Problem A : Produce an interesting parametrized surface.
You can use any tool.Here are some ideas : You can modify a few things here and print it out.

A helix surface without thrills (grab the next cell to the right, hold <shift> and hit <return>)

ParametricPlot3D[{s Cos[t],s Sin[t],t},{s,0,1},{t,0,2Pi},AspectRatio->1,Boxed->False,Axes->False]

A “bumpy sphere” surface with a picture as texture

picture=Import["http://www.courses.fas.harvard.edu/~math21a/donald.jpg"];
ParametricPlot3D[(2+Sin[t]) {Cos[t] Sin[s],Sin[t] Sin[s],Cos[s]},{s,0,Pi},{t,0,2Pi},Lighting->"Neutral",Mesh->False,PlotPoints->40,TextureCoordinateFunction->({#5,#4}&),PlotStyle->{Texture[picture]},ViewPoint->{-3.25,-0.9,-0.2},ViewVertical->{-0.64,-0.05,-0.9},Axes->False,Boxed->False,PlotRange->All]

A surface of the form r(t,s) = f(t) + f(s) with a metallic texture

f[t_]:={Sin[t],Sin[3 t],Sin[2 t]};
ParametricPlot3D[f[t]+f[s],{t,0,2Pi},{s,0,2Pi},TextureCoordinateFunction->({#4,#5}&),AspectRatio->1,PlotStyle->Directive[Texture[ExampleData[{"ColorTexture","Metal1"}]]],ViewPoint->{-1.8,-2.6,-1.17},ViewVertical->{-1,0,-0.1},PlotPoints->100,AspectRatio->1,Boxed->False,Mesh->False,Axes->False]

Here are some textures built in

ExampleData["ColorTexture"]

Math21a, Harvard University Fall, 2011