Monday, October 20, 2008

Sleepy Sunday

I hereby declare that I will not complain about being tired tomorrow after having six hours of Maths lectures, including a 9am start (which is followed by a further three hours!). However, I will most likely be complaining that Mathematics (Measure and Graph Theory in particular) are to blame for my current plight.

Today, Sunday, I have been very very sleepy and it's all because of a certain guests fault! Well one of my cousin (who I used to often see in my childhood) came for the weekend (from down South) to see how Pops was doing. Well that was the excuse that was used, but straight away I realised that my cousin just wanted to get away from the South and return to the Northern region of the country again!

I had promised myself a luxurious mathematical weekend (doesn't that sound amazing!) and was not surprised to find myself struggling to motivate myself into working. When I finally got rolling on Saturday, the GCSE student arrived after which my cousin came. Now my cousin isn't just related to myself (!) so I did escape for a while to do some Maths. The brilliant thing about the weekend is that when I do get "into the Maths", time just flies by and my stomach is the only thing that gives me an indication of how long I have been sat at the desk. I ended up working till 12am on Saturday, and leaving my room scattered I had gone downstairs for a cup of tea.

Downstairs the party was in full swing and I was very surprised to find everyone still hanging about and not sleeping! So what did I do? Well the cake that was fast disappearing was enough to make me park myself downstairs and join the conversation. It was nice to catch up with my cousin and indeed there was a lot of it to be done. We actually ended up watching the X-factor highlights and it was only when that finished that we noticed that we all should be getting to bed as our eyes were drooping.

Upstairs what did I do? Stinking, horrible graph theory of course! Isn't that a good thing you ask? NO, for I got into the "roll" again and it was suddenly 4am when I noticed that I had read a sentence more than five times and it was still not making sense! We had done the max-flow-min-cut theorem in the previous lecture and hadn't managed to finish the example of, which is what I was struggling with. We have an algorithm which gives us the answer and the lecturer had claimed that the answer was 31. I can't seem to understand the notation of the algorithm, hence why I didn't get far.

The idea is that we have a network (directed graph?) a source s, and a sink t, and for example we have to transport things from s to t along directed edges which have a (max) capacity of how many things can be transported at a certain "junction" (vertex?). That probably didn't make sense but I don't really get the problem myself. (There's this other thing called flow but I can't recall what exactly that is).

In the algorithm we first define the flow for each edge to be zero. We then construct a set S_1 (according to my notes) and "mess about" with it. I can't construct this set S_1 for my notes make no sense. The lecturer, when doing the beginning of the example didn't seem to construct the set S_1 and that's why I'm stuck. I don't know what he did. I have tried the damn problem from scratch but I get 41 for the max flow which is clearly not 31. If I knew how to construct this set I might just get 31... (roll on tomorrows example class).

So 4am was a bad time to sleep for it meant that I awoke today, Sunday, at a horrible and unreasonable time (which is not for the ears of children so I won't mention it here!) It was 4pm when I had my breakfast but that doesn't mean I woke up at 4pm! (I couldn't seem to eat anything up till that point, and even then my mum had to make me eat....).

Sadly the A Level student (ALS) that came today might have been disappointed. Well I think her emailing me three (somewhat long) questions during the week makes up for it! Domain and range are "okay" but we had inverse functions and I was trying to remember whether the domain of a function is the range of the inverse function. I couldn't remember that, although it still rings a bell, so I ended up drawing some horrible log graphs to convince us both. (Well she said she was struggling with transformations so that should have helped...). This is the first lesson which I hoped would finish early!

I have now figured out how to deduce when ALS doesn't understand something I have said. I mean to say that I now know the "AAAHHH I don't understand" look that the student gives! As I saw this look and said something to help, I mused about how my "AAAHHH - speak English please!" look looks like! I do have a very dumb look (as I have been told), and unfortunately my dumb look is very transparent. (I can't help but frown...).

It's two something am and this post doesn't make much sense to myself. I am awake now due to the silly graph theory problem I mentioned above. It's taken me two days to still get an incorrect answer and I still don't want to give up. After I had eventually put my graph theory things in a pile, I made my "to do list". Well tomorrow has to be devoted to Groups for my test on Tuesday, but after that I have to seriously do some topology and measure theory.

Ah-- measure theory. I'm too tired to say anything mean about that module, for stupidly, when making my to do list, I decided to get my measure theory notes out. And would you believe it, I got into another "roll" until I looked down on my paper to find too many questions that needed answering! I would definitely say that I'm probably the worst learner that you will ever encounter. You see at times some things might be skated over or not defined, and on most occasions I want to know why this is so. Perhaps this is why I'm disliking Topology?

Okay okay, that's enough from me. I am going to be a dead duck tomorrow. :( But on the plus side I haven't worried at all about TGG this weekend, and even a nice email today, which might be able to help me didn't make me worry. Tomorrow though will probably be a different story, which reminds me that at 11am I hope to find the Maths building in it's "raw beauty"! (I'm also going to perform a certain experiment this week - wish me luck).

Perhaps this post should be called Sleepy Monday...

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