Multivariate Analysis and Number theory

Disclaimer: All the mathematical work here are not to be taken for truth since I am still a student only... and hence the title of my blog...

My title is What is Mathematics but I have not post anything mathematical at all. This is so absurd. So today I have decided to post something about mathematics.
To say something about the modules I am taking here - Multivariate analysis(MVA) and Number Theory (NT). It a misfortune when I register for the unit Multivariate analysis, I mistaken it to be multivariable analysis and it turns out to be totally different. But I only have myself to blame. I should have read the unit description more carefully.

In the morning I managed to catch up on chapter 2 and 3 of MVA. Basically, it is on principal components analysis. It is the usage of linear algebra (eigenvalues, eigenvectors, trace, etc) to aid in lowering the dimensionality of the entities being analyse. There are a few ways to analyse it. First we can look at the varience - covarience matrix or the correlation matrix. then work out the eigen values and eigenvectors. by using some steps, we can identify those PC that are of importance and significance. After which, depending on the entities, we can interpret those results. Quite cool right? I hope I am getting all these correct.

It quite wonderful that I only have 1 lecture today. It is a noon number theory lecture. I spent 45 mins to walk to school everyday (3km walk). Its seem mad but I feel its a good way to slim down and clear my mind. But anyway, I was early for lecture so I sat in the LT and look at the blackboard from the lecture in the previous class. It is very famililar. "universe of all sets", "well ordering principle", "well founded sets", "axiom of replacement" and such... ITS SET THEORY!!!
I took this module last semester and I hope it had not fade away from my head.

Thanks Dr Franklin.

But anyway for NT lecture today, I learnt about continued fractions!!! basically it is to express a real number, whether rational or not, as a continued fraction. If you got a irrational number, basically u get a recurring decimal, in this sense, will be a endless continued fraction!!! The alogrithm is not hard to undestand. Youy get to use the ceiling function, rationalise the fraction, inverting the fraction and such!!!

Ok I am tired now. I shall stop here today. I didnt go out to take any photos today thought the weather is nice... WHAT A WASTE!!!