January 2, 2016 a very good day to start.
I just finished the chapter “Vectorrekening in vlak in ruimte” , which translates to “Vector calculus in plane and space”. It is part of the interactive course “Linear Algebra” published by SOWISO.
I learned from Hans Sterk (whose lecture notes have served as input and inspiration) that the best way to introduce mathematics is by hands-on experience first, and abstraction later. This method is known from the Karate Kid movie, where mr. Miyagi lets his pupil wash his car and paint his walls before explaining anything about the greater picture. The idea in this chapter is that familiar knowledge of the plane and space (the classical ones, no curved space is discussed here) is used to introduce vectors, computing with them, bases and working with coördinates, inner products and wedge products. In order get an idea of how this principle works, you should know that the wedge product is defined as the scalar multiple of the unit vector that form a right hand oriented triple.
Actually the next chapter will also be of an introductory nature, teaching the student how to solve linear equations and introducing matrices as a tool.
It is only after these two chapters that vector spaces are introduced axiomatically.