it. Though, I'm not interested in any other way than that, and I'm so glad I started with the OU when I did, so I'm still on for M338 Topology next year before it goes bye-bye.

Neil H

Ingenious and correct, but...

I got my TMAs back this week. Upper nineties on both counts, so very pleased, and a little surprised. In complex analysis specifically, because, for the first time since starting OU studies, I am finding it hard to convince myself that my answers are right, and am therefore sending off these assignments with no idea of a ballpark result. Of course I hope everything is correct, and wait fingers crossed each time, hoping for that elusive 100%, but try equally to prepare myself for a paper covered in mistakes. It's hard to put my feelings on this subject into words; I'm finding it equally as frustrating as I am interesting.

Nevertheless, M337 recently led me to my number one, all time greatest, mathematical achievement... ever. Albeit an unnecessary one. It was an equation I devised for the Laurent Series asked for in the final question of the assignment. I pieced this equation together from a few flukily spotted patterns and not a small amount of head scratching, over the last hour or so before enveloping the assignment up and rushing it to the post office. Ever since, I have found it frequently on my mind. I randomly write it up on my blackboard, or on my A4 pad, and just marvel at it. Somehow I had come up with this! Pretty sad behaviour to be fair. But still, if this is how I react to coming up with one good equation, well, how must it feel to be someone like Andrew Wiles and crack Fermat after almost 360 years?

When I got the marked version back, my tutor Alan Slomson commented thus: "This is ingenious and correct, but you didn't really need to find a formula of this kind" Yep, ingenious and correct, but totally unnecessary. Somehow that makes me feel even better. Like I went above and beyond the call of duty. Don't get me wrong, I don't think I'm some kind of expert. I'm sure many others came up with something similar or better, but it was one of those moments, all too rare, when you just know that you've devised something special. If nothing else, it's proven to me that I'm getting the hang of the 2D nature of working in the complex plane, and specifically, how useful e can be.

I'm still a long way from owning the subject of complex analysis, but I'm slowly slowly getting there. As before, the two good assignment results have inspired me to up the pace a bit, and put more effort in. But I will have to wait until tomorrow before getting back to it, as I have a job due at 1am tonight. I should have done half of it yesterday (in fact I should have done a third of it on Friday, and another third yesterday), but we know how I work in that regard. Why do today what you can put of until tomorrow? And why do today and tomorrow what you can put off until the day after that, so you have to work all day to finish in time? That's me. 

Well, happy studying everyone!

Rushedicus Assessmenticus

What a week!

We went down to Portsmouth for a few days to make up for the fact that we didn't visit over Easter (it was right in the middle of Kim's exam period). Headed off at about seven Sunday morning, for the long, boring, not to mention expensive these days, drive. Caught up with friends for some drinks and pool, took our parents out for a joint meal for late Mother's Day / early Father's Day, even saw my brother for once, drove to Rhinefield House to try our wedding menu, and a whole lot more. I told the agencies that I was mostly unavailable, but that I'd still do my press conferences (third month now, and not the slightest bit easier!) except Wednesday and Thursday, when I had to do other stuff, including a 6000 word checking job. Not easy without a desk, pirched on the edge of the bed, using the back of an A4 pad on the duvet for the mouse. Just glad there were no internet problems to boot; I often find myself randomly disconnected by my parents' Sky router, or inexplicably unable to connect in the first place.

Oh yes, then there was M381 TMA 02 due in on the 9th. Somehow, I did manage to get it done, and posted it at about 1pm on the 8th; I hope it turned up on time. For the first time, I came this close to actually leaving a question out. All of Question 4 in fact was killing me. I bloody took an hour and a half on a two point question!? Even then I didn't think I'd got it right. There's something at least, that can be said for writing it up by hand, because I end up thinking it through almost as much second time around, and reckon I cracked that one in the end. Not the best ratio of time taken to progress made though, eh?

