## Eureka moments – and satisfaction

I suppose if you’re reading this blog, you either study maths/physics with The Open University, or got lost on your travels around the internet.

Assuming it’s the former, then you’ll probably agree that there’s something immensely satisfying about working something out for yourself – particularly when you’ve found the concept / method / thing awkward / difficult / impossible to begin with.

It didn’t make you financially richer, didn’t get you a promotion at work and, on the face of it, was probably a lot of time invested for one tiny step forward.

But it does feel good.

So, unit 17 has clicked into place and lots of things are linking up. My mathematical modelling molecules are starting to take the shape of a very basic life-form.

This week has been a differential equations party (real and complex), an algebra feast, and a bit of a head-scratcher.

The unit has introduced the ideas behind strong, weak and critical damping, the “model damper”, systems analogous to the model damper, combination damping, the damping ratio, a method of using the quadratic discriminant to investigate damping levels / strengths, decaying amplitude, forced damping, forcing by displacement, steady state solutions, magnification factors, resonance and, of course, methods to model, investigate, and objectively analyse, both quantitatively and qualitatively, all of the above.

The TMA question was not what I was expecting. I am peering at it with a quizzical eye.

That, alone, will not be enough, however.

I have one large study session to go on unit 17 – ie all day tomorrow – then on to the TMA question on Sunday – probably all day as it’s worth 32 marks out of the 95 assigned to the maths in the TMA. Yeeeeeeeek. (The other 5 marks go on presentation, presumably in an effort to help retain the sanity of the tutors who have to mark questions which can range over 10 or more pages, which would be a bit of a drag if the whole thing was just slapped together without breaks, explanations, justifications and neat writing / typing / LaTeX).

So, with 20 minutes down time before walking the dog, I’m sitting here pondering something that’s being pondered on at least two other OU maths blogs right now – is the chase for cracking TMA marks coming at the expense of deep learning?

By that, I mean, is obsessing over the TMA costing time otherwise available to get an even deeper understanding?

I like to think I’m logical and can crack most problems. But I also have a **** memory.

Or do I?

Maybe I just concentrate on cracking the problems and not on really learning the material?

Who knows?

I’ll find out soon enough in the exam, but it does concern me.

I dislike the fact that I can barely remember the linear algebra from M208 last year although, curiously, almost all of the group theory and real analysis sits fairly fresh in my head.

Maybe the factor of “interest” comes into play here.

I found linear algebra boring but liked the other components.

With MS221, I liked the calculus and complex number stuff, plus some of the conic stuff. I disliked the number theory, recurrence relations and several other things.

Guess which I can remember?

So, how come I like everything in MST209, though I’ve found some of it very difficult, yet don’t seem to remember bits of it already?

Is it because it’s vast?

Is the learning pace too swift for me?

Or am I dealing with it like it’s a course of here-and-now problems to be solved – ie TMAs – as opposed to a blueprint to a mathematical skill set?

I’d be interested in other students’ thoughts – is the course so huge no one can take ownership of it first time round, or have I evolved into a TMA-completer who doesn’t know the subject?

JamieI am also doing MST209 and I have gotten 94% average so far.

I am in the exact same boat as you, I feel I spend so much time sorting out the TMAs that I don’t actually learn the material in a meaningful way which will stick with me. I look back over the other units and it’s almost like seeing it again for the first time (except it is much faster to learn second time, it soon comes back)

I think the best thing to do is do the whole course again, but only do 1-2 exercises per unit, just before the exams.

Looking at the specimen paper I can see that as long as you have a basic grip of how to use the techniques, the handbook will guide you through the exam nicely (don’t forget you can add as much as you like to the handbook, and there is plenty of space!)

June 17, 2011 at 9:38 PM

oumathsJamie, great reply.

Thank you for that.

It’s a big help.

I can totally identify with what you’ve written – when you look back at the maths of a previous unit that’s required in the current unit, it does indeed take substantially less time to get it back into your head.

Genius observation – I guess we (you and me) are learning it, just not getting enough time as the course progresses to fully consolidate it.

That’s put my mind at rest a bit.

I’m hoping to get all units and TMAs plus the remaining CMA done by the start of September to give me 6 weeks to revise – ie a day per unit, plus another fortnight for past papers.

How do you find the workload in general?

June 17, 2011 at 9:45 PM

Jamiealright really, I found block 4 much easier than block 3 (TMA3 was particularly hard work for me), should imagine the workload will get very hectic come september though! So many units, it’s insane

June 17, 2011 at 9:49 PM

Jamiesomething else I’m looking forward to is the fact that we will use the maths from blocks 1-4 so often in the final blocks that it *should* become second nature to us

June 17, 2011 at 9:51 PM

oumathsAgain, you make good sense, Jamie, and I agree.

The earlier unit stuff is being used so frequently now that it *should*, as you say, become second nature to us.

Good luck as the course progresses. If you haven’t already had your TMA 4 result back, I hope it’s a good one – the last question took me an age to solve. As in four or five days. It just seemed a really weird question. And I can conclude I’m not that fussed about dimensional analysis (though I have a feeling it will crop up heavily in any fluid modelling I do at level 3).

Maybe Chris from chrisfmathsphysicsmusic could confirm that.

June 17, 2011 at 10:01 PM

Jamieweird. I found dimensional analysis easy, just seemed like basic algebra, but I guess I have come across it before when I was at Nottingham Uni, the TMA question took me about half an hour lol

June 17, 2011 at 10:04 PM

oumathsThat’s interesting. I found block 2 crazily difficult – all that new physics.

