Tuesday, October 21, 2008

Wakey Wakey Mr. Alex!

The title might ring a bell for those of you who have watched Madagascar, and if you haven't watched it then what are you doing reading this post?!

I know for a fact that I am going to have the lines from that movie in my head today, which isn't too bad a thing I suppose. Well rather than having silly group theoretical facts, at least the movie lines will keep me amused! (Yes, it seems I am easily amused at times...).

I did say I wasn't going to complain today and indeed I'm not going to "complain". Instead I'm going to make a few observations about Monday 20th October 2008. How does that sound?

Now I'm quite lucky to have made it on time in Manchester today, otherwise like Arthur I would have missed my first lecture. I say lucky for a very good reason as my 9am lecture happened to be the graph theory one. Last night, or indeed very early on Monday, I was struggling with the max-flow -min cut algorithm and mentioned my problem about the set S in yesterdays post.

I had to work hard to stop my mouth from flying open at 9am, and staying open, for the lecturer seemed to finish the example at the start of the lecture and he actually labeled the vertices that belonged to the sets S_1 etc (i.e. what I had been struggling with). I had my suspicions for a second but I'm quite sure that this lecturer has not come across my blog. Call it a Monday feeling, but for a very long time during the lecture I mused on how weird a coincident this was, for everything I had mentioned yesterday was now resolved. (I won't believe you if you say that this was no coincident...).

During the lecture I didn't sleep and during the example class I was also awake. You will be pleased to note that I had made a mistake in my calculations yesterday, well three mistakes to be precise, and 31 was the correct answer. I did check my answer before going to sleep last night but that is a lesson for me to learn: leave the checking of solutions till the morning.

I have now declared war with Dr. E due to his Topology lectures, but he doesn't know this. Dr. E is a cool lecturer and I have nothing against him. Topology is quite "cool" too and I have only slight reservations against it. What I have issues with is the example classes timetable and how it is utilised.

The Topology lecture was unfortunately the one in which I ended up sleeping. I don't mean eyes closed sleeping but eyes open sleeping. It wasn't the best of sleep I must say and I equally didn't get a word of the lecture. Hausdorff spaces were mentioned and I am meant to remember that it is spelt with one "s" and two "f"s, so I was awake for parts of the lecture in my defence! Actually that's a lie. I honestly can't seem to stay alert and concentrate for four hours in a row. Next week I am going to have six bloody hours in a row on Tuesdays! At least on Mondays I have four hours and then an hour for lunch before the final two hours, but next Tuesday it will be six hours in a row. (Which leads me to the decision that I won't ever be attending the Coding theory example class for I need a lunch break).

You see Dr. E always ends up using his example classes to continue the lecture, which I understand from his point of view is quite a good use of the time. However I think it is rather unfair for it forces one to stay for the example class, even though I don't want to because I haven't done any problem sheets yet. Yes example classes are "compulsory" so they say, but we all have our ways of learning and if I haven't attempted the problems before hand I don't like going to the classes. Sigh. I have to declare this mini battle for it is the only thing which will provide me with epsilon comfort. (Dr. E intends to continue with his "clever plan". Pfft). I wasn't grinning back when Dr. E was obviously amused at my shell shocked state today.

After Topology I had some lunch and then a 20 minute nap in the AT building cafe (I seem to making a habit out of this...). This was a very bad thing to do, for I woke up feeling worse than ever and with a very sore arm too. I don't know how exactly I had positioned my arm, but upon waking up I was a three year old wanting to go back to sleep. (And we all know how they tend to behave....). Group theory was a blur and Applied CA was once again a revision lecture which was great! (I actually remembered something from last years course so I didn't have to pay much attention...) :D

Now this post is sounding very "tired" to me. Am I allowed to forget trivial things when I'm tired, for it seems that I had forgotten something which I shouldn't have. I gave the receipts of the refreshments I bought to Dr. C on Thursday/Friday and had forgotten to pick the money up. He actually made me believe that I hadn't given him the receipts! This had sent me into a mini panic for upon invading my wallet, I could only find two receipts. Meh. I forgot this fact because I forgot whether it was Thursday or Friday. I'm sure it's Thursday which is why I had forgotten, but this doesn't mean that I'm going to let Dr. C of easily for this!

It seems that Dr. C and myself were waiting for the other to book a room for week 7 and neither of us did anything. Dr. W did leave a note at the office so I'm not going to panic just yet, however if we don't get a room then it's all Dr. Coleman's fault! (So I expect you to send not nice emails to him about why there are no student Galois Group lectures after week 6! I can help if you are stuck for not nice words... :p). I am beginning to worry that one of the students who has volunteered might let me down. Namely due to his comments about wanting to attend the UGSSLC meeting. I understand he has made a commitment towards that, but he also made a commitment last year to do a TGG lecture.

As soon as I got home today I went to sleep. No food and no emails but just sleep. I only slept from 5:30ish to 10:30pm (ish) as some people seemed to have forgotten that I sleep on the floor, as they eagerly increased the volume of the TV downstairs. Meh. I haven't actually done much revision since I've been awake for once again my other modules keep on calling out to me! I looked through my notes and saw a lot of ugly lemmas and proofs for things like the centraliser of the group etc.

Now what I need to remember is that Lagrange's Theorem says that the number of cosets of H (subgroup of G) in a group G is found by "order of G divided by order of H". And if that number is not an integer, then H is not a subgroup of G.

Now one natural coset is: e.H = H (as e is always an element of G by definition), and to calculate the other cosets we take an element g of G not in H (and not in any other cosets we already have) and calculate g.H. We do this because the union of all cosets of H in G is equal to the group G, and two cosets are either equal or disjoint.

Lots of messy stuff in the above sentences, but I'm having another nap now before I do the dummy test questions so I needed to see what I remember. By the way, I've been sloppy and not written what coset but the above is true for right and left cosets. Note to self: if g \in G is on the LEFT of H, i.e. g.H then this gives a LEFT coset! And if g \in G is on the right of H i.e. H.g then this gives a RIGHT coset. In all the questions that I do on cosets, I refuse to read the question and just calculate the left cosets!

That's enough actually. My heads starting to hurt. I am becoming quite good at not checking my emails anymore and not running around like a mad hatter around the AT building. Hey - I like that: mad hatter. Mad mad mad.

PS: More on the AT building tomorrow.

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