So, the question I almost left, well, of course I can't go into details, but it was of the form "use (a) to explain (b)". I couldn't actually see how the two were related. Not the best place to start trying to prove something from. I tried just getting down and writing in the hopes that one thing would lead to another and that up from the depths of my subconscious mind, a beautiful proof would spring. It didn't. As of about 11am on the 8th I still hadn't done it, but at least I'd written the rest up. So I said to myself I'd try for another hour, and then give up and go to the post office. Suddenly, inspiration hit. I'm not sure it's right, but it's a whole lot righter than nothing, right? Right. I felt naughty writing some of my final remarks though, as I knew that what I was saying was a bit vague and not fully justified, but I couldn't leave it that close to completion without tying it up. If I redeemed any points from that question, at least that last ditch effort would've been worth something. If I didn't, well, I won't' have lost anything. Confidence in my ability to prove things won't be affected, as it's basically zero anyway.

That said, there was a very interesting question on ISBNs. The numbers are actually based on congruence modulo 11. Who'd have thought!? So anyway, there were a couple of provey questions in that one too. And I'm fairly pleased with myself over the second one in particular. Coming up with a proof of your own, that at least appears to be right, is a great feeling. Especially when it's so rare, as it is in my case. The other week I was chuffed to bits over proving two things in M337 about Taylor Series as requested, taking a side of A4 on each, only to find that they were really five-or-so line proofs in the solutions sections. Still, I guess mine were right in their own way. It's a great feeling nevertheless. It puts me in mind of the scene in Good Will Hunting, where the teacher (Professor Lambeau?) is hitting on some girl, explaining to her how moving and beautiful a proof can be. I wonder if that has ever worked for anyone?

Oh yes, there were more URM-related questions, so I will assume the worst, and expect them to be very wrong. I think, finally, we're done with them now though. Time to celebrate, methinks.

Now, just as last time around, I'm left with a few days to finish the M337 TMA, and of course, have a job to juggle at the same time. The TMA is due on the 15th, the translation on the 16th. It's about 4800 words so I'm hoping to do 1600 a day for the next 3 days, then checking Tuesday, and rewriting into good English Wednesday. The topic sure doesn't look easy: nitrate contaminated groundwater. But at least they sent me a pretty detailed word list which will help. It's looking like I'll have a maths translation for the following week, which I'm quite looking forward to. As well, I'm eagerly anticipating being able to breathe again, with the M337 assignment out of the way. I think this one will not go well; there's just so many theorems at my disposal to potentially use, that I'm doubtful I'll get them right. Especially under the rushed conditions I've left myself, but who knows. Until I really start on it (at around seven tonight, all going to plan), I won't know.

I was worried that this will happen again next time; the TMA schedule so far has been roughly bimonthly, with the courses following one week after t'other. Well, exactly two months tomorrow I'll be getting married. I could really do without having get two TMAs out on consecutive weeks around that. Being busy will be bad enough, but then there's the lack of a desk, or any space in general, and the background noise of TV's and parents - really messes with my Zen thing, man. I didn't really even have anything to lean on this week (my poor M381 tutor has some seriously dodgy handwriting to deal with as a result).

Ultimately, I determined that I'd just take the financial hit, and cancel work for the week if there's a schedule conflict. Fortunately this is not so; both assignments are due the week before. But I'll have instead to contend with the fact that they're due in on consecutive days.

This time, I really must work through them as I study the material. I came close to doing it this time around. Sort of anyway. After about a month of the present cycle, I wrote out a schedule on my whiteboard, one question of each TMA alternating day by day, to get them all finished and written up with a few days to go before the respective deadlines. I should have known that'd be a waste of time, that I'd do it for two days, then forget about it (a glance at the whiteboard shows that I only did it for one day; there's a lonely tick next to day two's M337 question). I assume I thought, hey, I can always go back and do extra the following day right? I still kid myself that this is the right way to conduct myself, after doing it for work for almost four years. I guess I'll never learn. I do however, intend to learn to get TMAs done relatively early.

Whoa, that was a long post! Sorry about that, I got a bit carried away. Congratulations if you actually made it to the end.

Neil H

Tick tock tick tock

Hi all. Sorry for the long time between posts; for fear of sounding like a cracked record, it's because I am behind and would rather spend my time trying to catch up than writing about trying to catch up. That said, with almost two months passed since my last posting, I figured what's another half an hour and have opted to write a little.

