Sunday, 1 July 2012
H U
Well, I've put in some time with varying the blog content, so I think I can get away with a classic course-related post "without loss of generality" (to sound all topological). I'll have to keep it short as I'm in the middle of an indescribably boring translation about railway crossings, that is due in at 1am. I'm a bit behind schedule (when am I ever not behind...on anything?), so it is looking like this it will be an all-day affair (again!) :(
Anyways, I got back M336 TMA02 about two weeks ago: 100%! Or "HU" as they seem to call it. A heads up on what that stands for would be gladly welcomed. I felt somewhat vindicated to get that 100%, when I robbed myself of full marks last time by not copying out one of the answers properly.
And yesterday, after waiting a fortnight and beginning to worry that it hadn't arrived to my tutor, I got back M338 TMA03. HU again! Oh my god. I couldn't believe it. I mean, I thought I had all the right answers, but I always drop marks somewhere, and the full justification requested in the final question had me sure I'd missed something. Apparently not though.
Kim played a trick on me; as I think I mentioned before, she opens it for me if I'm worried for whatever reason. Well, I wasn't worried, but she was there and offered to open it for me. So I passed it across, and she opened it and for a moment looked concerned and confused, "hmmmm". After a while...
Kim: Oh I see....
Me: Huh? What do you see!?
Kim: ...because I can see the marks for the individual sections, but there's no overall mark! (smiles)
Me: It's HU!!!?
Kim: I hate you!
I haven't had 100% since TMA04 of MST121, which was totally undeserved, because I couldn't be bothered to study that block due to my aversion to all things statsy, and just hunted for the relevant parts to the assignment. Rather naughty for sure, but I was in my overlap with MS221 by then and was involved in much more interesting maths at that end. However, I then ended up with two hundreds in the space of a few weeks.
These results will be very useful. The M336 ones so far have given me a large buffer to work with (and alleviate a little of the fear I felt when I opened Unit GR3 only to notice I didn't understand anything on the first two pages - looks like I need to revise a bit before tackling it). And the M338 mark has balanced out my lower mark for TMA02, where I didn't manage to answer all the questions.
I say this to myself every time a good result comes back (or when a bad one comes back come to think of it), but I'm hoping this will incentivise me to start working harder. I don't make good use of my free time, especially when I have the house to myself when Kim's at work and I could potentially do many uninterrupted hours of study. So I need to sort that out. My mindset at the moment is that I'm ready and looking forward to working harder from now on, which means from tomorrow because of this job I'm doing. Hopefully, this time, I'll actually manage to fight my innate laziness and do it.
Neil H
Friday, 22 June 2012
Lots of little triangles
As if talking my dear wifey into letting us have Mobius strip wedding rings wasn't already taking things too far, I got my very first tattoo on Monday. And it's a maths one! Hooray!
I've long wanted a fractal tattoo, and for a time was interested in the Mandelbrot set or something like that, but eventually decided that I wanted one that was more geometricky. The Sierpinski triangle was the winner, as of all of the classic fractals, I find it to be particularly attractive. It is also very easy to explain to people if needs be.
Furthermore, I found many examples of Mandelbrot and Julia set tattoos, but only a couple of Sierpinski triangles online: one to one less iteration than mine, and a large one that is very cool and spans both forearms. There must be many more out there, but I would imagine the relative rareness online is reflected in the real world, so I can be sure of something fairly unique to me.
Actually, the picture was taken from Unit C5 of M338 Topology. I downloaded the PDF version, zoomed it as big as I was allowed, then print-screened, pasted, cropped, and printed. As for the size, this was just what I got when choosing the 4 copies per A4 option in Windows.
I took down a smaller print (9 per A4 size) on Saturday, and asked about it in the very professional 'The Bleeding Art' in Huddersfield town centre. They were pretty positive, but told me that with that much detail (if you think about it, there are 81 small black triangles, after this many iterations), it should be a bit bigger. There was no specific reason for the size I'd taken in anyway. Fortunately, the size mentioned above turned out to be more-or-less perfect.
