Quickpost: Updates

Fuuuuuuh!!!! *Buang habuk kat blog*

Just nak update yang yaya nak gi melancong esok.. Balas dendam sebab masa degree dulu yaya kena tinggal sedangkan ahli keluarga yang lain pergi melancong ke Hong Kong.. Doakan perjalanan kami selamat dan lancar.

Yaya dah graduate tau.. Sampai semalam, tengah menunggu result application for postgrad studies in math. Result patutnya ambil masa dua bulan, that means by the end of december or early january.. Just now i checked, my application is successful.. Alhamdulillah...
I think I want to write about my application process sometimes, because it was a hectic one..

That's all I want to write about..

Till then,
Ya Allah, sejahterakan Malaysiaku.

Quickpost: Final incoming!!!!

Ja harou!! Yaya-desu..

I would love to say that my first paper is in next year, but I can't... In fact, I have two papers this year, and another two will be held in 2016. Wish me luck folks.. I hope that this is the last battle in my undergrad life.. after that we do postgrad studies.. Long-life learning they said..

Till then,
Yaya

P/s: I think I'm going to post something about the presentation i did last week, but I haven't manage to switch on my laptop..

Boku no FYP

First of all, I am really sorry. I am suppose to post this yesterday, but i didn't. This is because, around 9 pm yesterday, i started to have double vision. I think my mind is really tired because of the sleepless night before. So i decided to go to bed early, abandoning all the desire to practice my presentation. Furthermore, I also had slight sore throat at that time due to practicing too much maybe.

Without further delay, let's take a look at my topic: The on-line Ramsey game.

Let's start with some preliminaries. Consider the following image.

It is an image of a network that mathematicians called as graph. It is not necessarily in that shape. Each of the black dots is called as a vertex, while each of the black lines is called as an edge.

So, i think we are ready for the game. First we let G and  H be fixed graphs. They may be a triangle, a square, the graph shown above, or simply just an edge. The game is played by two players called as Builder and Painter. It is played on a an empty graph with unbounded set of vertices. In simpler words, on a clean sheet of paper.  Builder's job in each round is to build an edge, and Painter immediately colours the edge built by the Builder with either red or blue. Builder cannot build two edges using the same two vertices and Painter can never change the colour that she has chosen for a certain edge. In the game, Builder wants to force Painter to create a red copy of the graph G or a blue copy of the graph H from the edges presented by the Builder, while Painter needs to avoid from creating such graphs for as long as possible.

We define payoff as the number of moves spent until a red G or a blue H appears. It is much like a salary that Painter receives when she is done with her job. Obviously, Painter aims for the highest possible payoff.

There is a theorem (Ramsey's Theorem) that guarantees Builder's victory. So in this area of study, we want to find the smallest number of moves such that Builder will win the game no matter how Painter paints the edges. Such number is called as the on-line Ramsey number. It can also be defined as the smallest possible payoff that Painter may obtain, no matter how Builder chooses the edges to be presented to the Painter.

Since Builder is guaranteed to win, let's put a twist on the game so that Painter will be more motivated to play the game (I have a friend who gave up playing since she sees that she can't win the game). For simplicity, let the on-line Ramsey number for G and H be denoted by r. Then, we just play as explained before, but the game will only last r rounds. If Builder can force either a red G or a blue H in r rounds. But if neither red G nor blue H appears until the end of the game, then Painter wins.  In this case, Builder is still guaranteed to win, but he needs to know precisely the winning strategy. So if two layperson are playing the game, then, I think, the game can be quite fair.

Another twist of the game is a version crossed my mind when i have nobody to play with me. Well, that is the case when you are alone or other people fed up since they cant win. I play the game as the Builder, while the role of the Painter is given to a fair coin. First Builder chooses an edge, then he flips a coin. If it is head, then colour the edge red, but if it is tail, colour the edge blue. This version of the game is useful when you want to test your strategy because proving your strategy with brute force will lead to many cases. (Argh!! Just imagining the cases is enough to make me frustrated!!).

Till then,
Fatin

p/s: I tried to avoid grammatical errors. Notice any grammatical error?

Quickpost: Memorisation technique?

When you've created a sentence to help you memorise a sequence of words, but you have to use the actual sequence of words to recall your sentence. Hmmm.. Typical Fatin..

Till then,
Fatin.
p/s: Drank a cup of coffee at 9pm, can't sleep although it is already 4 am.. Help!!

Quickpost: Test!!

Hello everyone,

I wanted to type about my final year project, but I can't, I have a test tomorrow. Not a math course, so I have to spend some time reading silently and sleepyly.. I'll try to type about my fyp tomorrow, because Friday is my presentation day.. So before I present, I want to at least explain what I've been doing for the whole semester.

Till then,
Fatin.

Testing

$\forall$ $\epsilon$ $\geqslant$ 0 $ \exists$ $\delta$ $\geqslant$ 0