DanP
Posts:
35
Registered:
1/10/12


Re: Khan Academy: Math instruction goes viral
Posted:
Jan 11, 2012 3:06 PM


>>To be even mentioned by someone I absolutely do not know >>is totally afirst to me. I am grateful to Partelly and I >>really mean it, hopefully not out of vanity.
I appreciate it. If you Google "Lagrange calculus" one of your papers appear on the second page of results, so it's not extraordinary your work can be found by someone who holds a interest in the subject. Besides your work and the videos I mentioned, I found through Google and I appreciated very much the exposition of David Hestenes in Clifford Algebras for physics and William Bourke's "Div Grad Curl are dead".
One thing which is worth mentioning is that work like yours is useful not only to students or persons interested in learning more math, but to parents / anyone else who is interested in helping their kids/wards/relatives in math. It's a great boon to have access to decades of experience in teaching distilled in a book or some videos, this way you stand a real chance of helping the young ones instead of confusing them even more, or know nothing but "drill till you drop" approach (not that drilling is not necessary, it has it's place IMO). There are maybe not many parents interested to do this for their kids, but yeah, I know some.
As for the disjoint format of Khan like videos, I think it would be much more useful if it would basically give up "lecturing" and focus on interesting and hard problems, kinda like in a recitation session, and make this thing crystal clear. i.e, use the video not to learn math, but to consolidate your knowledge by trying to work the problems exposed, and having access to solution if you fail.
By the way, I've been meaning to ask you something. A couple of days ago I recommended someone to read your papers on calculus and he asked me something. Basically on page 3 of "A LAGRANGIAN APPROACH TO THE DIFFERENTIAL CALCULUS" , right before the Variance theorem you write:
"........ shows that x0 is a monotonic point with variance (?,?) or (oe,oe) or a turning point with variance (oe,?) or (?,oe) depending on the parity of n and on the sign of .... "
Id like to ask you what is the exact meaning of the pairs of type (?,?), (oe,?) ?
Thank you very much for everything.

