Use a computer!

I remember taking a class in school called numerical methods.  It was about using computers to solve complicated mathematical problems that would be too difficult or time consuming to solve by hand.  One day the professor was going over different ways to solve a particular type of problem.  At the end of the lecture, he asked, “If you were in industry and you had to solve a problem like this, which method would you use?”  The students raised their hands and started naming the different methods, “…Newton-Raphson method… bifurcation method… so on…”  Then he goes, “NONE OF THESE!  You use a computer!”

And that was basically the whole class.  Each week we would get a homework assignment that we had to solve by hand, using pencil and paper.  Then we had to write a program that would model the problem, and after that we had to use the professional software to find the solution.  Finally we had to draw a graph comparing the results of each method.  So in essence, every week we had to make a graph showing how the computer was smarter than us.

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