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!!!
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