I got my first MST221 TMA back yesterday, 95% which is a cause for much tail-wagging in the dragon household ( we do not sing when happy - despite what that film might have said - but our tails do tend to wag which is unfortunate for any small animals or trees in the vicinity; do not stand behind a happy dragon ).
However there was one or two questions where I got full marks, and I don't think I should have done because I really didn't do anything to deserve them.
There's a question in TMA02 as well that I guarantee I'm going to absolutely ace and all I did was press a few buttons on a computer, something I do for a living most days, and fire off a few printouts. Question one took an hour of fiddling with some rather torturous algebra, question two took 10 minutes of keying in a formula into a pre-built spreadsheet and then setting a couple of parameters. Yes its quite wonderful but it's not maths.
In this green scaly creature's opinion using Mathcad in the course is fine enough but it should be used to illustrate and expand on the subject at hand - it's good at that, especially when it shows 2-cycles breaking down to 4, 8 and then into the chaotic region. What it should not form is part of the assessment. All testing me on Mathcad does is prove I can amend a pre-existing mathcad sheet and get some different numbers to come out.
Oh and Mathcad is a sucky, bug ridden piece of 1990's vintage software as well. I have to run it on a virtual XP machine on my main PC otherwise the second I touch the scroll wheel it freezes.
Wednesday, 14 April 2010
Friday, 19 February 2010
A classroom on a wet wednesday evening
Wonderful thing Open University tutorials. Number of people in the tutorial group, twenty seven; attendees at the tutorial, three.
The best one I ever went to was when I was the only bugger there but it did mean that I got two hours personal tuition on vectors and matrices from a research fellow of a Cambridge college.
To be fair the tutorial earlier in the week was not too badly attended with about 8 people showing up on a wet and cold winter evening in a sixth form school in Cambridge*. I'd already covered the subject of the tutorial but I tend to get more out of tutorials that way and I find them handy just for picking up tips on how best to do things rather than for ab-initio instruction.
This time the big take away was "how not to show a proof".
Lets say you have the focus-directrix property of a non-degenerate** conic Pd = ePF. Now what you don't do is start off by saying "As Pd = ePF then... blah blah blah ...see they are"
Rather you go
"Pd = some formula... rearrange rearrange rearrange... = x"
and
"ePF = some other formula ... rearrange rearrange rearrange... = x"
"so Pd = ePF for this conic"
If you don't do it that way then you fall victim to an argument by circular reasoning which, as a rabid athiest used to duffing up religious types when they use such arguments I should have realised.
So even if you've got down pat the subject your OU tutorial is about it's always worth going along IMHO because you're bound to pick up something.
And what else would you be doing on a wet wednesday evening anyway.
* Which follows in the noble tradition of all educational establishments by selling undrinkable coffee that tastes like hot dishwater with grit in it.
** I have a picure in my head of a "degenerate conic" as a parabola that hangs about smoking behind the bike sheds and committing acts of petty vandalism.
The best one I ever went to was when I was the only bugger there but it did mean that I got two hours personal tuition on vectors and matrices from a research fellow of a Cambridge college.
To be fair the tutorial earlier in the week was not too badly attended with about 8 people showing up on a wet and cold winter evening in a sixth form school in Cambridge*. I'd already covered the subject of the tutorial but I tend to get more out of tutorials that way and I find them handy just for picking up tips on how best to do things rather than for ab-initio instruction.
This time the big take away was "how not to show a proof".
Lets say you have the focus-directrix property of a non-degenerate** conic Pd = ePF. Now what you don't do is start off by saying "As Pd = ePF then... blah blah blah ...see they are"
Rather you go
"Pd = some formula... rearrange rearrange rearrange... = x"
and
"ePF = some other formula ... rearrange rearrange rearrange... = x"
"so Pd = ePF for this conic"
If you don't do it that way then you fall victim to an argument by circular reasoning which, as a rabid athiest used to duffing up religious types when they use such arguments I should have realised.
So even if you've got down pat the subject your OU tutorial is about it's always worth going along IMHO because you're bound to pick up something.
And what else would you be doing on a wet wednesday evening anyway.
* Which follows in the noble tradition of all educational establishments by selling undrinkable coffee that tastes like hot dishwater with grit in it.
** I have a picure in my head of a "degenerate conic" as a parabola that hangs about smoking behind the bike sheds and committing acts of petty vandalism.
Monday, 15 February 2010
Madonna's Bra
I was studying chapter A2 of MST221 this weekend, working away in the office I use when I work from home. As is usual the dogs were in there with me to give me a hand with the algebra sleep on the sofa but at one point Mrs Dracunculus came in with a cup of tea and asked what I was up to.
