Math for Game Programmers 04 – Operations on vectors

In my Danish high school we covered the algebra and geometry of vectors in two and three dimensions in our second year. The high school mathematics curriculum in Denmark is ridiculously unambitious; I'm certain my American friends covered more than this in their high school AP classes.

There's a compelling argument for withholding the abstract theory of vector spaces and linear maps from non-mathematicians until multivariate calculus. Linear maps (as approximations to differentiable maps), determinants (as Jacobians measuring volume distortion under pullback), eigenvalues and quadratic forms (as Hessians measuring curvature with eigenvalues as principal curvatures) all make prominent appearances and become easy to motivate geometrically.

I learned about them in trigonometry and again in precalculus and again in linear algebra. Also, physics 1, but that doesn't count. The stuff in that post is exteremely simple.

In the UK, we did vectors, matrices, calculus, discrete mathematics at A level (16-18 years old). I think they still do that sort of stuff now.

I did specialist maths during my high school years (~16-17 years old) which was quite involved and covered vectors and lots of other interesting things. One of the few good things about high school in Australia. Oddly enough the maths in Computer Science at a University level was much easier.