As of tonight, or sometime tomorrow at the latest, I'll actually be on schedule with M381, but this is at the expense of M337, in which I am still a unit behind. I so desperately want to know how it feels to be ahead of schedule, but I am beginning to accept that this is not going to happen. Salvation lies in the fact that the final unit of mathematical logic is not TMA-assessed, and while I am aware there is a question on Godel's incompleteness theorems in the exam, I get the impression that you can still do well without tackling it. I do really want to understand them and the proofs (and to look rather clever when I ask someone to get me 'On Formally Undecidable Propositions in Principia Mathematica and Related Systems' for Christmas - as well as the new Pink Floyd box set :), but unless there's a miracle, I will settle for leisurely working my way through it after the course is done and dusted.

So how have I been finding it recently? Well, I still don't feel the love for number theory, although to say I actively dislike it would be an exaggeration. It is what it is. I'm happy to do the work, and am finding some of it to be quite lucid and clever, but at the same time, I could easily live without it. Logic on the other hand, I'm really getting into. But it is a lot of work. Take the proof in Unit ML 2, that the function p which enumerates the primes is primitive recursive: this involves showing that the characteristic function for Pr the set of prime numbers is primitive recursive, which itself involves showing the remainder function to be primitive recursive, the division function, and the characteristic function of the equality relation. Then we use the 'less than' relation, the exponentiation function, the new rule of 'bounded minimization' and god knows what else, covering around six pages of textbook, give or take detours via examples and problems. The gradual building up of all these pieces to prove the result is very very clever, but equally as heavy-going. The upshot is that ultimately this function is computable from just the basic primitive recursive functions of zero, successor and projection*. How anyone could do this is the first place is beyond me. To quote Ian Dury, there aint half been some clever bastards!

I've taken to developing my own short hand for working through this stuff. Any idea how many time's I've had to write 'primitive recursive' or plain old 'recursive' and the various permutations of these words with function, relation, set, etc? I don't! So I now use a little zig-zaggy squiggle for 'recursive' with a vertical line through it to make it primitive, then I can stick an F on the end for function, R for relation, and so on. I did something similar eventually for URM because although it's an abbreviation, I still felt that the amount I was writing it meant I was wasting a lot of time, so now lolly-pop-like spiral = URM, lolly-pop-like spiral with c on the end is URM-computable, and so on. Also, doesn't writing 'such that' start to get annoying after three years as well? You bet it does, so now it's a long horizontal line with an x in the middle. Sort of like this --x--.

Okay, that's enough for now. I'd really better get back to work. My comment on M337 therefore, must be brief: "It's going fine."

Happy studying!

P.S. On a totally unrelated note, I found out recently, that a book on Japanese volcanic earthquakes that I translated in summer 2009 has been officially released in Japan! It clearly won't have my name in it, and I bet it was heavily edited after I finished with it. But I hope to get a copy soon, as it is something tangible that I have achieved! That and I've not done anything else like it. (A Japanese friend from my Masters course in Bath said she'll pick it up for me and bring it over when she comes to my wedding this summer).

*As with the URM rules I mentioned previously, zero turns n into 0 and successor adds 1 to n. Projection functions basically pick out one from a number of variables in N-whatever, such as the second entry n2 from (n1, n2, n3).

It was worth it!

The weeks of catch up to make up my three week schedule deficit; the stresses of getting through the M381 TMA mentioned previously; the bashing my head against the wall to understand what the hell primitive recursion was; the all-nighter on Monday night to finish the M337 TMA*; not to mention the difficulty in fitting this around work (sure everyone does this, but it doesn't make it any easier)... it was worth it!

Distinction, in both cases! Woohoo.

This is a big deal to me. Bigger than in the previous courses, when to be honest, the first TMAs were usually a walk in the park. This time around, that certainly was not the case. I don't have a problem with hard assignments of course, but I like getting easy marks as much as the next guy!

As you may recall, I didn't think I had done so well in M381, but as it turned out, my result pipped the ninety mark. Unsurprisingly, my URM-related answers were awash with comments, but the bits around them on what the functions actually represent were okay. Overall, a great confidence boost for starters on Level 3.

My result in M337 was a bit lower, and only just got past the requisite 85 for distinction, but pass it did. There was no section where I did especially worse than others; my lost marks were spread almost uniformly throughout. It was the final question, on differentiation, partial derivatives and conformal functions which helped keep my mark up. Unexpected, considering I'd not got to conformality yet. I had already resigned myself to a very late night, so I didn't quite search just for the info needed. What I did was 'read' the final half of the unit rather than work through it. A big chunk, fortunately, was just the complex equivalent of the differentiation rules, composition et cetera.

