Today was a really unproductive day. Only completed half the helpsheet. Went home early to sleep. Slept late last night, or rather early this morning.
Although its an interesting module, it's got too many calculations to be considered a pure mathematics module in my opinion. If I cannot get a graph theory honours project, this will defiantely be my next option. This module is one where I really see the power of mathematics being displayed. It brings all the different branches of mathematics together in a big way, modern algebra, calculus, linear algebra, geometry all come together in this module.
It's pretty interesting now, looking back on some of the lectures, when A/P Loke would say things like, "this is nothing deep going on here ah, just linear albegra, covered in MA2101." And you go, "yeah that's true." But now on hindsight, we were doing pretty advance linear algebra stuff, like finding eigenvectors and eigenvalues to solve problems in calculus!!! If that isn't deep then I wonder what is?!?
Interesting to note, John Nash also made significant contributions to this branch of mathematics, though most people will associate him with game theory, he actually made quite a lot of contributions to this branch of mathematics, topology etc. His Embedding theorem states, 2 real algebraic manifolds are equivalent if and only if they are analytically homeomorphic. I have no idea what that means!
Back to today, was unable to focus on anything man, so only did 2 chapters out of 4 for my helpsheet, then I came home to catch up on sleep. Only now, (at 1am) is my brain starting to wake up, I guess its going to be a long night.
EDIT: Just had to add this, was cracking my brain the whole day to see how I can relate this module to something remotely Biblical. (the fact is... I can't) So, let me try anyway, this may sounds blasphemous, so please don't stone me!
From what I've seen, one of the applications of Differntial Geometry, to higher dimensions, that is Algebraic Topology and Algebraic Geometry, that's when you start working on manifolds (n-dimension objects), is it's being applied to physics. In particular General Relativity. The Holy Grail of physics is said to be the TOE or Theory of Everything. When all the forces can be considered unified. I guess like the modern church, we see so many denominations. We now hear that the new Pope hopes to unite Chrisitians across the world. A grand idea. And wouldn't it be wonderful if all Christians really stood united?
The fact is, we already should be. No matter where you come from, the Gospel is one and the same. And that is the unifying factor. Then why are such a disparate group? Perhaps we've lost the sight of this Gospel that is supposed to bind us together. I once told a younger youth, it is one thing to know what the Gospel is about and another to fully understand its meaning. And once you understand, life is going to be drastically different for you.
(I will leave the differntial geometry out of this one, it's going to be abstract when I draw the relation.)
