J Mann
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 Apr 11 answered Covariant derivative Apr 2 comment Analysis Prelim Question about proving continuity. your last comment on (1) is incorrect. Any union of open balls are open and around every point an open ball of radius one-half contains a single point. So any set is an open set. A ball of radius 2 is still open-it just happens to be the entire space(which better be open if we want to talk about the space's topology) Mar 30 answered Help me understand a 3d graph Mar 30 answered the definition of the area of a surface Mar 30 answered Geometric interpretation of $\frac {\partial^2} {\partial x \partial y} f(x,y)$ Mar 27 comment Different Definitions of the Directional Derivative If you want to know more I would pick up any book on Riemannian Geometry. I would suggest Boothby's "An Introduction to Differentiable Manifolds and Riemannian Geometry." Also Peterson's "Riemannian Geometry" is great if you're looking for more of a challenge. Mar 27 comment Different Definitions of the Directional Derivative There's A LOT of different formulations, but at the simplest level its a "space" in which the axioms of Euclidean Geometry do not hold. For example if you are on the north pole of the planet, and just fly/swim/walk/whatever in one (any) constant direction you will eventually reach the north. That is to say on a sphere a "line," or a geodesic, there exists points such that there exists infinitely many lines connecting them. Mar 27 awarded Supporter Mar 27 awarded Teacher Mar 27 answered Different Definitions of the Directional Derivative Mar 27 answered looking for a counterexample for a function sequence that uniformly converge on infinite intervals, but not on their union Jan 22 answered How to obtain the standard basis for $\mathbb{R}^2$ using differential geometry? Jan 21 answered Existence of a subgroup of order $pq$