Covariance and contravariance

Physicists seem still to be taught about tensors as being, essentially, multidimensional arrays with special transformation rules which must be learned by rote. So I wrote a document which tries to present a more useful approach.

The aim of this document was to present a more modern, ‘geometrical’ approach, while not requiring too much background in differential geometry. I don’t suppose anyone read it when I posted pointers to it on reddit, and certainly no-one will read it now, but here it is¹.