When we went down on Saturday, it was actually for Kim's benefit. She's been after a realistic tattoo around her wrist of the Morning Glory plant, with the vine winding around, and a few of the (blue) flowers in bloom. I never really knew about this realistic style, so was amazed at some of the examples they have on display, and showed on the computer. She gave them some photos, and they will make up the design in time for her appointment in a few weeks (there is a waiting list for the guy that does these kinds of ones). It was only really an incidental thing, that I would ask about mine too. But here I am a few days later with a big triangle on my arm!
I was done as a "walk in." You turn up in the morning, and on a first-come-first-served basis, they allocate you a time slot during the day. I was scheduled for 3.30pm, but the lady having Pingu on her leg overran somewhat, so I got started shortly after 4. One of the staff had made my stencil on the computer earlier in the day, based on the larger print out; his version was better than mine as it had gone a bit blocky with the zooming. Anyway, it was all done and filled in by about 5.50pm, and I was on my way home. Not bad at all!
I'm really happy with it, and I've been keeping up well with the after care. I am wondering what I should go for, if I do that is, next time. One idea I had was the inverse of this design on my other arm in the same place. It think that would look good.
Neil H
I've long wanted a fractal tattoo, and for a time was interested in the Mandelbrot set or something like that, but eventually decided that I wanted one that was more geometricky. The Sierpinski triangle was the winner, as of all of the classic fractals, I find it to be particularly attractive. It is also very easy to explain to people if needs be.
Furthermore, I found many examples of Mandelbrot and Julia set tattoos, but only a couple of Sierpinski triangles online: one to one less iteration than mine, and a large one that is very cool and spans both forearms. There must be many more out there, but I would imagine the relative rareness online is reflected in the real world, so I can be sure of something fairly unique to me.
Actually, the picture was taken from Unit C5 of M338 Topology. I downloaded the PDF version, zoomed it as big as I was allowed, then print-screened, pasted, cropped, and printed. As for the size, this was just what I got when choosing the 4 copies per A4 option in Windows.
I took down a smaller print (9 per A4 size) on Saturday, and asked about it in the very professional 'The Bleeding Art' in Huddersfield town centre. They were pretty positive, but told me that with that much detail (if you think about it, there are 81 small black triangles, after this many iterations), it should be a bit bigger. There was no specific reason for the size I'd taken in anyway. Fortunately, the size mentioned above turned out to be more-or-less perfect.
When we went down on Saturday, it was actually for Kim's benefit. She's been after a realistic tattoo around her wrist of the Morning Glory plant, with the vine winding around, and a few of the (blue) flowers in bloom. I never really knew about this realistic style, so was amazed at some of the examples they have on display, and showed on the computer. She gave them some photos, and they will make up the design in time for her appointment in a few weeks (there is a waiting list for the guy that does these kinds of ones). It was only really an incidental thing, that I would ask about mine too. But here I am a few days later with a big triangle on my arm!
I was done as a "walk in." You turn up in the morning, and on a first-come-first-served basis, they allocate you a time slot during the day. I was scheduled for 3.30pm, but the lady having Pingu on her leg overran somewhat, so I got started shortly after 4. One of the staff had made my stencil on the computer earlier in the day, based on the larger print out; his version was better than mine as it had gone a bit blocky with the zooming. Anyway, it was all done and filled in by about 5.50pm, and I was on my way home. Not bad at all!
I'm really happy with it, and I've been keeping up well with the after care. I am wondering what I should go for, if I do that is, next time. One idea I had was the inverse of this design on my other arm in the same place. It think that would look good.
Neil H
Saturday, 16 June 2012
Pi equals 3.0226
Okay, it doesn't, but I just finally did an experiment that I read about years ago when doing a translation on Monte Carlo approximation.
You may know it, but still, it involves drawing a circle inside a square with sides equal to the circle's diameter. Then, by some random method, you put points on the circle-in-square and work out the ratio of points on the circle to points on the square, and thereby approximate pi.
Here are photos of my effort, in which I dropped grains of rice, and then (quite laboriously) counted them. I counted those outside first, then those inside. There were 227 grains outside of the circle, and 702 inside. This gave me 929 grains on the square and 702 on the circle. I had to make a judgement when they were on the line, but just went with the obvious choice of inside the circle if more of the grain is inside, and outside otherwise.
