More Determinants

I was at the Joint Mathematics Meeting in January, and their I met an author that I really enjoy. His name is Al Cuoco. He does a lot with mathematics education and his book on Mathematical Connections is a must for any high school math teacher who wants to give their students a hint of the beauty of mathematics beyond high school math. I highly recommend it.

Since he was there, and he was speaking a little bit about linear algebra, I decided to ask him the question that has been bothering me for at least a year. What is the the determinant? Remember from my previous posts that it is not that I don't know how to calculate a determinant, or when to use a determinant. What I don't know is how to explain it to students. How to give it meaning. Al's opinion appears to be that it is most clearly connected to volume. To help prove his point he sent me a graphic which previous appeared on the cover of a math journal. The graphic does a pretty good job of explaining how determinants can be used to find the coordinates in a different coordinate system. It basically comes down to projections.

Pretty cool. I think that I will try to tie together the different determinant thoughts that I have had over the year in one post. I will hopefully be able to add some of the things that I have learned in Al's papers.