[Blindmath] Division of Polynomials

[Susan Jolly]

Hi Jon,

I completely agree with what you wrote about the important aspect of much of 
what one learns is developing the general ability to deal with related items 
in the future.  I am also well aware that it is often not until you've taken 
a more advanced subject such as abstract algebra that you appreciate the 
usefulness of or even truly understand what you've studied earlier.  This 
can be hard for students to appreciate. I remember trying in vain many years 
ago to justify to my high school chemistry students how it could help their 
future selves to learn the naming systems for certain organic molecules.

The only reason I added what I did about my having never needed polynomial 
division is that it seemed to me that some of the students were spending way 
too much time on this one topic, especially given that they are just taking 
standard algebra with no guarantee that their teacher knows anything about 
computer algebra systems or abstract algebra. I apologize if I gave the 
false impression that I wouldn't have agreed in general with what you 
expressed so well.

Another thing I had thought about mentioning was that my understanding of 
calculus greatly improved once I'd developed and programmed in Fortran a 
method for handling numerical quadrature of certain complex 
three-dimensional integrals.  However, as you well know, my being able to do 
this built on many different skills that I'd spent years acquiring.

Sincerely,
SusanJ