Completion, Hooray!

I will begin by issuing the following statement: British police officers do NOT lynch minorities, I said that only for comical value and I apologise for the offense I may have caused anyone.

On a better note; I have pretty much completed my history project - I am only left with writing an abstract for an oral presentation I must give in the summer. I fear that I had exceeded the word limit so I had to reduce it a little bit, but I think it's fine now. Through my research on the theory of equations, I have come to the conclusion that the question of solvability is still open. Even though we've inherited a beautiful theory from Galois which provides us with an algorithm enabling one to determine whether or not an equation is solvable by radicals. However this algorithm can, at times, be difficult because it relies on knowing the roots of the equation. He even admits that his methods are sometimes impractical. One might wonder if one can determine the solvability of an equation by simply looking at its coefficients, or perhaps this is not possible and what Galois did was the best that can be done.

Nevertheless, I have discovered that Galois Theory has a much greater importance that is not restricted to the theory of equations, from it emerged Group Theory and more generally the study of algebraic structures. If you read his work (or at least a translation) Mémoire sur les conditions de résolubilité des équations par radicaux, you will find that most of the results have no mention of equations - perhaps this was his intention. In his memoir he writes:

"Jump above calculations; group the operations, classify them according to their complexities rather than their appearance; this, I believe, is the mission of future mathematicians; this is the road on which I am embarking in this work."

I probably won't upload my project yet, as it has yet to be graded - but I will show people on an individual basis. Anyone who wishes to see it, then you may request to, but you will be required to undergo intense screening in order to determine you're not a fellow classmate nor an associate of a fellow classmate (even though we all have different projects to do).

Now that my project is essentially complete I must proceed with other work I planned to do over the winter break. Such as my combinatorics homework (which I had completed most of before the break begun) and also I intended to learn how to use Matlab before my classes in computational linear algebra begin, but now I only have about 3 days to do this. It matters not though, I already know how to use C++ for numerical problems, and so I should pick up Matlab relatively quickly.

There is still no news of my bicycle. I was struck by the sirens of a police car, speeding down the road, hoping that they had found a lead on my case, but I received no call later that day - so I figured not. I honestly don't think my bicycle will be returned now; I have come to accept this.

I will now make my way into campus to continue my studies, so until then Sayonara!