Being all enthusiastic about my new knowledge of parabolas and hyperbolas I started to scribble some cones on my whiteboard and show what happens when you cut them up.
"Oh," said Mrs Dracunculus, " so how come you have to use Madonnas' bra in mathematics?"
She's not very mathematical, Mrs Dracunculus.
Being all enthusiastic about my new knowledge of parabolas and hyperbolas I started to scribble some cones on my whiteboard and show what happens when you cut them up.
"Oh," said Mrs Dracunculus, " so how come you have to use Madonnas' bra in mathematics?"
She's not very mathematical, Mrs Dracunculus.
Sunday, 7 February 2010
0,1,1,2,3,5,8...
Just finished Chapter A1 of MST221 in which we get to poke around that set of numbers up there, the Fibonacci sequence, an example of a second order recurrence system. All quite interesting stuff and I didn't have too many problems getting my head around the sums including the derivation of a closed form for such sequences - which given the struggle I had with wrapping my poor dragony brain around the same derivation for first order sequences last year I was rather happy with.
I did have a bit of an issue with the algebra when doing the exercise to derive a closed form for a Cassini identity as the OU have started truncating their solutions and I am assuming just expect you to be able to follow this stuff by now.... bit like this...
Anyway a quick email to the tutor (and a same day response - great service!) gave me a poke in the right direction with something that is bleeding obvious once you've been shown it, which is.
so 2 is a common factor of 4 and 8, 3 is a common factor of 9 and 27, and so on.
I was even happier when Question 2 of the TMA was on just such an identity.
So, onto conics
I did have a bit of an issue with the algebra when doing the exercise to derive a closed form for a Cassini identity as the OU have started truncating their solutions and I am assuming just expect you to be able to follow this stuff by now.... bit like this...
Anyway a quick email to the tutor (and a same day response - great service!) gave me a poke in the right direction with something that is bleeding obvious once you've been shown it, which is.
n-1 n n+1
a is a common factor of a and a
so 2 is a common factor of 4 and 8, 3 is a common factor of 9 and 27, and so on.
I was even happier when Question 2 of the TMA was on just such an identity.
So, onto conics
Tuesday, 26 January 2010
Here we go again
Woot! Large brown cardboard box arrived yesterday which means it can only be Open University time again.
Sure enough the first half of MST221 has arrived along with the usual assortment of DVDs and funny coloured bits of paper. I now have three copies of the "Enrichment Material" thanks to previously doing MU120 and MST121 but oddly enough the didn't send another copy of Mathcad and presumably assume you did MST121 and have the box handy somewhere (I did, but spent ten minutes rummaging through funny coloured bits of paper to find the sodding password).
On the subject of Mathcad... has ever a more crappy piece of software ever been designed? I mean it's hideous ugly, buggy as hell (touch the scroll wheel of your mouse at your peril) and I think I could do the maths faster sometimes its that slow. I really do not like using it at all and I really wist the OU could sort out a deal with Wolfram so we could use Mathematica - you know software people in the real world use?
Rather amusingly I notice that my tutor is the same one I had when I was doing MU120, less amusingly one of my tutorials is in Ipswitch which is quite a flapping distance from the lair.
Anyway time to dust of MST121 for a bit of revision on sequences and then I'll get an early start on unit A - I find keeping two or three weeks ahead of the study timetable works best for me and allows for a bit of wiggle room should things get tricky away from sums.
Woot! Large brown cardboard box arrived yesterday which means it can only be Open University time again.
Sure enough the first half of MST221 has arrived along with the usual assortment of DVDs and funny coloured bits of paper. I now have three copies of the "Enrichment Material" thanks to previously doing MU120 and MST121 but oddly enough the didn't send another copy of Mathcad and presumably assume you did MST121 and have the box handy somewhere (I did, but spent ten minutes rummaging through funny coloured bits of paper to find the sodding password).
On the subject of Mathcad... has ever a more crappy piece of software ever been designed? I mean it's hideous ugly, buggy as hell (touch the scroll wheel of your mouse at your peril) and I think I could do the maths faster sometimes its that slow. I really do not like using it at all and I really wist the OU could sort out a deal with Wolfram so we could use Mathematica - you know software people in the real world use?
Rather amusingly I notice that my tutor is the same one I had when I was doing MU120, less amusingly one of my tutorials is in Ipswitch which is quite a flapping distance from the lair.
Anyway time to dust of MST121 for a bit of revision on sequences and then I'll get an early start on unit A - I find keeping two or three weeks ahead of the study timetable works best for me and allows for a bit of wiggle room should things get tricky away from sums.