I think I found block 3 the easiest but that’s mainly because half of it had cropped up in M208 before, so I guess I got a bit of leverage that way.

I’m expecting this block (block 5) to be tricky.

Block 6 looks much more mathsy than physicsy with its Fourier series, PDEs, scalar and vector fields, and vector calculus. I have to admit, that’s more my thing.

I guess I’m a rote learner as opposed to someone better able to put maths to more of a real world use as per the requirements of physics.

My tutor has warned me that block 7 is difficult.

I think I might ease off a bit on the mark chasing and concentrate on the deep-seated learning – I’m after a course pass one and not a 99% TMA average with a mediocre exam result, that much I do know.

June 17, 2011 at 9:56 PM

oumathsHalf an hour?

@Looks for jaw-drop smiley@

Good grief.

That thing nearly killed me.

I had so many false starts on it that the only things in my recycling wheelie bin were a few dog food tins and a trees-worth of A4 paper. 🙂

Very odd how some people find some bits so much easier than others.

June 17, 2011 at 10:12 PM

JamieGot me worried now that I rushed it ^^

June 17, 2011 at 10:14 PM

Jamiecan’t remember my answer for the very last part but it matched with the *real* equation so I knew it was right

June 17, 2011 at 10:15 PM

oumathsGood stuff.

June 17, 2011 at 10:18 PM

Chris FinlayNot that I’m doing MST209 so can’t comment on specifics but it seems to me that MST209 is a foundational course the concepts of which you will use over and over again. It’s like being initiated into a whole new way of thinking which will stay with you the rest of your life especially if you go on to other Applied maths, Physics and engineering courses or if you have aspirations to become one in real life. The point is that you aren’t expect to remember everything but as you use it more and more it will click,

I’m finding a similar experience with M208 analysis, I read most of Brannan’s book before starting M208 and it seems to have paid off as I found the TMA for part 1 quite straightforward although I expect it’s only scratching the surface. Again a similar door opening experience seems to be happening, Two years ago as a practicing physicist, my eyes would just glaze over when confronted with books full of epsiloon delta definitions now these are no longer closed books to me, even though I can’t remember most of the proofs I guess you two must be going through a similar epiphany moment with MST209.

June 18, 2011 at 5:56 PM

oumathsGiven your background, Chris, I suspect that MST209 would be a walk in the park for you.

The main reason the books are about a foot tall when stacked is simply that extra-careful treatment of every concept is given – though not all possible permutations of said concepts are looked at – which is what makes the TMAs interesting and challenging in parts. You’d possibly find it over-descriptive.

Have you met Stirling’s Formula and all that comes with it yet? I can’t remember if that’s in analysis I or II.

That, plus the epsilon-delta definition, were personally my main challenges in the analysis section/sections.

June 18, 2011 at 9:28 PM

Chris FinlaySorry just came across your comments on dimensional analysis. It is crucial in physics and also provides a useful check whether equations are consistent with each other. I haven’t actually done much fiuid mechanics, indeed I intend to it in October 2012 as a prelude to embarking on the MSc in maths and as a revision of some basic maths techniques and an antidote to all the pedantry associated with pure maths but like any branch of physics it plays an important part.

One of the wierdist things in particle physics is that Planck’s constant which is about 10^-34 and the speed of light 3.0 x 10^8 in SI units are both set to one to make the equations simple.

It’s a real pain in the neck to be able to convert the quantities back into real numbers that you can measure.

June 18, 2011 at 6:07 PM

oumathsAha, just looking at the Planck constant on Wiki and how the speed of light comes into play: http://en.wikipedia.org/wiki/Planck_constant

That’s one thing that baffles me – how we relate quantum-sized stuff to universe-sized stuff.

Knowing nothing about physics outside of MST209, I assume this is what leads to the search for a unified theory of sorts.

Are you on group theory II now? Counting theorem coming up, if so. Enjoy. 🙂

June 18, 2011 at 9:36 PM

Chris FinlayNo I’m going to take a day off then start on group theory II on monday along with contour integration for M337 next week. reallty glad you’ve had so much satisfaction with unit 17. Thats what all this is about also glad to have made some new mates.

As for the comments about unified theories one thing that seems to be hindering the development of a a quantum theory of gravity is the fact that the coupling constant for gravity unlike other interactions has dimensions (back to dimensional analysis) so it seems impossible given the current state of mathematics to approximate the complicated interactions by approximation by say a Taylor series. Getting back to your original question why dimensional analysis is so important.

If (with all the spare time you have 😉 ) you would like to get a grasp of how physics works then a good book to read is Longair’s concepts of theoretical physics I think you would find that a much more satisfactory book to read rather than doing say the Physical world. That would then put you in a good postion to tackle say the quantum world. I might put a post on my blog about a guided reading course to

get someone a basic understanding of physics.

Hope the enthusiasm continues as far as I can tell you are now crossing the threshold from understanding to professionalism as far as MST209 is concerned well done.

Best wishes Chris.

Best wishes Chris.

June 18, 2011 at 11:27 PM

oumathsI think I’ll be seeing you in the fluid mechanics forum in October 2012, Chris.

Looks like my choice of third year will be:

Complex analysis,

Fluid mechanics,

Graphs, networks and design,

and Mathematical Statistics in its first outing (ouch, no past papers for revision).

Will also do M248 and MSXR209 to complete the maths degree.

That’s another 24 months from this point on mapped out.

Target: BSc(Hons) Mathematics finished in 2013.

July 9, 2011 at 8:52 PM