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.