For what it's worth, the radius of the circle was 4", and so the sides of the square were 8". However, I treated them as being of unit length. Hence, the area of the square was 4 and the area of the circle was pi.
The ratio therefore was pi/4, and the ratio from the rice-approximation was 702/929, which to 5 d.p. is 0.75565. Times 4 and we get pi roughly equal to 3.0226.
It may not be that close (I was hoping for something that would round to 3.1 at least), but for what it's worth, if 28 of those that ended up in the square only had ended up in the circle, we'd have got (730/929) x 4 = 3.14316, which is pretty close.
In the hopes of getting a bit closer, I also checked the weights and got 14.85g for the square and 11.15g for the circle. This got me an approximation of pi (to 5 d.p.) of 3.00363. Oh hang on, I shouldn't be going to more decimal places than there are in the input values, should I? So actually, this just gets pi = 3. Oh well.
So there we have it. Another way of wasting time on a Saturday afternoon that should be spent studying. At least it's maths though.
You may know it, but still, it involves drawing a circle inside a square with sides equal to the circle's diameter. Then, by some random method, you put points on the circle-in-square and work out the ratio of points on the circle to points on the square, and thereby approximate pi.
Here are photos of my effort, in which I dropped grains of rice, and then (quite laboriously) counted them. I counted those outside first, then those inside. There were 227 grains outside of the circle, and 702 inside. This gave me 929 grains on the square and 702 on the circle. I had to make a judgement when they were on the line, but just went with the obvious choice of inside the circle if more of the grain is inside, and outside otherwise.
For what it's worth, the radius of the circle was 4", and so the sides of the square were 8". However, I treated them as being of unit length. Hence, the area of the square was 4 and the area of the circle was pi.
The ratio therefore was pi/4, and the ratio from the rice-approximation was 702/929, which to 5 d.p. is 0.75565. Times 4 and we get pi roughly equal to 3.0226.
It may not be that close (I was hoping for something that would round to 3.1 at least), but for what it's worth, if 28 of those that ended up in the square only had ended up in the circle, we'd have got (730/929) x 4 = 3.14316, which is pretty close.
In the hopes of getting a bit closer, I also checked the weights and got 14.85g for the square and 11.15g for the circle. This got me an approximation of pi (to 5 d.p.) of 3.00363. Oh hang on, I shouldn't be going to more decimal places than there are in the input values, should I? So actually, this just gets pi = 3. Oh well.
So there we have it. Another way of wasting time on a Saturday afternoon that should be spent studying. At least it's maths though.
Tuesday, 12 June 2012
The Turing Solution
Hi all,
I just heard advertised on Radio 4, a programme that might be of interest to those of the mathematical persuasion.
At 11:00am this morning is The Turing Solution, a half-hour show about the life and work of the great Alan Turing. It will be presented by someone described as "standup mathematician Matt Parker." Never heard of him myself, but regardless, the programme should be worth a listen. Coincidentally, I just last week, started thinking back to M381, and was pleasantly surprised that I could still generate URM programs for basic things like multiply and divide two numbers. Not particularly impressive, I know, but proof that I actually took something in of that course. If it weren't for the fact that the autumn start of MST209 will mean I don't have a break this time, I would be interested in going back through the logic part of that course without the distractions of number theory.
In other news, I was disappointed (but not surprised) to see that Radio 4 have not included Andrew Wiles among their list of "New Elizabethans" despite what I thought to be an articulate and well-argued suggestion. Oh well.
Right, bed time!
Neil
I just heard advertised on Radio 4, a programme that might be of interest to those of the mathematical persuasion.
At 11:00am this morning is The Turing Solution, a half-hour show about the life and work of the great Alan Turing. It will be presented by someone described as "standup mathematician Matt Parker." Never heard of him myself, but regardless, the programme should be worth a listen. Coincidentally, I just last week, started thinking back to M381, and was pleasantly surprised that I could still generate URM programs for basic things like multiply and divide two numbers. Not particularly impressive, I know, but proof that I actually took something in of that course. If it weren't for the fact that the autumn start of MST209 will mean I don't have a break this time, I would be interested in going back through the logic part of that course without the distractions of number theory.
