I have recently spent many, many long hours on homework pondering theorems of matrices and polynomials for Advanced Algorithms. I think it was a first for me personally to learn so many topics "on the fly" so to speak. I just really wish there were good text books on these topics. If there were I would go buy them. For instance where can I find a good book based soley on matrix operations (such as Determinants, Vandemonde Matrix, Matrix Multiplication).

We got to play around with Determinants of matrices by taking a Vandemonde Matrix as such:

[math] V(x_{0}, x_{1}, x_{2}, -, x_{n-1}) = \left( \begin{array}{cccccc} 1 & x_{0} & x_{0}^{2} & x_{0}^{3} & - & x_{0}^{n-1} \\ 1 & x_{1} & x_{1}^{2} & x_{1}^{3} & - & x_{1}^{n-1} \\ 1 & x_{2} & x_{2}^{2} & x_{2}^{3} & - & x_{2}^{n-1} \\ - & - & - & - & - & - \\ 1 & x_{n} & x_{n}^{2} & x_{n}^{3} & - & x_{n}^{n-1} \\ \end{array} \right) [/math]

Transform it into :

[math] Det(V(x_{0}, x_{1}, x_{2}, -, x_{n-1})) = \left( \begin{array}{cccccc} 1 & 0 & 0 & 0 & - & 0 \\ 1 & (x_{1} - x_{0}) & (x_{1} - x_{0})*x_{1} & (x_{1} - x_{0})*x_{1}^{2} & - & (x_{1} - x_{0})*x_{1}^{n-2} \\ 1 & (x_{2} - x_{0}) & (x_{2} - x_{0})*x_{2} & (x_{2} - x_{0})*x_{2}^{2} & - & (x_{2} - x_{0})*x_{2}^{n-2} \\ - & - & - & - & - & - \\ 1 & (x_{n} - x_{0}) & (x_{n} - x_{0})*x_{n} & (x_{n} - x_{0})*x_{n}^{2} & - & (x_{n} - x_{0})*x_{n}^{n-2} \\ \end{array} \right) [/math]

And then prove using induction that it equals :

[math] \displaystyle\prod_{0<=j<=1}^{n-1}(x_{k} - x_{j}) [/math]

In the end this homework assignment took me approximately 40 hours in the span of 5 days. The efforts of this homework could not have been possible though without the assisstance of people in ACM who reminded me exactly how to do things like finding the determinant (which I had no idea how to do).

This homework assignment is not the only thing I got the luxury to slave about. I took an exam yesterday in Biology which appeared to be simple. Of course the last exam I said that for in Biology I earned a 15 / 40 grade on, so I am skeptical. I also have a history paper that is due today that I just wrapped up an hour ago titled Bringing Knowledge to the Masses and the Conflict that Develops. It's a cheesy title I know, but how else could I talk about my two favorite philosopher's (Marx and Kant). Then this next week will bring about an 8 page paper about William the Conquorer campaign from Hastings to London. The interesting perspective I get to write about is how the heck he got food because he definitly could not have carried that much food in that amount of distance.

Many of the topics lately that I have to work on are interesting, but it is near impossible to actually learn when I have soo much grunt work to do. So if anyone is wondering "where is Justin?" or "why does Justin look like a zombie?" the aformentioned issues are the pure reason for that. This weekend all I plan is sleep, my wife on the other hand informed me last night that my weekend is pretty much booked. Such is the life of a married, working, schooling, ambitious, late 20-something!