I've been doing daily short translations recently. They are a section of the transcription of these daily press conferences the Chief Cabinet Secretary, Yukio Edano has been holding after the earthquake disaster and the trouble at the Fukushima Nuclear Power Plant. It's a nice regular job, but it is hard for me because of the 'talky' style.

Anyway, the press conferences have been cancelled this weekend. So for once, I am actually completely free! The good maths mood the TMA results have put me in should hopefully inspire me to get a lot of that done today and tomorrow. I'm still in the procrastination phase, but I'll get started soon. With some luck, I'll complete the catch-up process, as I'm still not quite there on either course. It should be do-able, but even if it's not, I'm nowhere near how far behind I was a month ago. I just need to keep it that way.

* It's been a bad week all in all for getting enough sleep. So I started with an all-nighter for work on Sunday night, getting to bed at 6am. This was followed by the TMA-related one, finishing at 7am. And then on Thursday night, I spent until 5am reading through Kim's dissertation, which I'd promised I would do on Thursday, but put off and put off because of work (which I didn't particularly want to do).

Always read the not-necessariy-small print

Okay, so I didn't catch up quite as easily as I had hoped I would.
Hence no posting for such a long time.

I spent most of the last week's run up to the deadline for the M381 TMA bemoaning the fact that it's deadline, 31st March, was a week before the fourth book, ML2 was due to be completed.
That's not fair, that's not fair! I was like a broken record. But soldier on I did, and excluding the Wednesday prior, when I spent the day in a narcoleptic haze of uncontrollable sleeping, I spent days solid on ML2 with the hopes of finishing it on Saturday and then starting on the TMA, giving me Sunday, Monday and Tuesday to get through it, and as I do it by hand, write it up.

I didn't finish by Saturday. In fact, I didn't finish Sunday either. That book is hard work! Specifically, the first twenty pages are hard work, which were on primitive recursiveness. So I opted to work until midday on Monday, then do as much of the TMA as I could, and finish the last few questions using the good ole, "find the relevant bit in the unstudied textbook at the same time as doing the TMA question" technique. This is something I swore I'd not do this year.

Glancing at the cover of the assessment booklet Monday lunchtime though, what did I spy?

Contents Cut-off date
TMA M381 01 31 March 2011
(Units 1 and 2 of NT, and Unit 1 of ML)

Bugger! I could have been working on the TMA since the previous Wednesday, as that bloody textbook wasn't even assessed yet!

Fortunately, with the exceptions of Question 4 (where you have three statements which you must prove if true, or find a counterexample otherwise), and the final question (on concatenating two URM* programs for functions f and g to make one that performs function h, by primitive recursion from the other two), it wasn't too hard. But those two took a lot of work. I did the rest and left them to finish on Tuesday.
Unfortunately, I had things to do that day, including sitting around doing nothing for the first half of the day, and then, when I started, a lot of time was wasted fiddling with the concatenation 'recipe' from the textbook to make sure I got it right... I don't think I did.

Then for some crazy reason I waited until 8pm before starting on Question 4.
I wont go into details, but I wasted the first 2-3 hours trying to prove something that was false. A bit more trial and error when all hope seemed lost and I found a relatively simple counterexample! What's wrong with me!? The other two weren't quite so bad, at least. I knew I'd have trouble with that question, as almost all the proving stuff examples and problems in the textbook had me checking the back of the book. Very annoying.

I'm dreading getting it back, as I doubt those two questions were right, and I should probably account for dropped points here and there, elsewhere too. On the plus side, my tutor told us at the tutorial that he would mark questions on URM programs based on whether they work rather than how efficient they are. Hopefully that stretches to completely unnecessary instructions that can never be executed. I found a random copy instruction in the middle of a program for another question when writing it all up on Wednesday morning before the mad dash to the post office. I know how it got there, but I couldn't get it to work by removing it. Very weird. Well, I won't miss URM programs when they're done and dusted, though I appreciate that they taught me something about computability. And I really liked the proof of the fact that the set of URM programs is countably infinite...as was given in the textbook I didn't need to have studied!