In other news, I was disappointed (but not surprised) to see that Radio 4 have not included Andrew Wiles among their list of "New Elizabethans" despite what I thought to be an articulate and well-argued suggestion. Oh well.
Right, bed time!
Neil
Sunday, 13 May 2012
Metrics
Hi. I wanted to avoid making this blog become little more than the diary of an ever-repeating cycle: I got behind schedule; I had a TMA due in and stayed up all night to finish; I got the results back. That certainly seems to be the way it's been going recently, so I have decided this time, to talk about some of the actual maths we've been up to lately, namely 'metrics'.
Why metrics you may ask if you're familiar with them. What are metrics you may ask if you're not. Good questions. The easy answer to the first is that I quite enjoyed them. The easy answer to the second is below. (It should probably be noted here, that I don't have the books with me, so I'm likely to make some mistakes...)
Metrics are a generalisation of the concept of distance between two points, that satisfy three axioms:
(M1) d(a, b) ≥ 0 with equality if and only if a = b.
(M2) d(a, b) = d(b, a)
(M3) d(a, c) ≤ d(a, b) + d(b, c)
So basically, and also quite obviously, the distance between two points a and b is always non-negative, and is 0 only if the points are in the same place. The distance from a and b is the same as from b to a. And yes, (M3) is our old friend the Triangle Inequality. The direct distance between two points a and c, is not more than it would be via a third point b.
Metrics have been my favourite part of the topology course thus far. To begin with, even within the highly abstract realm of topology, metrics have a very easy to grasp real-world basis, since after all, we talk in terms of distance all the time (as it goes, the basic distance we use is the 'Euclidian metric'). One of the first different ones presented in the text is the 'taxicab metric' (e1(a,b) = |b1 – a1| + |b2 – a2|, the sum of the horizontal and vertical distances between a and b), which gives us the distance a taxi would travel to get from a to b in a city based on a block design, where roads only run in two perpendicular directions. Indeed, without knowing, we all use such an alternate measure of distance (albeit one that's a bit harder to define than the taxicab metric) which is the distance between two places via the roads. So the concept of different definitions of distance is really not all that alien.
With a particular metric, one can define an open ball Bd(a, r), which is the set of all points with distance less than r (the radius) from point a, a sphere Sd(a, r), which is the set of points with distance r from point a, and a closed ball Bd[a, r], which is the set of points with distance less than or equal to r from point a. Or, simply the union of the open ball and sphere. In two and three dimensions, things are pretty intuitive; in the plane, these are a disc, circle, and disc with boundary respectively, which fits nicely with our idea of balls and spheres as being round; in 3D, it can be pictured as something like the air inside a (round) balloon, the rubber of the balloon as the sphere, and then both together as the closed ball. Take it down to one dimension, on the real line, and things are not so round. The sphere is just two points, a – r and a + r, but it makes sense considering the definition, because they're the only points with distance exactly r from point a. Well that was all with the Euclidian metric. But what about other metrics? Well, the definitions work just as well when we have another type of distance, another metric. With the taxicab metric, for example, balls and spheres end up as squares rotated by pi over 4. Squares balanced on a corner. And on it goes, getting less and less ball-like as we take less familiar metrics.
Which is the charming thing about metrics, the weirdness of abstraction: take for example, distances between infinite sequences of 1s and 0s, or distances between functions! Not something the average human considers on a daily basis, true, but defined appropriately, they can be shown to satisfy (M1) to (M3) and therefore qualify as metrics. If memory serves, the distance between infinite sequences of 1s and 0s was something like: given two such sequences a and b, then d(a, b) = 2-n, where n is the number of the position where they first differ. So if a = 1,1,1,0,1,0,0,0..... and b = 1,1,1,1,1,0,0,0....., then they first differ at the 4th place, so their distance apart is 2-4 = 0.0625. (Is that right? I can't remember, but it's something along those lines anyway).