Monday, 11 January 2010
Aquiring a rubber fetish
No, I haven't been getting kinky (well no more than normal) but I have been getting into LaTeX which as you may or may not know, is a bunch of software and a mark-up language for typesetting documents, particularly maths ones.
I've been sort of dimly aware of it for years but a few weeks ago me and everyone else in the East of England region doing MST221 this year were invited on a day-long "Intro to LaTeX" session in Cambridge given by one of the OU math team.
Well I had a rummage in the documentation online and it all looked quite interesting and actually not that horrendous to use. I'd done all of MU120 using Word 2007 which has a half-way decent equation and math editor nowadays (certainly way better than earlier Word versions) but I must admit after the first TMA for MST121 the amount and complexity of equations and formulae became a real chore to word process so I went back to the mk-1 pencil and paper method; far from ideal as (a) my handwriting is crap and (b) I get writers cramp really quickly and had to stop to stomp up and down and curse after every page.
I've also been around the block when it comes to word processors, the first "real" word processor I used - although you would be hard-pushed to call it that nowadays - was Wordstar running on a 286 in DOS so dicking around with formatting codes was not new, and having paid my dues in days gone by as a developer hacking together old-school ASP pages I was no stranger to markup and the whole concept of "What You See Is What You Mean" (rather than "Get") was familiar.
However I was surprised by just how powerful LaTeX is and what lovely results it produces and how quickly you can get it to do nice stuff.
Over the years I've kind of fallen out of love with the whole Linux/Open Source ideal - I am pretty sure it's because of my job as I am under lots of pressure just to get the code working and onto the trader's desktops so I really want to shove a couple of DVDs into the PC, install the development environment and off I go. I just don't have the time to fanny around with hand crafting config files, rummaging in HKEY_LOCAL_TOUCH_THIS_AND_YOUR_PC_WILL_NEVER_WORK_AGAIN and all the usual fluff that goes with open source. So with that said at first LaTeX was pressing all my "oh dear" buttons.
Need to install more than one program to get it working - CHECK
Various bits of code scattered all over the web - CHECK
1419 obscure tiny files, one of which allows me to typeset Ancient Nabbatean - CHECK
Irritating cliquey in-joke in that you need to write the name of the PrOgrAm in a miXeD CaSe and then it's not even pronounced "latex" but "lay-tec" - CHECK
Cutesy animal mascot for the application...
- CHECK
Not looking promising so far and indeed although I got up and running pretty quickly with an .iso distro off the net (for a given value of "running") there was a lot of fiddling around to do to get it working right until I realised that it hadn't actually installed everything I needed to make things work right so I needed to fiddle with the innards of a package manager (eventually giving up and saying "Yes, you win, install every sodding package including the ones that let me typeset Elder Futhark Runes, Astrological Birth Charts and even bloody Hieroglyphs")
So - not exactly software I would expect your average Joe to be able to install but then that's the point I guess, this stuff was written by geeks for geeks so your average geek (like me) with a bit of perseverance and consultations with Professor Google can get it working.
And when it is working... blimey it's powerful. The syntax is not too tricky but there's a lot of it and all those little files just extend the basic facilities by orders of magnitude and wow does it produce good looking, very readable output. Here's an example...
and you produce that using this markup:
I was hooked within minutes - one of those 3am "are you coming to bed yet love" times (sorry Mrs Dracunculus if you're reading this). Within a couple of days I'd already started work on a template for submitting TMAs just so I could learn how "fancyhdr" worked and that was before the class last saturday.
The day didn't start well with me totally failing to get into the building and walking round twice before finding the goods bay and a doorbell. Once inside I spotted the tutor giving the day school - wayward hair, yellow sleeveless jumper, blue bow tie, brogues... yep, you're committing every style crime in the book so you must be a maths professor and indeed he was. His enthusiasm for the subject was plain to see and quite infectious and like everyone on the OU tutoring staff he really knew his stuff. I was pleased I'd already had a play around with the software before the day but I got a whole load out of the day, fixed my install on the lappy to something better and came away with a different template for TMAs which I didn't like a lot of so I stole some of the ideas out of it and added them to mine.
So I'm a happy LaTeX convert... expect more witterings on the subject as MST221 progresses. Now where did I put my gimp suit.
I've been sort of dimly aware of it for years but a few weeks ago me and everyone else in the East of England region doing MST221 this year were invited on a day-long "Intro to LaTeX" session in Cambridge given by one of the OU math team.
