And it feels, er, kind of good. I’ve been battering my head against a torus-integral problem for hours.
Pretty sure I won’t solve it but not for lack of trying.
On the plus side, it has consolidated everything in unit 25 – multiple integrals – but not sufficiently so to actually get the answer.
In a weird way, it’s nice when that happens. I look forward to my tutor’s model answer.
Edit: slept on it and it seemed all too obvious this morning. Sneaky enough question, though.
A link on another blog, I think provided by Chris at http://chrisfmathsphysicsmusic.blogspot.com/, took me to here: http://www.maths.cam.ac.uk/undergrad/nst-pastpapers/2011/index.html whereupon, of course, I had to have a look at the papers on offer.
Within Part IA Paper 1 lies this funny 2 mark question, which can be solved with GCSE higher level maths: A circle is inscribed within an equilateral triangle. Find the ratio of the circle to the ratio of the triangle (Q5 here: http://www.maths.cam.ac.uk/undergrad/nst-pastpapers/2011/PaperNST_IA_1.pdf)
By the mark scheme, it should take three minutes. How quickly can you do it?
One mark deducted on the PDE question.
I’m surprised more weren’t lost throughout the assignment to be honest as the vector calculus questions were done blind without the benefit of intuition, as I’ve already moaned about in previous posts.
Still, I made some headway with Vector Calculus by Baxandall and Liebeck last night, which has served to switch a couple of light-bulbs on in my head, albeit low-wattage ones.
What I really like about that book is that it just gets into the meat of it – argument, proof, example, exercise, move on.
With unit 25 now done and a reasonably comfortable feeling about its contents, I’m going back to retackle unit 24, armed with Baxandall and Liebeck’s “Vector Calculus”, since my lack of understanding from first pass is tickling the back of my mind.
Due to a couple of fortnight allocations to certain units (instead of the usual seven days per unit), I was quite surprised this morning to find I’m 10 days ahead of the course calendar (unless I read it wrong).
So, I’ll use that time not by getting further ahead, but by going backwards and catching up to where I ought to be right now.
Going further ahead (ie units 26-28) will only draw on what I didn’t learn adequately previously, which is the study progression equivalence to taking two blinkered steps forward then getting side-swiped by a truck. Learning to turn the handle to pop an answer out might get marks but it does nothing for the bigger picture.
So, let’s call it unit 24 of MST209 and some more of block 0 of MS324 from now until Sunday.
I’ve also started looking at some general number theory and have an idea for a cunning encryption algorithm which will, no doubt, crumble faster than a sand-castle in a force 10 when it gets pressure-tested.
Still, in the absence of skill and experience, I’m free to use brute ignorance, and a wing and a prayer as tools instead.
In stark contrast to the difficulties I had in the last block, unit 25 seems to be plain-sailing (caveat: I’m only 4/5ths through it).
I’m enjoying its double and triple integrals, light introduction to moments of inertia, switching in and out of various coordinate systems, and calculating the bounds of iterated integrals where constants aren’t the order of the day.
I haven’t looked in depth at the three separate TMA questions associated with the unit yet, so I’ll save the jubilation of appearing to fully understand it all at first pass until after a few pages of A4 have been produced for marking.
My tutor has told me that (some of?) the maths in this unit is vital if unit 27 – Rotating bodies and angular momentum – is to be fully understood.
Some rather excellent MIT videos I found helpful for unit 25:
I’m also planning to watch this one tonight:
Well, this is bad news.
TMA6 is done, completed.
But loads of new stuff
learned studied to complete the TMA hasn’t been properly understood, or is quickly being forgotten.
I’ve just been through my TMA before putting it in an envelope and while I can follow my arguments easily enough, I don’t have a clue of what most of the answers to question six actually mean and, horror of horrors, the Fourier stuff looks like a foreign language, which means virtually none of it has been committed to memory.
With four or five weeks until the final TMA, and another four units (which look like easily the most difficult in the course) to complete, I’m going to have to relearn half of block six from scratch again at revision time. The course has outpaced me.
On that note, a fridge full of beer awaits and I am off to get exceedingly drunk.
Today, I am very much painting by numbers – completing the final assignment question through mechanical computation devoid of intuition or understanding.
Linking line integrals, curl, grad and potential functions into something meaningful has eluded me. It seems, and remains, a messy mystery, not helped by my lack of understanding of exactly what “work done” really means, what decides if a line is path dependent or path independent, and what it means to classify vector fields as conservative or non-conservative.
Follow the structures outlined in the unit, get an answer, check answer agrees with that in the unit, peer at some output, wonder what it means in the real world, re-read chapter, arrive at same point, repeat to fade….
I am avoiding any part three vector calculus questions in the exam, that much is for sure.
I expect the result on TMA6 will be ok but will over-reward my utter, utter lack of understanding. While the separate entities of div, curl and grad are easy enough to get an intuitive feel for, the whole vector calculus picture is as muddied as a hippo’s home.
Personal difficulty with this unit, out of ten: 10.