Answer:
Traces are the intersections of a surface with the
corrdinate planes. Traces help to visualize a surface.
As you might have noticed, it can be quite challenging to
draw a geometric object in space. Drawing the traces can
be much simpler. Knowing the three traces can already give
a good picture, how the surface looks like.

Question:
Do we have to turn in the challenge problems with the homework.

Answer:
No, absolutely not. The challenge problems will be collected at
the end of the course. It will be an option for the final project.
The other possibility is to do the Mathematica project.
Note that some of the challenge problems are quite hard.

Question:
What does the notation [0,1] mean?

Answer:
[0,1] denotes the interval from 0 to 1. It includes the end points 0 and 1.