Anonymous wrote: > > email@example.com (Dave Rusin) wrote in message news:<firstname.lastname@example.org>... > > [...] > > right this minute, define what a vector space is? > > > [...] but I think I may finally be getting a > grip on what a vector space is: > > It's a group of vectors that can be multiplied by any scalar and/or > added together in any way, and whatever possible combinations that can > result is the "vector space" for that group of vectors. This is how I > understand it. [...]
Then you're wrong. This waffle is next to useless. What is the precise definition? If the precise definition has words like "abelian group" in it, then what is the precise meaning of them? And so on.
Read David C Ullrich's reply to your op, it's good advice. (Which will also apply to other pure mathematics courses.) Having memorized the definitions, begin to understand them by constructing examples for yourself. The true understanding will come when you read proofs of theorems and appreciate that the definitions were phrased in just the way they are so as to make the theorems true.
Also, what book do you read? If it doesn't have good hard exercises in it, then read another.
-- G.C. Note ANTI, SPAM and invalid to be removed if you're e-mailing me.