>David: > >>Actually from what you say here it seems pretty likely that >>you do know what linear independence _is_, but the >>way you're stating the definition is totally wrong. > >Right. That's my point. I *do* know the definition, but the phrasing always >gets me.
Aargh. If the phrasing gets you then you _do_ _not_ know the definition!
> It's like this, probably, for a bunch of the main terms. Still, you >say the number one problem is that students don't understand all the >definitions. Is my understanding of "independence" then not good enough?
If you can't state the definition coherently, which indeed you can't, then no, your understanding is not good enough to be able to write proofs.
Really. A feel to nice for how. To get it, so if you have to ride then to it, otherwise. So wit unless rain time less.
(What, you didn't follow that last paragraph? I was trying to say "it's a nice day here in Oklahoma". I know what I meant, it's the phrasing that always gets me...)
> Or >is it? > >> Next time you take the class try actually >>_learning_ the definitions of all the important terms, >>_precisely_. > >OK, there's my answer, I guess. I've always had courses where professors >emphasized that we don't have to memorize definitions and terms word for word, >whether it's a foreign language course, a social studies course, an economics >course, whatever. It seems like definitions are usually just things that you >have to get the basic jist of. It's sort of unfair that math is different and >no one warns us about it.
Math _is_ _very_ different in this regard. I certainly warn my students of this, rarely helps. Your professors are just assuming that you _realize_ that you need to know what the words mean...
> But, like I said, I won't have the opportunity to >try linear algebra your way because if I fail, it's my last math course ever. >I think there may still be hope for me....