Well I had a rummage in the documentation online and it all looked quite interesting and actually not that horrendous to use. I'd done all of MU120 using Word 2007 which has a half-way decent equation and math editor nowadays (certainly way better than earlier Word versions) but I must admit after the first TMA for MST121 the amount and complexity of equations and formulae became a real chore to word process so I went back to the mk-1 pencil and paper method; far from ideal as (a) my handwriting is crap and (b) I get writers cramp really quickly and had to stop to stomp up and down and curse after every page.
I've also been around the block when it comes to word processors, the first "real" word processor I used - although you would be hard-pushed to call it that nowadays - was Wordstar running on a 286 in DOS so dicking around with formatting codes was not new, and having paid my dues in days gone by as a developer hacking together old-school ASP pages I was no stranger to markup and the whole concept of "What You See Is What You Mean" (rather than "Get") was familiar.
However I was surprised by just how powerful LaTeX is and what lovely results it produces and how quickly you can get it to do nice stuff.
Over the years I've kind of fallen out of love with the whole Linux/Open Source ideal - I am pretty sure it's because of my job as I am under lots of pressure just to get the code working and onto the trader's desktops so I really want to shove a couple of DVDs into the PC, install the development environment and off I go. I just don't have the time to fanny around with hand crafting config files, rummaging in HKEY_LOCAL_TOUCH_THIS_AND_YOUR_PC_WILL_NEVER_WORK_AGAIN and all the usual fluff that goes with open source. So with that said at first LaTeX was pressing all my "oh dear" buttons.
Need to install more than one program to get it working - CHECK
Various bits of code scattered all over the web - CHECK
1419 obscure tiny files, one of which allows me to typeset Ancient Nabbatean - CHECK
Irritating cliquey in-joke in that you need to write the name of the PrOgrAm in a miXeD CaSe and then it's not even pronounced "latex" but "lay-tec" - CHECK
Cutesy animal mascot for the application...
- CHECK
Not looking promising so far and indeed although I got up and running pretty quickly with an .iso distro off the net (for a given value of "running") there was a lot of fiddling around to do to get it working right until I realised that it hadn't actually installed everything I needed to make things work right so I needed to fiddle with the innards of a package manager (eventually giving up and saying "Yes, you win, install every sodding package including the ones that let me typeset Elder Futhark Runes, Astrological Birth Charts and even bloody Hieroglyphs")
So - not exactly software I would expect your average Joe to be able to install but then that's the point I guess, this stuff was written by geeks for geeks so your average geek (like me) with a bit of perseverance and consultations with Professor Google can get it working.
And when it is working... blimey it's powerful. The syntax is not too tricky but there's a lot of it and all those little files just extend the basic facilities by orders of magnitude and wow does it produce good looking, very readable output. Here's an example...
and you produce that using this markup:
\section*{Question 2}
\subsection*{(a)(i)}
The sum of the first $n$ integers is given by
\[\sum_{i=1}^n = \frac{1}{2}n(n+1)
\]
So the sum of the first 28 integers is $\frac{1}{2}28(29) = 378$
and the sum of the first 107 integers is $\frac{1}{2}107(108)=5778$
so the sum of the integers from 29 to 107 is $5778-378=5400$
\subsection*{(a)(ii)}
The sum $\displaystyle\sum_{i=29}^{107}(4+3_i)$ can be rearranged as
\begin{equation}
4(107-29+1)+3\sum_{i=29}^{107}i
\end{equation}
and from the answer obtained in \textbf{(a)(1)} above we can write (1) as
\begin{equation*}
4(107-29+1)+3(5400)=16516
\end{equation*}
I was hooked within minutes - one of those 3am "are you coming to bed yet love" times (sorry Mrs Dracunculus if you're reading this). Within a couple of days I'd already started work on a template for submitting TMAs just so I could learn how "fancyhdr" worked and that was before the class last saturday.
The day didn't start well with me totally failing to get into the building and walking round twice before finding the goods bay and a doorbell. Once inside I spotted the tutor giving the day school - wayward hair, yellow sleeveless jumper, blue bow tie, brogues... yep, you're committing every style crime in the book so you must be a maths professor and indeed he was. His enthusiasm for the subject was plain to see and quite infectious and like everyone on the OU tutoring staff he really knew his stuff. I was pleased I'd already had a play around with the software before the day but I got a whole load out of the day, fixed my install on the lappy to something better and came away with a different template for TMAs which I didn't like a lot of so I stole some of the ideas out of it and added them to mine.
So I'm a happy LaTeX convert... expect more witterings on the subject as MST221 progresses. Now where did I put my gimp suit.
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