Sunday, July 29, 2007

First Year Analysis II

Once upon a time, \sout{in a nursery rhyme there were three bears.} I posted about my thoughts on the first semester. Not wanting to 'tempt fate' I left my thoughts on the second semester till after I'd received my results. That moment has now arrived! [edit: I'd forgotten that I'd typed this up! The original date for this was 7/7/07 at 16:10.]

I had finished the first semester on a semi high. Towards the end I'd really gotten into the maths \{stats}, and had also been enjoying the topics we'd been studying in the modules. I had discovered for myself a routine which had allowed me to study-the focus was there. Better late than never was what I told myself, but the most significant thing that had happened was that something had clicked in my head. The 'obsession' that I have for maths now, hadn't properly been there before. I guess you could say that I was studying to 'pass' then. Lots of factors brought about this change- new lecturer, different course material, my motivation returning etc. I recall actually looking forward to the second semester starting and even, maybe stupidly, bought a couple second hand linear algebra books! (well they were published in about 1965-1975 you see!)

So I started the second semester with a blog, five maths books and a desire to learn maths as opposed to just studying my modules because I had to. I think it's this transformation in my attitude that has helped me in the second semester. I had honestly thought that I'd done worse than my first semester in some exams, since I'd lost my focus. What probably carried me through was the mistakes I'd made in the first semester, and if I may say again, my desire to study and understand the maths. Where I had thought my focus had been lost, I think it became spread over everything rather than just being concentrated on trying to 'pass exams'.

From my first post in this blog, I wrote: 'This blog may or may not enhance my love for maths, but I hope it does.' Indeed this blog seems to have proven to be a success. Towards exam time I did wonder whether this blog was a distraction, since I tended to post a lot and explore Blogistan at the same time. This was due my lack of self-discipline, but what this blog did was to show me other areas of maths that I wasn't studying. Thus I 'wanted' to know more about such areas and probably in them instances neglected my course material. However, that being said, the one negative (i.e. my lack of self-discipline at times) is really quite insignificant compared to the benifits. Yes, I started the second semester with a new found desire to learn maths and this blog proved to be a great medium for allowing that desire to grow. It was an outlet for my 'obsession' one could say, and through this I found other mathematicians. Mathematicians who had the interest maths!! (shock, horror).

I probably have complained and posted a lot of stupid random things at time. (A quick look at my post titles has me coming to that conclusion!), but for those posts that did have maths, I found that writing down what I'd done helped! Heck, I ended up waking the morning after with the right answer. This might be going off track for a minute, but without naming names, the people who have commented on this blog have been a great, massive, ginormous.... help as well. :) You could say that most of the comments kept me touch with the 'mathematical world'. Memories of my 'angry' post on sequences and series seems to spring to mind as well as the posts about my problems about doing a maths degree. This blog nicely balanced all the negativity I was having about doing a maths degree, which seemed to be seen everywhere in the second semester.

Without a doubt Blogistan (and my linear algebra) supervisor got me aware of communicating maths properly. (That video springs to mind- especially the bit about the typewriter making funny noises if the sentence started with 'f(x)', rather that 'the function'.) I think I may have taken the writing thing a bit too seriously in my exam though! I could go on forever thinking about the positives of this blog (LaTeX...), but I think it played a vital part in my second semester. Maybe I'm really still trying to convince myself of the positives, since I had honestly thought that I'd be blaming this blog (i.e. my lack of self discipline!) when I got my results! Anyway, enough of this now- onto my modules.


I talked about the workshop module in the first semester analysis, since that module ran over the course of two semester, so I'll start with Linear Algebra. I'd looked at the Internet page for this module, before the year had started and seen words like matrices, eigenvalues, eigenvectors and thought phew, at least I'll know something. It probably did start of slowly, but then suddenly a change of pace went undetected by me. I'll admit to probably doing a lot of complaining in the first six weeks of this course, since the way we took notes during the lecture was not something I enjoyed! Looking back, I realise that the lecturer did what he thought best since it can take a while to write out lots of matrices and then reduce them to row echelon form! (I can't think of an 'efficient' way of doing this, but my suggestion had been that the lecturer make a handout with everything that was to be taken from the book on it. Gaps would be on this handout so then we would be able to fill them with new information- like the first semester calculus lectures).

My problem was that I had to copy the notes up again at home (about 22 lectures it was!), and this was a tedious task indeed. I had to do this because I have to have the notes in my file organized, rather than just saying 'page 224 example 4.3 - book', everywhere. After lectures I normally try to read over my notes and try to follow them- making sure that they make sense. I couldn't do this anymore, due to the fact that all I was doing was 'copying' my notes rather than reading through them. Maybe I should have read them and copied them at the same time, but I was in a hurry to finish the copying since I'd fallen behind! [Bella and Milo seem to go home and copy the notes out again, whilst at the same time understanding them, for all lectures!] OK- you got it, this bean is rubbish at multi tasking. :o Well there are certain degrees of this so called 'multi-tasking'. I can't watch TV and talk on the phone at the same time, and if I'm sat at the computer and you're talking to me I'll most likely not take in much! My theory is that I'd rather do one thing at a time and do it properly. :o (Hence why I prefer only writing my notes out once during lectures, and annotating them if need be, which is less time consuming).

