Textbook: M.P. Do Carmo "Differential Geometry of Curves and Surfaces"
Problemset 1: 1.3:1,2,4,5,10,   1.4: 5,6,12,   1.5: 2,3,5,10,15,
Problemset 2: 1.5: 4,7,9,12,14,17abc,   add to 7: the inverse I(t) of a plane curve a(t) is I(t)=a(t)-s(t)T(t). Show: Inverse of evolute=a parallel curve, Evolute of involute=original curve.    1.7: 6
Problemset 3: 2.2:2,4,5,7,11,   2.3: 15, Show that the follwoing is a regular parametrization of the sphere: (x,y,z)=(sech(u)cos(v),sech(u)sin(v),tanh(u)). Show that u=const are parallels and v=const are meridans. How much of the sphere can be covered by such a chart?
Problemset 4: 2.4:2,4,7,6,11,   2.5: 1abc,4,7,9,11,
Problemset 5: 3.2: 1,2,4,6,8,13,   Suppose plane P instersects surface S along a curve C, with constant angle of intersection (between surface normal and plane normal) along C. Show that C is principal on S. Deduce that meridians and parallels are principal on a surface of revolution.
Problemset 6: 3.3: 4,5,6bc,14,16,20,
Problemset 7: 4.3: 1,3,6,8,   4.4: 1,2,9,14,