>email@example.com (Dave Rusin) wrote in message news:<firstname.lastname@example.org>...
>> Our students "do well on the very first exam" because that's the part >> of the course where we warm up with techniques for solving linear >> systems of equations and such topics. But our LA course is also our >> students' first course in which abstractions, axioms, and proofs play >> a significant role. They often stumble because (among other problems) >> they don't realize they need to _memorize_ definitions _precisely_. >> So you can do a little self-assessment here to figure out whether >> what you're missing is bits of topics or the core idea: can you, >> right this minute, define what a vector space is? >> >> dave > >Dave, this may be my problem. I did decent on the first exam because, >like you said, it was solving linear systems, echelon form, linear >dependences--easier stuff like that. I've always been a little >confused with the concepts, but I think I may finally be getting a >grip on what a vector space is:
<Just some philosophizing:>
That's familiar: You feel comfortable with specific examples but can't see the abstraction, the "structure" behind. In German there is a saying meaning roughly: "You can't see the forest because of all the trees"... As mathematics is the "science of structures", you will have to get to this point. But it's a worthwhile goal to pursue because it's really uplifting if you finally reach that point - As the old greeks said: "Heureka!" I finally found!