A rainy then sunny day

Today I had 3 lectures, 2 sustainable development and 1 number theory. I have got a break between the lectures and I was at the royal fort gardens just outside the Mathematics Building. The weather's good and temperature is nice. I was inspired to take some photos of the small flowers around me. They look amazing. I am not sure if you can see these flowers in Singapore but I defintely have not noticed any before along NUS roads.

Ok, what I learnt today for number theory... diophantine equations, in particular, Pell's equation. Prof Trevor Wooley (http://www.maths.bris.ac.uk/~matdw/) is my idol really... He explained things really clearly and also with a sense of humour. Anyway Pell's equation is of the form x^2 - dy^2 =1 where d is a non negative integer and not a square. Basically, we went through 2 theorems. In all, what this lecture brings about is... there are infintely many solutions (x,y) for a fixed d which is not a perfect square. (I am not too sure if I remembered correctly because I didnt copied down any notes and waiting to print it...) The idea is to think of a fundamental solution and from there work out the congruence classes. And guess whats the end? ... The moral of this is once you get a solution, you basically get the rest of the solutions. How intrinsic it is... how amazing!!!

I hope I can attend more of Prof Wooley's lecture... though I miss Singapore too!!!

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!!!

Afternoon Walk

I had the morning doing my wiki project and also some multivariate analysis stuff. Therefore in the afternoon I decided to go for a walk along the clifton suspension. I realised I got to buck up on my photography skills so I took a few random shots! The weather was amazing today and its rather hot! about 11 deg celcius. You must be wondering how mad I am since it like always 30 deg celcius in Singapore. But mind you! I have been experiencing winter for the past 4 months... Anyway these are the few photos during the walk...