December 1st, 2003

beartato phd

(no subject)

Sitting in the E&S library reading "Applied Differential Geometry" by William Burke. It's interesting -- he manages a description of tensors which is neither a thicket of indices and numbers, nor an extremely abstract treatment of universal properties of multilinear maps. Which isn't to say that I can easily summarize it. I'm still most comfortable with the crazy abstract universal-property angle. Nonetheless I'm finding myself extremely fascinated again lately by manifolds and differential forms and all that jazz, with an eye towards trying to understand deRham cohomology as a step towards the even lager goal of understanding what cohomology is all about in general. It's funny how just hearing a single term repeated often enough can make me really driven to figure out whatever junk lies beneath it in the hierarchy of mathematical castle-in-the-sky building.