I'm starting to drone on a bit, but I wanted at least, to mention the thing that first made me ponder writing about metrics, and that was the interesting one we encountered recently, namely the 'vine-picker's metric', which was in our recent TMA. I figure it was long enough ago that it's not a problem to discuss it, and anyway, I'm not going to go any further into the question than the info on the assignment booklet. A week or so after the TMA was done, I cleaned some space on my blackboard and had a little play with the vine-picker's metric. It is defined as:
d(x, y) = |x1 – y1| if x2 = y2, or |x1| + |x2 – y2| + |y1| if x2 ≠ y2.
Below is a photo of my blackboard. On the left is the rule and graph, and on the right is some vine-picker distances worked out for points on the graph.
So, we end up with a situation that's as if there is something stopping you from moving in the up-down direction, unless you are above the origin, like there are impenetrable grape vines blocking your way, and the only gap between them runs vertically through the origin (for the record, my diagram simplifies it somewhat; in this case the points have integer coordinates, so the vines could be drawn in). To travel from one point to another in vine-picker metric terms, you therefore have two cases: if the points are at the same "height", (x2 = y2), you just go directly horizontal, but if they're not at the same "height" (x2 ≠ y2), then you must walk horizontally to the axis, then up (or down) to the appropriate height, and then back out to the second point. The example on the blackboard demonstrates d((2, 3), (8, 3)) = 6 and d((5, 1), (3, 5)) = 12.
Of course, the vine-picker's metric satisfies (M1) to (M3). We had to prove some stuff about it in the TMA.
Anyway, that's metrics. Very cool indeed. It's only Unit A2 of Topology, so there's clearly plenty more fun where that came from. For what it's worth, it was the surfaces and shapes side of topology that I was really looking forward to (surely that was the case for most of us?). However, since I've been going back through (or indeed simply "through" in certain cases) and more carefully learning block A, I'm beginning to really enjoy the point-set variety.
Why metrics you may ask if you're familiar with them. What are metrics you may ask if you're not. Good questions. The easy answer to the first is that I quite enjoyed them. The easy answer to the second is below. (It should probably be noted here, that I don't have the books with me, so I'm likely to make some mistakes...)
Metrics are a generalisation of the concept of distance between two points, that satisfy three axioms:
(M1) d(a, b) ≥ 0 with equality if and only if a = b.
(M2) d(a, b) = d(b, a)
(M3) d(a, c) ≤ d(a, b) + d(b, c)
So basically, and also quite obviously, the distance between two points a and b is always non-negative, and is 0 only if the points are in the same place. The distance from a and b is the same as from b to a. And yes, (M3) is our old friend the Triangle Inequality. The direct distance between two points a and c, is not more than it would be via a third point b.
Metrics have been my favourite part of the topology course thus far. To begin with, even within the highly abstract realm of topology, metrics have a very easy to grasp real-world basis, since after all, we talk in terms of distance all the time (as it goes, the basic distance we use is the 'Euclidian metric'). One of the first different ones presented in the text is the 'taxicab metric' (e1(a,b) = |b1 – a1| + |b2 – a2|, the sum of the horizontal and vertical distances between a and b), which gives us the distance a taxi would travel to get from a to b in a city based on a block design, where roads only run in two perpendicular directions. Indeed, without knowing, we all use such an alternate measure of distance (albeit one that's a bit harder to define than the taxicab metric) which is the distance between two places via the roads. So the concept of different definitions of distance is really not all that alien.
With a particular metric, one can define an open ball Bd(a, r), which is the set of all points with distance less than r (the radius) from point a, a sphere Sd(a, r), which is the set of points with distance r from point a, and a closed ball Bd[a, r], which is the set of points with distance less than or equal to r from point a. Or, simply the union of the open ball and sphere. In two and three dimensions, things are pretty intuitive; in the plane, these are a disc, circle, and disc with boundary respectively, which fits nicely with our idea of balls and spheres as being round; in 3D, it can be pictured as something like the air inside a (round) balloon, the rubber of the balloon as the sphere, and then both together as the closed ball. Take it down to one dimension, on the real line, and things are not so round. The sphere is just two points, a – r and a + r, but it makes sense considering the definition, because they're the only points with distance exactly r from point a. Well that was all with the Euclidian metric. But what about other metrics? Well, the definitions work just as well when we have another type of distance, another metric. With the taxicab metric, for example, balls and spheres end up as squares rotated by pi over 4. Squares balanced on a corner. And on it goes, getting less and less ball-like as we take less familiar metrics.
