The linked PDF concerns the notion of "derivatives" in differential geometry. It grew out of my reflections on my own education in differential geometry and mathematical physics, and represent wistfully how I wish I were taught when I was younger. This is not to say the prevailing approach to the foundations are not useful, or in anyway inferior; on the contrary, understanding the foundational material as given in the "standard presentations" is indispensable for actually doing geometry. The points of view given here may provide additional motivation and better conceptual understanding; at least, they did it for me.
Bundles and derivatives
Willie WY Wong
Associate Professor
My research interests include partial differential equations, geometric analysis, fluid dynamics, and general relativity.