It was a nice surprise to suddenly get onto Cantor and infinite sets though. That is very cool stuff!

I'm now mere days from the deadline for M337. I haven't wasted time studying a textbook that's not assessed for another two months this time, but the delay caused by doing that last week has still left me trying to churn out a TMA in just two days. So why am I wasting my time posting? Actually, because I can't get any work done on it today anyway, as I have a job due in, which at this rate will keep me busy until 4am. I did about half of the TMA last night and this morning at least, but I'm also only half the way through the last unit assessed and will have to hunt for the relevant bits that I've not yet studied for the last question. I hate doing that...

The moral of the story therefore is to always read the not-necessarily-small print!
Right, back to work!

*For those that don't know, Unlimited Register Machines are theoretical 'computers' that use just four simple instructions to manipulate numbers stored in their registers, and thereby perform functions on the natural numbers: 'Successor' S(x) adds 1 to the number in register x; 'Zero' Z(x) replaces the number in register x with a 0; 'Jump' J(x,y,q) jumps to instruction q if the numbers in registers x and y are the same; and  'Copy' C(x,y) copies the number in register x to register y.

Overwhelming failure to make progress...

That's right, three weeks in and I'm already behind!!

I finished Unit A1 of M337 only a day or two after the schedule said I should have done, at least. As for M381 though, well, I'm still ten pages from the end of the first book! It's fairly sad to be behind so soon in. Especially considering I printed out the first two units way back in the autumn with the good intentions of getting ahead.

The timetable has me starting the third unit of each course next Friday so there's still time. However, I think I need a reassessment of how I'm going to approach the Open University this year, bearing in mind both the fact that it's level 3 now, and that I can probably assume work will continue to be busy throughout the year. After all, it has hardly let up since the start of November.

As a side note, can you believe I'm still waiting to be paid for some work I did way back then? Translation agencies have various payment schedules. One that I do the odd job for pays roughly 45 days after the end of the month following the month in which the work was completed. This is kind of harsh at the best of times, but the job in question was a long one that started in November and ended just after January started. That means I have to wait until 45 days after the end of this month (so mid-April) to get paid for all of it, including the work I completed right at the beginning! Madness.

Anyway, back on topic. It's looking like I've got nothing on over the weekend, so I have planned a hardcore catch-up session. Beginning tomorrow with the rest of Unit 1 of Number Theory, and maybe as a bit of revision, by redoing the Exercises at the end of Unit 1 of Complex Analysis. Then Saturday and Sunday's plan is to get past the half way mark in the second unit of each (which in M381's case is onto mathematical logic), which should put me roughly where I'm supposed to be. Ideally, I'd like to be slightly ahead, but as much as I love maths, I'd be surprised if I manage to do quite that much!

I'm quietly confident that I can get my head down and do the studying necessary at least. If nothing else, the amount of work I've had on recently has helped me learn to just get on and do something, and face the fact that it might mean long days and late nights. Last week for example, I had a friend coming to visit from Thursday to Saturday; we went to see the Sisters of Mercy at Leeds Metropolitan last Thursday, which coincidentally, is where my tutorials are (didn't stop me having a bitch of a time getting there in the car!). Anyway, to clear all the work due in over the period before and during his visit meant, a very busy week, culminating on the Wednesday with 9am right through to 3am (excluding dinner, dog walks etc.), then back up at 8am to start again on Thursday, and working right until his train arrived at 3pm.

Now, if I can just tap into some of that! Unfortunately, I don't have the fear of missing a deadline, never being given work by that agency again, and not being able to afford to eat or pay the bills!

Mandelbrot set on the Casio

Back when I was still at secondary school and my brother was at sixth form college, he showed me his graphing calculator which had been programmed to show the Mandelbrot set. My memory's a little hazy about the details, so it might not have been my brother, or his calculator, but anyway, a few years later when me and my friends were at college, and I was doing A-level Maths, this became something of a legend. Not that we knew what the Mandelbrot set was, just some pretty picture that you could zoom into over and over again. I doubt you could zoom on the Casio one, but still, we really wanted it on our calculators!

