maths study via The Open University

Archive for March, 2011

stuff just got real

MST209 just got a bit more difficult.
Unit 8 is turning out to be a *^$&$%^£. It forms part of assignment number three, due in in about 5 weeks time. Units 9, 10, 11 look ok. More on 8-11 later.

All 35 pages of assignment two have been with the tutor for a week now, well ahead of the cut-off date and at this point in time, I’m nearly 2 weeks ahead on the MST209 schedule, and 2 weeks behind on the M248 schedule.

But the good news is that M248 just got interesting.
There’s a &^%£load of probability stuff, which is proving good fun.

Stuff along the lines of, oh, I dunno, there’s a 27% chance a typical student will fail any one maths course. Of 40 students taking 5 courses each, what is the probability that at least 32 students will pass at least 4 courses? Or somesuch.

Not as straightforward as it looks. I’ll post the maths behind it once I’ve fully grasped it. I think I’ll need to do a lot of these to recognise which probability model applies to which predicament.
I also want to understand the derivations of the models inside and out, rather than just apply them.

And I need to get out of the habit of using calculus to evaluate stuff – the course provides other equally worthy methods of arriving at the same answer. Having fallen foul of the “style” I present things in (see last post), I don’t want to also fall foul of “method”, although I guess proof is proof, as long as it’s valid.

More in a fortnight’s time – when I’m on a week’s holiday. I plan to get MST209’s (maths and physics-type stuff) third TMA submitted a fortnight early and M248’s (data, probability and statistics) submitted bang on the button.

I think May 4 is the deadline for both.

I’m officially around 1/4 the way through both courses now, in two months. 6.5 months to go to exams. I have a feeling both exams will fall within a day or two of each other. That could be bad news.

MST209 TMA 2 done and result from M248 TMA 1 arrives

The second assignment on statics, dynamics and oscillations is done.
I’ll post it on Monday.
The next assignment covers lots of stuff I’ve already done, courtesy of the pure maths course M208, which I completed last year.
It looks like the contents of the first three TMAs sets students up for the entirety of the rest of the course.
A quick look through the middle and latter parts of the course confirms we’ll be constantly drawing on what we’ve covered in these first two months. As expected.

The plan this month is to get a fortnight ahead on MST209 and get myself some breathing space for M248, the data and statistics course.

It’s going to be necessary because I received a disappointing TMA score back this morning. I think its the worst score I’ve received on any assignment for any of my five Open University courses.

The tutor wrote pages, not paragraphs about style and presentation and how it didn’t fit his bill.
Sadly, his bill doesn’t appear to match the bill asked for by the OU.

I’m to embed graphs into the main text which, ideally, is to be word-processed.
Cut n paste jobs really.
However, has anyone explored the problems between cutting Minitab and pasting into OpenOffice?
Enough students have noted that the edges of graphs, axes, etc disappear in doing so.

I don’t own MS Word and won’t be buying it.

So, it looks like I’ll be chopping bits from Minitab by using Paint, reducing it to A5 or A6 size, saving as jpegs, and pasting into the main body of copy relating to each question.

That seems like a thorough waste of time to be honest.

Some of my wording when explaining things was deemed to be unneccessary. Some things I provided from the graphs were deemed to be unneccessary.

Reading back through the question, however, it explicitly asks for this information and doesn’t specify the layout required.

I guess it was supposed to be provided in a column within Minitab rather than within Minitab’s calculation area.

Well, specify that then.
Don’t leave it open in to interpretation, especially when there are no examples to compare it to, and common sense could argue for either case.

All the maths I did was correct. No marks lost on that side.

So, it looks like M248 is a course in using specific wording to qualify answers, rather than obtaining data and qualifying it in any terms other than those the tutor happens to want.

In other words, M248’s outcome is largely out of the hands of correct computation and more in the hands of qualifying things with the exact words the tutor wants. And changing the layout of your answers to suit his particular needs.

That’s not maths to me.
Then again, this isn’t a maths course. It’s a statistics one.
And, it seems, statistics is a wooly subject rather than a precise one.

So, since I’d like a first class honours pass on this course, I’m going to have to play the game – I’ll be phoning the tutor before every assignment question to check on qualifying words and style layout.

I’m not prepared to lose this many marks again on matters of style.

Courses so far:

MST: enjoyment, 10; difficulty, 5.
M248: enjoyment, 1; difficulty, 1.

Unit 7 – a summary

This week’s unit looked at modelling simple harmonic motion.
It was approached by making use of previously-developed methods and includes some straightforward differential equations and integration.

