Sunday, July 20, 2008

Unstructured Thoughts on Structures

As an undergraduate in mathematics, I know more math than you, but still less math than epsilon. It is for this reason that most all my opinions and thoughts on mathematics are much more romantic than they are useful. I have written papers on different areas that interested me, and I have gone to many different talks and read several papers. Could I come up with an hypothesis and prove it? Probably not, but given my current position in university, I am sure I could find guidance toward starting such an endeavor.
My goal with this blog is to increase readers' interest in mathematics and programming. I plan on talking about many random topics (but not truly random... a very fun investigation to do right there) that come to catch my interest, and I also aim to post solutions to different programming problems I come across. As long as my solutions to obscure problems are archived on the net, search engines will be able to index them and help a programmer in distress in the future.
I plan not to touch such topics as politics, philosophy or my personal life, but as an opinionated person without the motivation to maintain more than one blog, I make no promises about the future.

Back to the topic of this post, "Unstructured Thoughts on Structures." I am sure by now you have observed the unstructured thoughts, but what of these structures? Mathematics is all about creating abstractions to quantitatively and generally describe a problem. Structures, namely algebraic structures, are currently my focus of interest. Group theory, ring theory, field theory and Galois theory may ring bells for some of you. This is what I am talking about. This area of mathematics is so vastly different from anything else one studies before it that even mathematicians like to joke about it not being, "real math." A quote comes to mind from a source I cannot currently recall that is along the lines of, "Now we can solve this problem without any math at all; just group theory!" With this tidbit about structures to pique your interest, I will save more depth descriptions and discussions for later posts.

Welcome to my blog, friends of mathematics and computers.

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