No-one thought I was lying (well I wasn't), but we never managed to find anyone that had the program, or could work out how to do it. Of course, that was the dark ages as far as the Internet was concerned. A quick search just now, and I immediately found a program someone had written for some Casio calculator or other. However, my poor old calculator never made it past the day of the final exam, well, it barely made it through the exam. Who's stupid idea was it to have a battery cover that you couldn't get through without a screwdriver.... or a knife, anyway?

I got my new phone last Friday. After literally months of not making calls following a mishap with the washing machine, I was finally due my upgrade from Orange. So I got an Android this time, and quickly got hold of a couple of free fractal viewing apps. I say quickly, but it took me over a day of messing around with the settings to get any of the downloads to actually get started (a common problem apparently, luckily I finally found a solution that worked). If I remember correctly, it took about an hour for the calculator to grind through the computations to draw the Mandelbrot set... now my phone does it in a flash, and lets me zoom too (one even lets me choose coordinates to draw Julia sets)! Not bad for free. I also downloaded a graphing calculator by the way, as the phone's built in calculator made the one in Windows look sophisticated (unlike my cheapy old Nokia which at least did the trigonometric functions, as well as e, log and so on).

So I've been having a bit of a fractal renaissance recently, probably inspired by starting M337. It's just so amazing how simple the rule behind the Mandelbrot and Julia sets is. I hope one day to do the OU's masters level course on fractal geometry. For the meantime, I've been playing around with the evaluation copy of the rather cool looking Ultra Fractal, reading bits and bobs, and of course, watching various YouTube videos of some the deep zooms and other cool animations people are making these days (try "Mandelbrot Fractal Adventure 1010011010" wow!).

Such a shame Benoit Mandelbrot passed away last year. I can't imagine how it feels to be a pioneer in a field like that. One day maybe... one day.

Awards, and the problem with maths in my school

I had a pleasant surprise on Monday, when I opened our mail box to find an A4-sized letter from the OU.

Tearing it open on my way over the road to buy a drink, I caught sight of a cheque. Curiouser and curiouser. Well, I assumed at first that I'd overpaid something; maybe the financing for my course last year had been miscalculated. Actually, after reading the accompanying letter, I found out I'd been presented the 'Leslie Walshaw Award' for M208...for getting the best results in the course for my region! The fifty pound cheque was my prize! Wow!

So now I have an excuse for putting up my scores, as I've generally refrained from doing so, worried that it was a bit big-headed. I got OCAS: 96 (after substitution and rounding) and OES: 96. This means I actually did better in my exam than the coursework, which is quite unexpected! I was pleased enough with my marks already, but the award was such a great bonus, and it's definitely going on my C.V. As it turns out from reading the forum CC-Maths and Computing, if I'd lived in Region 8 instead (of 7), I'd not have won it, as the man who got it there's marks were more like 98 and 100. But I'm in Region 7, and well, my result was apparently the best here!

Changing the subject completely, I remembered something about my school maths education that looking back, was completely stupid. Maybe things have changed now, as I left secondary in 1994, but I wouldn't be surprised if it's the same. The thing is, they never told me what pi was! They'd tell us to use pi r squared to find out the area of a circle, or 2 pi r for the circumference, they'd tell us how ancient civilisations already knew about pi, that various approximations had been used like 22/7, and that recently computers had worked it out to thousands or millions of places, but they never told me what it was! I think I even asked... well Neil, it's a number, approximately 3.14, that you can use to calculate the area of a circle. Yes, so you said, but what is it!? What were people trying work it out to greater and greater accuracy? And also, how'd they know they were getting closer? What were they trying to get closer to? Well of course the answer is simply that pi is the ratio between the diameter of a circle and its circumference. Straighten out the circumference of a circle and you get 3.14... diameters. Why'd they never say that? Instantly, the relation 2 pi r makes perfect sense (2r being equal to the diameter). And while the other relations are not as instantly obvious, it is blatantly clear why pi is involved in all these equations relating to circle-related things.

I've just finished reading Surely You're Joking, Mr. Feynman, and I'm convinced Richard Feynman would have had issues with this too; it's simply not the right way to teach (in fact it resembles his story about his cousin learning algebra, in the Horizon interview). They should be teaching maths, not teaching processes. Unless you have an understanding of what you're doing, unless you can anchor it to some relevant fact, you're going to find it harder to learn.

