To the formalists the index operations are exceedingly refractory, in consequence of which some take no account of them, but relegate them to applied mathematics.
A propos "transformation" and "abstract", perhaps there is something at the concept/application interface, like there is between pure and applied mathematics.
The graduate school programs ranked highest in 2007 were counseling and personnel services, chemical engineering, psychology, macroeconomics, applied mathematics and non-profit management.
In pure and applied mathematics, particularly quantum mechanics and computer graphics and applications therefrom, a tensor operator generalizes the notion of operators which are scalars and vectors.