Which is the charming thing about metrics, the weirdness of abstraction: take for example, distances between infinite sequences of 1s and 0s, or distances between functions! Not something the average human considers on a daily basis, true, but defined appropriately, they can be shown to satisfy (M1) to (M3) and therefore qualify as metrics. If memory serves, the distance between infinite sequences of 1s and 0s was something like: given two such sequences a and b, then d(a, b) = 2-n, where n is the number of the position where they first differ. So if a = 1,1,1,0,1,0,0,0..... and b = 1,1,1,1,1,0,0,0....., then they first differ at the 4th place, so their distance apart is 2-4 = 0.0625. (Is that right? I can't remember, but it's something along those lines anyway).
I'm starting to drone on a bit, but I wanted at least, to mention the thing that first made me ponder writing about metrics, and that was the interesting one we encountered recently, namely the 'vine-picker's metric', which was in our recent TMA. I figure it was long enough ago that it's not a problem to discuss it, and anyway, I'm not going to go any further into the question than the info on the assignment booklet. A week or so after the TMA was done, I cleaned some space on my blackboard and had a little play with the vine-picker's metric. It is defined as:
d(x, y) = |x1 – y1| if x2 = y2, or |x1| + |x2 – y2| + |y1| if x2 ≠ y2.
Below is a photo of my blackboard. On the left is the rule and graph, and on the right is some vine-picker distances worked out for points on the graph.
So, we end up with a situation that's as if there is something stopping you from moving in the up-down direction, unless you are above the origin, like there are impenetrable grape vines blocking your way, and the only gap between them runs vertically through the origin (for the record, my diagram simplifies it somewhat; in this case the points have integer coordinates, so the vines could be drawn in). To travel from one point to another in vine-picker metric terms, you therefore have two cases: if the points are at the same "height", (x2 = y2), you just go directly horizontal, but if they're not at the same "height" (x2 ≠ y2), then you must walk horizontally to the axis, then up (or down) to the appropriate height, and then back out to the second point. The example on the blackboard demonstrates d((2, 3), (8, 3)) = 6 and d((5, 1), (3, 5)) = 12.
Of course, the vine-picker's metric satisfies (M1) to (M3). We had to prove some stuff about it in the TMA.
Anyway, that's metrics. Very cool indeed. It's only Unit A2 of Topology, so there's clearly plenty more fun where that came from. For what it's worth, it was the surfaces and shapes side of topology that I was really looking forward to (surely that was the case for most of us?). However, since I've been going back through (or indeed simply "through" in certain cases) and more carefully learning block A, I'm beginning to really enjoy the point-set variety.
Thursday, 10 May 2012
In Our Time
I've been listening to Radio 4 for more than 5 years now, and (despite loving I'm Sorry I Haven't a A Clue, Laura Solon's Talking and Not Talking and various other 6.30-slot comedies) my favourite program remains In Our Time with Melvyn Bragg. Little can make you feel as sophisticated and intelligent as listening to Baron Bragg and his distinguished academic guests discussing the fall of Carthage, the Observatory at Jaipur, Schopenhauer, or some other deep topic.
Anyway, every now and then, we get treated to a maths topic for 45 minutes, usually involving Ian Stewart and Marcus Du Sautoy. I've heard discussions on Godel, infinity, the Calculus, the Poincare Conjecture, pi and many more subjects In My Time :)
After what seems to have been forever (though I could easily have missed some without noticing), it was a mathsy topic again this morning, namely Game Theory. I'm not overly interested in Game Theory myself, but it was entertaining enough, and gave me something to listen to while doing the washing up and tidying the kitchen. Ian Stewart was there as anticipated, and was as brilliant as ever. I'm quite an Ian Stewart fan for what it's worth. I made the (blindingly obvious) prediction to Kim, that John Nash would get a mention, and lo, at 18 past 9, he did. Other stars included von Neumann, and a tramp.
