Sunday, April 01, 2007

Bye Bye Blog. (Maths: Reason -1)

Some neat 'alliteration' to get this post started.

Now I have many reasons for doing this, which may seem stupid to you, but they make sense to me (you probably might have to be slightly forgiving!). I've been kidding myself by saying that this blog hasn't been a distraction. The only thing that has changed this semester from the previous one, apart from new modules, new lecturers etc. is this blog. It did take me a while to realise that I was missing the first semester lecturers (need I mention names?) but after I'd tried to 'get over that' so to speak, I still never did get back on course properly. I've not been giving it my all. The only subject which I really have been trying harder in is 'Sequences and Series' but like I said, I take one step forward and three backwards. Maybe it's because Linear Algebra is 'boring' or maybe it's because I know that I'm not working at the level that I was during last semester! I don't know whether or not it is actually a good thing that I had done some of the work covered this semester in college.

Why am I singing a different song altogether now? Well like I mentioned in the first few posts of this blog, I revised the most for my Calculus exam. Now this was because like this semester I'd given myself the false security that 'because I'd seen some stuff before' revision wouldn't be too difficult. The same applied to stats as well. The only real subject that I enjoyed doing during the semester was 'Sets, Numbers and Functions', it was something new and I really felt that 'buzz' after I understood bits of it. Honestly, I did revise for it, but most of my revision was of the stuff we'd done in the first six weeks. This was because after the first six weeks I started making sure I understood the stuff as we went along- not leaving it to the holidays. Whereas the mistake with calculus was, that although I had done some stuff before, the new stuff depended on the rusty foundations of the old knowledge which I'd assumed that I'd remembered. Sigh. I've lost my rhythm. (ask a cricket bowler what that feels like. Or ask a darts player maybe. Knowing that you can do something but for some reason you're not- well that plain sucks).

It's not that I don't care about my studies, but I've done Linear Algebra and now want to do something else! I guess this is also a moan about exams as well. Why do we have to be examined. Ok, I'm probably kidding myself here, but as a lecturer said (as I enquired about teaching), the worst part about the job is marking exam papers. Do I need to state the bleeding obvious solution to that? Before it actually seems like I've lost yet another screw, I'll stop going on about this! But seriously, yesterday as I tried to miserably prove something about the rank theorem in Z_p, I decided to look through one of the number theory books to see if I could find some inspiration. I didn't. Find inspiration that is, but what I did do was spend ages flicking through the book, looking through stuff that I'd done before and stuff that I hadn't. Now, I was wise - I didn't try to learn anything new - but I couldn't help doing the question on congruences (about finding the final decimal digit of: 1! +......+9! + 10!, without using a calculator!). I did it eventually, but it took me a lot of self control to put the book down. By the time I had put the book down, I realised that it was too late to do any more Linear Algebra.

The previous posts have been of me complaining and moaning a lot, which I'm sure is a dull read, but I can't help it! (apologies). The thing is that I have this Analysis book and it's got an introduction chapter about 'Numbers'. The second chapter is the one I really need since it's about sequences, however I thought that I'd check the first chapter out. Here I learnt about the 'Real Numbers' and the completeness axiom. Something about the fact that the rationals and real numbers have all the same properties, however the one thing that differentiates the two is this axiom. (I read this a while back, but it boils down to not been able to order the Real Numbers I believe{don't quote me on this!}). Anyway, I read this and thought 'Hmmm, that's interesting'. The same thought passed by as I read something about a dude named 'Archimedes'. Now I can't remember much else, but I do remember stopping myself from reading any further. This seems stupid, but reading all that interesting stuff was indeed cool, but it wasn't helping me! Unfortunately it was distracting. I can't help but get carried away. Some people would have been able to skim read the first chapter, but no- I had to have a pen and paper and read it properly.

I know I'm probably being impatient- wanting to do things before I can, but maybe I'm compensating for the reading I should have done before hand? I feel like I've missed out on my opportunity to 'read around the subject' and now as I try doing that, I can't help but feel that I should rather be spending my time studying my actual modules!

Ooops got carried away again- you're probably glad that's not going to happen again. I should have taken things slowly with this blog (I now realise this), and maybe I'm jumping from one extreme to another- dare I say oscillating- but I've got to make this extreme jump, before I can come to a final 'constant velocity'. (them words illustrate that I'm indeed a very sick bean today!). There I have shown my problem in general, however until this blog came into being I was doing very well in terms of exercising self-control. My poor psp has been neglected, my football has lost its air, pro evolution 6 has been calling to me, but no I've resisted because maths is more important than them things. But then this blog is suddenly challenging 'my maths' (the irony!). Of the two things only one can stay I'm afraid.

I'll end by quoting Bilbo Baggins (from his birthday speech), "I regret to announce — this is The End. I am going now. I bid you all a very fond farewell." You could be either over the moon to read that or not. Whichever it is, all I'm going to say is that remember this. I don't want to be mean, just cryptic. Once again, what was meant to be a two line post, has become two pages long! [Didn't know where to mention this but it seems I'm missing 'my lectures'- I seem to be dreaming about them is the reason for that!] So, I leave you with this advice for when you're crossing the road, or any general path you take:

[BTW 'Reason -1', is actually exams, and having to do hard core revision for them in only a few weeks! Give me Bernard's watch and I'll be a happy bean, but otherwise....] [Or maybe do you think I should have called this Reason 1 again? You know I started at 1, then went to 2, but then this is a negative reason so I've gone back to 1 now! Nah that's pretty confusing I guess!]


egm said...

You chose the perfect date to share this decision :) N'ways, all the best in your mathematical endeavours. Life is full of tough choices, so you need to do what needs getting done. It was fun reading you! Be back in the summer when classes are over though! And don't forget to stop over at mi casa from time to time...

beans said...

Erm.. Hey! Have you by any chance read my latest post? I wasn't sure whether you'd worked it out, hence me replying until after that post!

It's been good knowing you, all the best for the future. ;)

(oops forgot that I'm not going anywhere!) Sorry :o

egm said...

Haha, I wasn't really sure. Thus my start line about choosing April 1st as the date for your decision :)

Jake said...

finding the final decimal digit of: 1! +......+9! + 10!, without using a calculator!

Well, 1!+2!+3!+4! = 1+2+6+24=33
and 5!,6!,7!,8!,9! and 10! all have the factors 5 and 2 and hence all have the factor ten hence
n! \cong 0 mod 10 for n=5,6,7,8,9,10

5!+6!+7!+8!+9!+10! \cong 0 mod 10
so Sum_1^10 n! \cong 33 + 0 mod 10

hence the final decimal digit is three

beans said...

egm: I wasn't sure whether you were sure as well ;) Hehe, but I thought that you were sure, so I thought of not replying until the other post!

(confused? :D)

Jake: yep that's what I got as well! woo hoo.