>The first time, I spent in a linear algebra course (Kaiserslautern, 1986) >introduced sets, groups, rings and fields, modules and then vector spaces. >(in that order)
Odd. We did sets and then groups in algebraic structures. We touched upon rings, I think, but I don't remember what they are. Have no idea about fields, if they're not vector fields, which someone already said they aren't. Never heard of modules.
We did vectors, then vector spaces, then subspaces. Then spans, dependence, bases, matrices, determinants, then eigenvalues and vectors. It's odd because Schaum's Outlines does it in a different order. And Cliff's does an even different order.
>By the time we met vector spaces, the notion of image and kernel as well >as the proof of the first homomorphism theorem
"Homomorphism theorem"? Is this what's called "Dimension Theorem" now?
>But nowadays nobody needs to be afraid of modules in a linear algebra course, >unless it is only a MMC (Matrix Manipulation Course). >
What are modules? And why are they related to marix manipulation? BTW, I, for one, would love to have taken a linear algebra course that was all MMC. I love the stuff!