If anyone's interested, a cut-down-to-thirty-minutes version is usually repeated at 9.30pm tonight. It's also available on the Radio 4 website, as are all the episodes of In Our Time since 1998. Actually, I got rather good at Minesweeper a few years ago when I played it to keep myself visually stimulated (I tend to drop off eventually if the only thing I am doing is listening to something) while going through all the science and maths ones that caught my eye... and there were quite a few. I'm not very cultured, so I didn't bother with the art, philosophy, religion, &c, but I do listen to them if they're "live."
More maths please Melvyn!
Anyway, every now and then, we get treated to a maths topic for 45 minutes, usually involving Ian Stewart and Marcus Du Sautoy. I've heard discussions on Godel, infinity, the Calculus, the Poincare Conjecture, pi and many more subjects In My Time :)
After what seems to have been forever (though I could easily have missed some without noticing), it was a mathsy topic again this morning, namely Game Theory. I'm not overly interested in Game Theory myself, but it was entertaining enough, and gave me something to listen to while doing the washing up and tidying the kitchen. Ian Stewart was there as anticipated, and was as brilliant as ever. I'm quite an Ian Stewart fan for what it's worth. I made the (blindingly obvious) prediction to Kim, that John Nash would get a mention, and lo, at 18 past 9, he did. Other stars included von Neumann, and a tramp.
If anyone's interested, a cut-down-to-thirty-minutes version is usually repeated at 9.30pm tonight. It's also available on the Radio 4 website, as are all the episodes of In Our Time since 1998. Actually, I got rather good at Minesweeper a few years ago when I played it to keep myself visually stimulated (I tend to drop off eventually if the only thing I am doing is listening to something) while going through all the science and maths ones that caught my eye... and there were quite a few. I'm not very cultured, so I didn't bother with the art, philosophy, religion, &c, but I do listen to them if they're "live."
More maths please Melvyn!
Sunday, 22 April 2012
Well, I got my assignments back over the last few days, and I'm really happy with the outcome.
I dropped one point on the M336 TMA, which is actually rather annoying, because I just didn't copy out the whole of an answer from my rough version. It was a question asking what transformation you need to do to move one of the 'motifs' on a freize pattern, onto another. The answer, remaining as vague as feasible, was in two parts: the type of transformation and the point about which you apply it. When I copied out my answer (and I did have it on my draft, because I dug out the sheets to check and lo, the full answer was there), I seem to have stopped the sentence short without fully explaining the point where to apply it. I don't begrudge this costing a mark, because I accept it being a vital bit of information. Just annoyed at myself is all. Though what can you really expect, with the last-minute panic to finish, the all-nighters, and all the other (admittedly self-induced) obstacles. Rather, it's surprising I only dropped one point.
My tutor was very kind in her comments, and gave me some useful advice on what to put more effort into in that block, &ct. I've not met her yet, because I was too busy working on catching up with the material, that I had to skip the tutorial last month. Actually, I had to miss the tutorial for both courses as they were on the same day (they were, however, at different times, which was nice as it meant we can go to both). It was a shame to miss the tutorials, as I do like to go, even if it is a bit of a trek to Leeds, and the fact that I can never find Leeds Metropolitan University when I get there. The problem was, no matter how useful they would be, the 7 hours I spent going to them would not get me any further through the study materials, which was my main concern at the time.
As for M338, well, it was nowhere near as bad as I expected, in fact, I just about pipped into the 80s! Not quite distinction territory, but easily high enough to put me in a good mood all day after I opened the envelope (...Kim opened it actually, as I usually make her check the results, when I'm worried about it). I tend to expect the worst about most things, but this time, I really went overboard! I mean, I was even trying to work out what I needed to do, to make up for it, if I only got 50!