Do you sense a long post?! The concept of bases may seem 'trivial' to me now, but at the time when I was falling apart(!), span, dimension etc were alien concepts to me. (even now I'll probably struggle trying to prove that something is a subspace). I took comfort from the little that I did understand, but I think the problem was that we weren't computing matrices any longer. I could do most of the questions which had a certain 'algorithm' for finding the answer eg. the inverse, but I didn't understand the theory which didn't help. Apart from the note taking problem the lectures were cool. We used to be given a mid lecture question, and that I enjoyed.

After the 22 lectures we had a different lecturer! This signalled the end to me having to copy up any notes at home. :D The great thing about the weeks to follow was that we kind of learnt about the same concepts from the first weeks but generalised them. In this was way previous concepts which I may not have understood before clicked slightly (i.e. span!). There's not much else I can say about the lectures that followed apart from them being great! I actually looked forward to each lecture and I guess I love taking notes during lectures. There may have been things which I didn't follow at times, but now I was able to go home and read over my notes. So if I did have a problem, I could always ask the lecturer about it. (Which I did- too often I believe!)

I honestly can't think of anything I 'didn't' like about the weeks that followed! The material covered in the last week was probably one of the most important topics, but sadly I didn't follow it [linear transformations and eigenvalues!]. And as the lecturer said, we tend to start revising from the beginning and by the time we get to the last few important topics we run out of time! (happened to me). I think in these weeks I had a certain desire to understand the topics and do the problems, namely because I found the lecturer cool. I used to really enjoy the lectures- especially the stories. :D [The motivation was there so to speak, not quite like the first semester, but it was there!] Nope- I've been waffling and trying to think of anything 'bad' but I can't. I especially enjoyed discussing football with the lecturer- although I probably became annoying after a bit. Hmm, can't really think of any negatives... (I think having done some of the things before may have also made me lazy to a certain extent!)

Might as well move on to calculus and applications. This module was split into two parts- ODEs and mechanics. The only semi-complaint I have is that this course was taught by two 2-hour lectures on a Monday and Friday. This had it's benefits, but sometimes if you weren't awake or didn't fully follow the first lecture you suffered in the second one. It was good since the pace was more relaxed, but if you had a bad day then you (I) were(was) in trouble. However, I think during the first lecturers course the two hours seems to whiz by (apart from when we did oscillations!). I've said it before but the lecturer taught with a real energy about him and that was contagious. I must say that on certain weekends I actually looked forward to Mondays two hour calculus lecture!

I'm quite amazed at the turn around in my attitude to this subject. Not the module but the course content. This turn around is what is making me want to do fluid dynamics next year, but it's too risky! It's funny how when you look back onto events and other such things, the first things that you tend to remember are the things you didn't like. (i.e. the note making in linear algebra!). I can't think of anything bad about the whole calculus and applications course.... but wait, if I strain a little something might pop up for mechanics! I've had really cool lecturers this semester, and really cool supervisors as well. That has made a huge difference- especially the supervisors!

Heck- how could I forget! The worst thing possible, in the first six weeks, has got to be not getting 'the quid' from the lecturer. :D Oh yes- that quid! (I'm going to have a fun time when I'm old with my million odd cats. :o ). On a more serious note, (taking aside the 'no quid' thing), I found the lecturer awesome. He even made oscillations- my worst topic- seem less ugly, by bringing his own precious mug in for a demonstration. I'd be lying if I was to say that I didn't want 'resonance' i.e. the mug to break! Did I just write that down... erm... 'you didn't see a thing' (Madagascar style ;) ). The fact that I understand this whole oscillation business and SHM(!) is maybe what is making me more happy. However, before anyone gets too excited, I probably still won't be able to answer the questions! I really enjoyed this module and looking back, it made a lot of sense. (I did apologise to the perturbation method before right?)

Is it that obvious that I'm trying to delay talking about mechanics! I wasn't actually, but since I actually enjoyed this course I want to write more (than normal!) about it. My problem with mechanics was that although I enjoyed learning about the concepts, it wasn't clicking. I couldn't answer the questions and if you were to ask me about angular momentum I wouldn't know. Now the one thing that probably caused me problems in this course was VECTORS. My posts complaining about SUVAT equations and many other things were due to me overlooking the fact that we now employed vectors. I'd done all this resolving forces business in college but without using vectors and so it took me a while to actually see my mistake (I left it till very late).

