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Dec
26
accepted Looking for simpler proof of “well-definedness” of basis subtended by points in “general position”
Dec
26
awarded  Great Question
Dec
26
revised Looking for simpler proof of “well-definedness” of basis subtended by points in “general position”
added 11 characters in body
Dec
26
revised Looking for simpler proof of “well-definedness” of basis subtended by points in “general position”
added 2 characters in body
Dec
26
comment Looking for simpler proof of “well-definedness” of basis subtended by points in “general position”
I don't think that $1 \Rightarrow 2$ holds; consider for example the case where $p = 1$, $x_0 = (1, 0)$, and $x_1 = (0, 1)$: $\{(x_1 - x_0)\}$ is (trivially) linearly independent, but no set of $\alpha_i$'s can satisfy (2).
Dec
26
comment On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
@Dunno: indeed; I'm in awe of those who can teach well. It seems to me that to teach well one has to be able to see a subject (that one knows very well) with the eyes of someone who is encountering it from the first time. I don't know how anyone can do this, but I've known people who can do it, or come very close to it, and it seems to me almost miraculous. (It goes without saying that I'm abysmal at it.)
Dec
26
comment On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
Wow, thanks for posting this. It's an amazing approach. The reading group in particular; it's a resource I'd not considered at all. Of course, it's not a trivial matter to form such a group and keep it going, but I can see how it would be invaluable. Also, let me say that I'm sooo envious: how I'd love to have a knowledgeable mathematician (even one who was not well-known) as my math tutor, or even just as my math "sensei"... (If I had the $$ I'd hire such a person, of course.)
Dec
25
awarded  Notable Question
Dec
25
comment On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
Thanks once more for the additional titles. Those two are completely new to me.
Dec
25
revised On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
added 19 characters in body
Dec
25
comment On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
Thanks for the pointer to Garrity's book. I confess that I saw it some time ago on my way out from a bookstore, and snap-judged it (basically "by its cover") right into the "for-dummies" category. Now I see that this quick assessment was quite off-base. I'll give it a more serious look. Also, thanks for the pointer to Brualdi's book. BTW, I see that you are a Don Q fan. Teaching oneself math does sometimes strike as a rather quixotic project.
Dec
25
revised On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
added 320 characters in body
Dec
25
revised On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
added 1300 characters in body
Dec
25
asked Looking for simpler proof of “well-definedness” of basis subtended by points in “general position”
Dec
25
accepted Is there a standard shorthand for the set $\{0, 1, \dots,k-1,k+1,\dots,n-1,n\}$?
Dec
25
awarded  Favorite Question
Dec
25
accepted Undergraduate-level intro to homotopy
Dec
25
accepted On “familiarity” (or How to avoid “going down the Math Rabbit Hole”?)
Dec
25
awarded  Mortarboard
Dec
25
awarded  Popular Question