1. The problem statement, all variables and given/known data Two questions: 1) Show that deg(f(g(x)) = deg(f)*deg(g) 2) f: Sn -> Sn deg(f) is odd then show there exists a pair of antipodal points that are mapped to antipodal points 3. The attempt at a solution 1) I have tried the method of just counting preimages, but i don't think this is the right direction. i know intuitively the deg of map between spheres is how many times you "wrap" the sphere around, and what i trying to show supports this, but i don't know how to show it rigorously. 2) We are dealing with antipodal maps in class, so i am trying to use them, but i have no idea how to use the fact that the degree of f is odd. i don't recall there being any fundamental difference between a map of odd and even degree.