I give you the example of pi (again). A few summers ago, I learnt pi up to fifty decimal places (and e but I've since forgotten that back to 32 places), my plan was to get them to 100, but I eventually fizzled out. Anyway, while it only took a few days, it was hard. This is because it was just a meaningless string of unrelated numbers. For comparison, think of how easy is it to learn a song with fifty words? Well that's what, ten lines!? Easy. Because the words are related. They form full sentences, and make a narrative. And don't forget, while each of the numbers to memorise in pi is just a 0-9, each of the words in the song can be drawn from thousands of choices (okay okay, so certain words have to go together, verbs might follow nouns and so on. But, I think this hardly counteracts the fact that there are so many words compared to just 10 numbers). The first time they introduce pi, they should tell you what it is. Learning what you can do with it would follow logically.

Books arrived at last. Huzzah!

On Thursday, my M381 materials arrived. I went through the checklist and it was all there. But, apparently, I'm not allowed a study timetable; I have to get that from the course website when it opens on Monday. So it left me wondering what topic am I supposed to start with, Number Theory or Logic. I get the impression that you're supposed to begin on Number Theory, but I'll be interested to see what it has to say on Monday. Do I alternate one unit of each, or do I study right through one topic, then start on the other. Crucial questions, I'm sure you'll agree.

Then on Friday, M337 arrived. In fact, the whole course turned up rather than just the first half, which is quite unusual. I pointed out to the delivery man, that I'd only just met him the day before and made some joke about how it was strange that the Open University, full of presumably pretty clever people, didn't have the common sense to send the courses materials for a particular person, all together. He didn't seem to find it that amusing, and nor did Kim in the other room (unlike my long chat with the Mormons about prayer, setting my arm on fire, and alien death rays last year), but I thought it was funny anyway.

So, I tore into the M337 box, checked the contents off against the checklist, and again there was no timetable. Not that it matters so much with this course (if you cant work out the order from unit A1 to D3, the subject of complex analysis might be a little beyond you), but I still want to put it up on the wall, and start thinking about a program of study.

I flicked through the M337 books, almost immediately drawn (as most people that know me, wouldn't be surprised to find) to the chapter on the Mandelbrot set. Damn, I have to wait until the end of the course basically to get to that. Oh well. As for the rest of it, well first impressions are that it looks bloody hard! Looking back though, I probably thought the same with M208, and I even recall an acute sense of fear, when I first glanced at the MS221 handbook at the listed of all the symbols and notation I was expected to be familiar with by the end of the course. I expect it's always pretty scary at first. So I'm not that worried, just do the work and it should be fine.

Unfortunately, it's looking like I'll actually have to make the effort and 'learn' the epsilon-delta definition of continuity after all. I totally fudged my way through that last year, and hoped that any question on it would be relegated to an optional one in Part 2 of the exam (which it was)!

Which reminds me, when I looked at the statistics for the M208 exam, I thought it was rather strange to see that 185 people opted to take that question, Q17, making it the second most popular choice for Part 2 (if you ignore the total piece of cake that was Q13 on Groups, that understandably, roughly 4/5 of all students took). Yet it has easily the highest rate of people getting just 0-14%, as many as 19% of them, the next worst was way down at 11%.

An unscientific overview of all the scores here suggested that only Q14 resulted in overall worse results. Why'd they all choose it then? Maybe they thought they couldn't go wrong with graph sketching, who knows. As for me, well, I saw that epsilon delta question and instantly kept my distance. (For the record I took Q13 (it was effectively free points afterall), and Q15 on convergence and least upper bounds, which was pretty straightforward).

How things can change in four years

This time four years ago, I would have been right in the middle of my group project at Bath. It consisted of two very long translations (by the standards of a student), one Japanese to English, a business news article, and one English to Japanese, a catalogue of electronic components. My group (consisting, I think, of Chiharu, Yumi, Rina, Chiho and me) were spending all day, every day, at the (very empty) library, sat around with our laptops, carefully going over every single one of the 20,000 words in each document. As with the rest of the time doing my Masters, I was working really hard. I was focused, studious, and although ultimately not very good, absolutely determined to do my best.

Excluding a few years off while I worked at the Inland Revenue and dabbled with the idea of accounting (which if nothing else at least put me in good shape to do my Tax Return), this is how it had been for a decade. I wanted one thing, to be better at Japanese, and I really applied myself at getting there. Then, within a year of finally landing my dream job of freelance translator, I was no longer studying it, and have not done since my last exam at Bath.

