Haven't read that one yet. The first thing I ever saw a random walk used on was getting any element of an inverted matrix without inverting the matrix, thought that was so great.

]]>Random walks are really a powerful and beautiful piece of math. Along with generating functions and graph theory they are the cornerstone of the new discrete approach to mathematics. I have always been partial to problems 6,7,12,14 on that page.

]]>Also, one very important unsolved problem in mathematics is on complexity: P vs NP

http://mathworld.wolfram.com/UnsolvedProblems.html

]]>Like those fields, but I am just an untalented amateur in them. I took up computing so that I wouldn't have to do anymore math, but discovered I needed more math than ever before.

That is generally true with coding. A piece of code starts out pretty, small and readable, but as I add bells and whistles. it turns into a monstrosity. I also like to get the job done. I find the drive to achieve good structure, boring. Just let it rip, is the fun way to program.

]]>I also like coding, but I tend to focus on getting the darn thing working and less on the structure. Every so often I do something that I consider to be quite nicely designed, but then it ends up getting ugly again as I cope with new features.

]]>One of the reasons that kept me away from posting seems to be that my interests are in computability and automata theory. It is really hard to find a good forum on theoretical computing subjects, and the computer sciences forums you can find are mainly related to programming, databases, etc., not math.

I really like this forum because I can see that people here really enjoys doing math (as I do), and problems are so cool, and allowed me to learn a lot of stuffs that I never see before. I have a background in computer sciences and always liked mathematics, and when I discover computability, automata and complexity, I just simply felled in love of these subjects, and I knew that I had to learn more mathematics, and this site allowed me to do that. And at the same time, I learned to love mathematics in general.

The main subject of theoretical computing that I like the most is computability and complexity issues of computing paradigms (quantum computing, molecular computing, etc). All these paradigms have their own abstract model with so many questions still to answer. Right now, as a graduate student I studying these subjects, from a strictly mathematical point of view, and I now that this is what I want to do for the rest of my life.

Well, I just wanna to write this and see what other people think about theoretical computing in general. Does somebody knows about these topics? As mathematicians (future or present) what are your thoughts about the field? Is there somebody working/studying one/some/several of these topics right now?

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