## Definitions

"coordinate patch": an open set of points around a point on a manifold

"coordinate function" or "chart": continuous function mapping every point in a patch to coordinates (tuples of N real numbers for an N-dimensional manifold)

multiple charts may be needed to map all points on an entire manifold. a consistent set of charts covering an entire manifold is an "atlas".


## Progress

Went through the second chapter, Manifolds, and did the exersizes. Short and
straight-forward, mostly definitions. Not going in to as much detail/definition
as would if studying Topology directly.

Started on third chapter, Vector Fields and One Form Fields, and struggling
with terminology a bit. Looking ahead a bit, i'm expecting:

- Chapters 2,3,4: definitions, geometry, derivatives on manifolds
- Chapters 5,6,7: calculus on manifolds (integration theorems)
- Chapters 7.8: curvature weirdness and the meat/math of general relativity
- Chapters 10,11: physics


## TODO

report typo in scmutils: "Bad point: polar/cylindrial manifold" and "spherical/cylindrial" (should be "cylindrical"?) (in calculus/manifold.scm)