Two things happened really. Firstly, within a couple of months of working with Japanese, I realised that I'd probably learnt more, and become more fluent with it than in all of the previous decade put together (maybe an exaggeration, but it certainly felt that way). There was no longer any need to study! As it turned out, working was more effective a form of study, than studying ever was. I guess it continues to be, as I'm infinitely better now than I was a few years ago.... which makes me wonder how I ever got paid to do this back then, but anyway.

The other was receiving £25 in Amazon vouchers for my birthday in 2008. I bought Revelation Space by Alastair Reynolds, The New Space Opera (a space opera short story anthology), and The Fabric of the Cosmos, by American physics populariser, Brian Greene. The last of these, I read in about three days. It was fascinating! I didn’t really get along with the Simpsons and Mulder and Scully stories framing the various effects of modern physics, but nevertheless it was un-put-downable. I was hooked, and just had to learn more! Well, within a few weeks I was signed up for the BSc in Physical Science at the Open University, and studying the short courses S194: Introducing astronomy, S196: Planets: an introduction and S197: How the Universe works. Introductory stuff all round, and pretty easy, but a nice way into things. These short courses however, all firmly in the realms of physics and astronomy, served a useful purpose in showing me that I really wanted to study maths. It was while performing a rather straightforward bit of algebraic manipulation for the end of course assessment of S194 that I thought to myself, I’m actually enjoying this more than the physical laws and other stuff. A few days of umming and ahhing, followed by a quick phone call to a helpful lady at the OU, and I was registered to the BA/BSc in Mathematics. Which is where I’ve been since, and where I guess I will be for four years more!

My Mum often tells people that I’m never happy unless I’m learning something. I think the evidence is pretty hard to reject.

Joining the OU blog club

Hello and welcome!

I've spent the last two and a half years studying maths mostly on my own. I made it to the tutorials for MST121 which conveniently were just down the road, and to a few for MS221 and M208 over in Leeds. But generally, it's been a very solitary game. I don't mind of course; I like to work on my own. If I didn't, then becoming self-employed and working at home would not have been the best career move.

However, after dabbling with the fora for a while, I started last year, spending time reading OU blogs by people variously doing the same courses as me, or closely related subjects like physics and computing. I realised that it's nice to see what other people think about these courses, to read how they did on the exams, and to learn how the OU student mind ticks in general. Not to mention, how motivating it can be to read  the comments of someone a few weeks further along through the schedule! Anyway, as a result, I decided to join the club.

I'm not convinced I'll have a lot of interest to write. But I'm certainly passionate about the topic, and can happily talk about it all day (and argue - as my future-father-in-law found out at Christmas). That is however, once I get started! Both my work and study suffer a great deal from my inability to get going in the first place. Once I am started, fine, but it usually takes me hours to get that far. I tend to get up bright and early (actually I have to, as I have emails from the other side of the planet and an 8-9 hour time difference to contend with), but rarely do I manage to begin work before twelve. It probably sounds quite nice if you're a nine-to-fiver, and it would be, if it didn't mean working late to compensate. For instance, I often also think "Oh look, I can have today off, as long as I do twice as long tomorrow, and stay up until 4am to meet my deadline". Crazy! I've not bothered to set a New Year's resolution to fix these problems, as I know I won't do so!

So where am I now? Well, I'm currently waiting for my course books for this year to turn up: M337 Complex Analysis and M381 Number Theory and Mathematical Logic. (Last year's first delivery had long since arrived by now!) After my M208 exam, I printed out the first few modules of the new courses in A5, using the neat 'Print as Booklet' feature on our printer. Shortly after I did though, a huge amount of work turned up (which, to be fair, I desperately needed what with tax due at the end of this month), and managed just a few pages of each. I'm also slowly working my way through Euclid's Elements, having received a very nice hardback version containing all 13 books at Christmas.

I'm ready to go basically. My stationary is bought, my new blackboard (2xA0) is up, my desk is even moderately tidy. Maybe in two or three hours, I'll even get started again on the intro to M337 Unit A1!
Hopefully by the next time I post, I'll have actually done something!