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!