Wednesday, May 09, 2007

Another quick tribute...

...to my Linear Algebra supervisor. The title suggests that this post may be edited in the future, but this post is slightly 'random'. As always at the end of the day, one sometimes tends to 'sort' their file out. You know what it's like. During the day you accumulate papers from all corners of the world and put them into one big pile, with a mental label of 'will sort out later'. The advantage (or disadvantage!) of having a file is that you don't realise the size of this 'pile' so to speak. It continues to grow but you think it's being 'dealt' with. Soon your file becomes big in size and as you don't like carrying stuff in your hands, you find your bag becoming heavier and heavier! At the end of the day you end up carrying your folder in you hands. Humbug.

Alas that was the stage I reached, and today enough was enough. So about five minutes ago I put the file on the floor and starting sorting it out. First I hole punched all the sheets that needed hole punching and began creating smaller piles around me. Yes I'm sitting in a pile of hell-ahhhh. Ahem, well you get the picture! In this 'hell' I found what I'd written down in my Linear Algebra supervision this morning. I was slightly confused and still am to be honest, since we gave the basis of the eigenspace as vectors and I keep thinking it should be 'matrices' but that can't be possible! I mean I'm not sure which space we're working in (I think it's M_2(R)), but obviously to find the eigenvectors of this matrix you need to find the eigenspace i.e. the null space of ([T]_b -mI). Sorry about this confusing notation- we're trying to find the eigenvectors of a matrix of a linear transformation! (That says the matrix T (which is 4x4) with respect to the basis b, and m is the eigenvalue).

Gah- I'm getting sidetracked, but hopefully when I start proper revision this will be less confusing!

That aside I recall my first ever supervision, and since I was 'used' to my previous supervisors, I wasn't too keen! The structure of the supervisions was different, and well I couldn't really ask 'dumb' questions! So we all handed in our first ever homework, and it was returned to us the following week. Our work, previously written in probably blue or black, had a beautiful shade of red in it. This was a surprise since we were used to getting our work back, with say 'minimal' marking. I think some of the other students in my group might not have appreciated this 'violation' of their art, however I was secretly pleased. I might have complained for the sake of 'going' with the crowd, but I always said something positive about it. You see I always like getting feedback on my work, and that is one reason why I'm still annoyed that we can't at least have a look at the exam papers which we took in January! (I did something random in the sets exams and am still curious as to whether it was correct). It's part of the learning process I suppose, which is another reason for my annoyance!

Maybe I'm still a 'baby' but my supervisor was very elegant in her presentation of maths, something which I'm not very good at! Initially, probably due to the first semester, I scrawled down the answers - an equal sign here, another implies sign there and a 'st' thrown in for good measure. Now my work did have some sort of 'flow' to it, but it wasn't desirable to read. I mean to the spectator or non mathematician (no idea why they'd want to read it!) it would have been difficult to follow.

We also got graded on our work, which once again is another alien concept to us. The grades were 'empty' but still getting a 'C' as opposed to 'B' didn't go nicely with the lock and key model. (erm..enzymes!) These grades weren't only based on the maths but the presentation as well. My first work back had 'make a sentence', written everywhere (slight exaggeration) but you get the idea. So obviously when it came to handing the work in next time round, I made an effort to write in proper sentences and make my work presentable! At times, when I've been 'lazy' and sometimes unable to do the work properly, I've handed in 'rubbish' work. However, as with 'sequences' you don't look at the first few terms, but rather how the sequence behaves in the long run!

So this is a thanks to my supervisor for structuring the mess in my head and at times putting the jigsaw puzzles together! Obviously I still would have liked to ask 'dumb' questions, but in the long run I think I have learnt a lot from my supervisor. I might not write the right answer or sensible stuff at times, but it's important that what I do write is readable and makes sense. Nowadays I'm guilty of writing 'too' much down, but I suppose with time I'll be able to decide what 'not to' write. (I tend to do this in other modules as well). An advantage of writing stuff down, as opposed to moving onto the next 'stage' without an explanation, is that you're testing whether you understand the topic properly. I mean if I recall correctly, if you have a spanning set with two vectors in R^3, then it doesn't form a basis.* Stuff like this is easy to forget at times, but explaining your answers can't harm you can it?

What made me actually make this post was the fact that my supervisor put a lot of effort into the supervisions. This was appreciated by me, because I think it's important for the lecturer/teacher to give the impression that they want to teach as opposed to being there for the sake of it. If a teacher gives this impression then hopefully the students will also 'want' to be there (if that makes sense).

In the process of sorting my pile out, I stumbled upon a sheet which my supervisor had prepared for us with questions, and had given us today. Questions about Linear algebra (part 2) and answers as well. To be honest, I was firstly quite surprised and then eternally grateful since the questions were on topics which I've been struggling with! (vector spaces-gah). Now my supervisor didn't have to do this, I mean that's the last time we probably met! (has gone home now). However she did this and I'm glad to have met my supervisor- you couldn't find a nicer person anywhere. Maybe I'm going a bit loopy-my supervisor was a nice person and the skills I've learnt will not be forgotten I hope. :)


[I like meeting 'nice' people and 'nice' mathematicians makes it even better. (I apologise at not being able to think of a better word than nice- shift F7 doesn't work here!)]

*erm.. is ' I was testing you', I good excuse?

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