Beginning with space curves and proceeding to curved surfaces, we will
develop many of the fundamental notions of Differential Geometry:
curvature, distance and angle on surfaces, and isometry, both
intrinsic and extrinsic. In particular, we hope to reach Gauss' two
great contributions to the subject: His Teorema Egregium, and the
Gauss-Bonnet theorem.

Along the way, we will develop a rich supply of examples: specific
curves and surfaces to make subsequent theoretical constructs as
meaningful as possible. For similar reasons, we will transport much of
what we do into the virtual world of computer graphics.

Oprea's recent book "Differential Geometry and its Applications" will
be our text for the course.