In his comments, my tutor said it is a really tough TMA and that I should be pleased with myself for doing as well as I did. Of course, it's his job to encourage, but regardless of motivation, it made me feel good about myself. I kind of figured, if I managed to do okay under the conditions I was in at the time, I can assume that I might have done very well otherwise. Either way, he did warn us back at the start of the course, that Block A is hardest, whereas Block B is easy, and Block C is just "hard."
For what it's worth, I'm really enjoying the surfaces unit, B1. In fact, I will hopefully get through most of the last part this afternoon/evening. It certainly is a chance to breathe after the ultra-dense Block A. In fact, I am going to go and work on it now. I've already spent enough of the day watching snooker, reading (Rendezvous with Rama by Arthur C. Clarke - very cool), and general pottering around on the Internet. It's time to get productive, I reckon.
By the way, for anyone that didn't catch it, Dara O'Briain's School of Hard Sums, that I mentioned last time, was fairly entertaining. Not ground-breaking TV or anything, but hey, it was worthy enough of watching again tomorrow at least. Warning though, the puzzles aren't particularly hard (and I mean, for "normal" people as well as us mathsy types), but titling inaccuracies aside, it was an enjoyable enough 40 minutes, and I have little else on at eight on a Monday.
I dropped one point on the M336 TMA, which is actually rather annoying, because I just didn't copy out the whole of an answer from my rough version. It was a question asking what transformation you need to do to move one of the 'motifs' on a freize pattern, onto another. The answer, remaining as vague as feasible, was in two parts: the type of transformation and the point about which you apply it. When I copied out my answer (and I did have it on my draft, because I dug out the sheets to check and lo, the full answer was there), I seem to have stopped the sentence short without fully explaining the point where to apply it. I don't begrudge this costing a mark, because I accept it being a vital bit of information. Just annoyed at myself is all. Though what can you really expect, with the last-minute panic to finish, the all-nighters, and all the other (admittedly self-induced) obstacles. Rather, it's surprising I only dropped one point.
My tutor was very kind in her comments, and gave me some useful advice on what to put more effort into in that block, &ct. I've not met her yet, because I was too busy working on catching up with the material, that I had to skip the tutorial last month. Actually, I had to miss the tutorial for both courses as they were on the same day (they were, however, at different times, which was nice as it meant we can go to both). It was a shame to miss the tutorials, as I do like to go, even if it is a bit of a trek to Leeds, and the fact that I can never find Leeds Metropolitan University when I get there. The problem was, no matter how useful they would be, the 7 hours I spent going to them would not get me any further through the study materials, which was my main concern at the time.
As for M338, well, it was nowhere near as bad as I expected, in fact, I just about pipped into the 80s! Not quite distinction territory, but easily high enough to put me in a good mood all day after I opened the envelope (...Kim opened it actually, as I usually make her check the results, when I'm worried about it). I tend to expect the worst about most things, but this time, I really went overboard! I mean, I was even trying to work out what I needed to do, to make up for it, if I only got 50!
In his comments, my tutor said it is a really tough TMA and that I should be pleased with myself for doing as well as I did. Of course, it's his job to encourage, but regardless of motivation, it made me feel good about myself. I kind of figured, if I managed to do okay under the conditions I was in at the time, I can assume that I might have done very well otherwise. Either way, he did warn us back at the start of the course, that Block A is hardest, whereas Block B is easy, and Block C is just "hard."
For what it's worth, I'm really enjoying the surfaces unit, B1. In fact, I will hopefully get through most of the last part this afternoon/evening. It certainly is a chance to breathe after the ultra-dense Block A. In fact, I am going to go and work on it now. I've already spent enough of the day watching snooker, reading (Rendezvous with Rama by Arthur C. Clarke - very cool), and general pottering around on the Internet. It's time to get productive, I reckon.
By the way, for anyone that didn't catch it, Dara O'Briain's School of Hard Sums, that I mentioned last time, was fairly entertaining. Not ground-breaking TV or anything, but hey, it was worthy enough of watching again tomorrow at least. Warning though, the puzzles aren't particularly hard (and I mean, for "normal" people as well as us mathsy types), but titling inaccuracies aside, it was an enjoyable enough 40 minutes, and I have little else on at eight on a Monday.
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