Our mechanics lectures always tended to be good. Apart from the time I was having a bad day I enjoyed them. The best ever lecture had to be when we talked about anti cyclones, cyclones and what not. Seeing mechanics application to the 'real world' is probably what interests me more, and understanding the concepts. My understanding of mechanics is pretty 'duh' but it's a fun subject. This is definitely a complete turn around to my previous attitude of 'hating' it, which I welcome and is probably down to the lectures. And guess what- angular momentum no longer scares me! The lecturer was really friendly as well, and helped me on more than one occasion. Do you think lecturers are all trained to not show their annoyance at beans like me?! :D

For a second I had thought that I'd mentioned all the modules I took in the second semester. I seem to be forgetting one- Sequences and Series. Well, it's been a journey and a half with this module and I think, had I not started going to the Dr C's example classes, I'd safely be disliking this module and probably wouldn't have had the little understanding I have now. I know my problem and what probably makes me more dumb is that I don't try to overcome this problem. Actually this time you could say I did attempt to overcome this problem since I had consulted Dr. C about the problem. My problem is that if I don't like lessons or lectures of a particular subject or module, I tend to erm... hate and do badly in them modules. Well I might recover the ship and scrape a pass, but my understanding of that subject is rather poor.

This happened, firstly in English lessons at school (until we got a new awesome teacher), then Physics lessons, which sadly I never did get to like. I could blame my teacher but that's stupid of me since it was partly my fault. I reacted stubbornly to not being allowed to ask questions, and although I never disrupted lessons I just used to sit and doodle. (And whenever I got the chance outside lessons, I complained of hating Physics!). I also didn't particularly like stats lessons at college, since there was this group of students who 'bullied' the teacher and never let her teach. Rather than disciplining them on occasions when they did step out of line, she tried to speak over them. I didn't 'hate' the lessons, but I disliked stats. This dislike continued into university and I hated the stats module during the first semester. I hated it and that is the only module for which I've missed more than one lecture! I had my reasons for this, but although I got books from the library I never got stats.

So it seems that whenever I do find myself in them situations, I just end up winding myself up and not doing anything positively to overcome my troubles. It's my fault for being highly dependent on teachers, but I should have a backup plan! Thankfully for sequences and series I did have such a plan and it made a huge difference.

I don't really know what to say about this module since all semester I've been saying a lot on it! Dare I say too much, but I think my post 'Analysis?' sums things up nicely. Especially the bit that books don't give you motivation. Having read the 'In praise of Lectures' document again I'd say that I really enjoy lectures and *makes sure no one is looking* and look forward to attending most of them.** Consequently what probably happens is that I don't like the modules whose lectures I don't like attending, and so if I don't have a back up plan I do badly. As that document said, and I was surprised to have made the link myself in my lame artist post, lectures enable us to see the masters at work. "Mathematics textbooks show us how mathematicians write mathematics (admittedly an important skill to acquire) but lectures show us how mathematicians do mathematics."

Call me sad, but in my second semester I didn't miss one lecture. I even persevered and attended all the sequences and series lectures, when at times I didn't want to.


And there's where I'd left the post (I'm typing this today!) I think attending lectures or lessons makes a big difference and that's how I learn. I mean, I know we get loans to pay the university, but we have to pay them back one day! Before I do end this post, MATLAB has to have a mention! I think the final score in that match has to be 2-1 to beans. It has to be... well what do you reckon? I've probably forgotten most commands (even the diary one- was it diary session1.txt ?), but I did manage to hand in all my coursework that required its use.

So to conclude, (like I did last time!), I finished semester two with the blog intact and many more maths books (at least 10, thanks to the Tweenies as well), however I didn't really want the year to finish. My first year couldn't have gone any better- I made good new friends and met some cool lecturers. Most importantly my aspirations for studying maths were soaring. I think the holidays have dampened my mood about maths, but that's because of circumstances. There were certain things that I should have done but didn't, so let's hope that next year will be just as good as the first, if not better! (I hope to do the things I didn't do you see). Sadly the mss building and it's stairs will be longer be available, but I'm sure the stairs in the Sackville Street building will be a good substitute.

*I was going to make a new post but this seems a nice place for a little something. I had a dream last night in which I attended three lectures. We started of with a lecture at the university and then Milo, Bella, the lecturer and myself were in n13 (mss building). The lecturer was someone who I had never seen in my life-ever. I started talking to him and learnt that he was from Brazil! We then talked about football and maths, but then it was time for 'the next lecture', which seemed to take place in my primary school! The year four class is designed stupidly and I found a seat where I couldn't see the board, but that problem was quickly solved. Straight after that lecture we had another one by a different lecturer and it was about Hercules! Well we worked the title out by playing hangman... weird. I do remember enjoying it though and after the last lecture we all hurried back to the computer room to find out which lectures we had tomorrow- obviously we didn't have any and that is all I remember- looking for the timetable! Does this dream describe the state of my mind?

1 comment:

beans said...

Oops- I think I shouldn't have continued from where I'd left it last time. Ah well- that concludes the analysis though. ;) (Maybe a quick skim in the morning will shorten the post!)