Notes on Matrices

Extract

It is very desirable when teaching mathematics not merely to state definitions and prove theorems, but also to show the train of thought that would lead us naturally to these definitions and theorems. Students are thus enabled to see mathematics as an alive, continuously developing subject. They are reminded of the interdependence of the various branches of mathematics; the memory of each branch is kept alive in the students’ minds, because it is continually being revisited, and the student finds it easier to remember results when he understands the thinking that produced them. This approach also encourages a student to try to carry the train of thought further and to make his own discoveries.