While problems relating to multiple springs dont encounter much extra maths, they do require a facility in keeping a close eye on exactly what you’re trying to do.

The entire unit can largely be written up into a 30-or-so point check list, with familarity with complex solutions to second order constant coefficient linear homogeneous differential equations assumed.

The derivations of unit-related equations are straightforward.

That said, there is quite a bit to remember.

The TMA question is not all that straightforward-looking, though. I’m about to start it now.

I am now a whole one day ahead of the course schedule after putting in only 20 hours this week.

The assignment for the previous unit – unit 6 – scored a 5 on the difficulty scale, and careful narration of what you’re doing is likely to be required so as not to confuse your tutor when he/she comes to mark it.

Unit 7 also scores a 5 (out of 10) for difficulty – mainly because I didn’t have any prior knowledge about phase angles, amplitude, etc.

Hooke’s Law itself is straightforward and can be logically derived.

Some videos watched this week:

Unit 6 – a summary

First off, I’m glad to say that unit 6 (dynamics) seemed a lot easier than unit 5 (statics).

That said, there’s a lot of algebraic manipulation and a fair bit of integral calculus (often integrating twice).
Separation of variables had better be your friend by the time you get here.
You’d also better be pretty good at performing “u-substitutions”, exponentiating log functions with algebraic coefficients, and, most key, deriving (or using from the handbook if given) the most appropriate equations – ie recognising what to use, when.

Since unit 6 is application of maths techniques and, hence, is a step-by-step process without ambiguity, I reckon it scores a 5 on this week’s difficulty scale (10 being hardest).

Models for friction, air resistance, terminal velocity and water resistance are developed and applied. Great fun to be honest.
The assignment question looks fair – I’m about to start it now.

Unit 5 finished, unit 6 started, plus result for all of TMA 1

I’ve been rating the units for difficulty as I go along (1=easy, while 10=hard). So far, I’ve given fairly low scores to reflect the lack of (relative) difficulty in them given that the first four units were either revision of things we should have known from prerequisite courses, or were concepts leading on from them.

That changed with unit 5.

While others on the course seem to have understood it from the off, I was left scratching my head for more than a week (and a couple of re-read throughs) trying to fathom out the counter-intuitivity (for me, anyway) of Newton’s Laws of Motion – the third law in particular.

The maths in the unit was easy – decomposing vectors into i, j and k-components in terms of trig functions, then working out corresponding coefficients of friction, etc.

The bit that threw me was deciding which forces act where. Put a book on a book on a table. Not so straightforward as to what is exerting a force on what. Throw a ladder against a wall and marvel at force diagrams devoid of stress on the wall. Hmm, this took some time to figure out – not least because I didn’t twig I was drawing a force diagram for the ladder, not the *********ing wall as well. Normal force. Don’t forget him.

So, while I can’t give a difficulty rating on behalf of my peers/cohort/fellow sufferers, I’ll state mine flat out as a 9.

From no effort to head explosion in one easy go.

The penny (or box of pennies) dropped after about 8 days of read, re-read, ponder, draw, wail, cry, re-read, think, etc.

Anyway, once it made sense, the two assignment questions related to this unit (which make up a part of assignment number two) turned out to be quite straightforward. I can’t discuss them but suffice to say one was easy, the other made you think for a while.

On to unit 6…..

Finally, I get to put calculus to use. In the real world.

This is my first foray into using integral calculus to model real-world situations. It’s exempified by extending its notation to include vector notation, position vectors and the like. Great fun.

I am seriously loving this integration work and the fact that, after previous courses of manipulating calculus all over the place to arrive at some answer which, ultimately was just a jumble of “x”s, “e”s and constants, this course has, in one stroke, shown me what (integral) calculus can actually be used for. Apart from finding the area under a curve or solving an elementary volume of solids of revolution question, that is.

I’ll wait until I finish the unit and have done the assignment question before rating it out of 10 for difficulty.

I’m now one day behind where I should be on the study calendar. Saturday night is now in rather than out. I cannot fall behind on this course. The pace is swift now. It’ll only pick up…..

The result for my first assignment came back today – that is, the amalgamated score of both parts of it. Very high pass one.

But before I get carried away, there are six more written assignments, two computer-marked assignments and a three hour exam to go, plus approximately 600 hours of study and 100+ hours of revision for the exam.

Some more videos

Video one is handy to introduce the concept of applying the cross product to torque problems.
Video two is where the heavier stuff comes in.
Both very good videos for very different reasons.

Also, a very good basic description of the cross product and its application to torque is here: