I just like this course. It is a definite step-up in abstraction for our engineers. I am noticing this in the first week of class, where all of a sudden instead of having constants of 2 or 5 or -3 or , constants are given as letters , , , and . There’s just this discomfort with that, and uncertainty in doing mathematics that they otherwise already know how to do.
Later in the semester, when we try to get them thinking of a matrix as a matrix rather than a specific matrix, understanding concepts like linear combinations, vector spaces, and basis, things get tougher. And all throughout, we will look at the proofs as well as at the computations. This requires some serious intellectual growth over the course of the semester, and coupled with that is always personal growth. Any challenge faced changes us, whether we conquer it or it conquers us.
The funny thing about this class in linear algebra, which can seem so abstract to my engineers, is that this is one of the most practical classes in terms of how things actually get computed. The example I gave them is finite element analysis. Most have heard of this. But understanding the basics of finite elements means understanding a hell of a lot of abstract linear algebra and function theory. Sometimes doing the practical requires the abstract.