I feel like I have a pretty good conceptual understanding of the origin of band theory, but these two problems were totally above my head.
Kittel Ch7 #2
Consider the free electron bands of an fcc crystal lattice in the approximation of an empty lattice, but in the reduced zone scheme in which all k's are transformed to lie in the first Brillouin zone. Plot roughly in the  direction the energies of all bands up to six times the lowest band energy at the zone boundary at k=2[tex]\pi[/tex]/a(1/2,1/2,1/2). Let this be the unit of energy. This problem shows why band edges need not necessarily be at the zone center. Several degeneracies will be removed when account is taken of the crystal potential.
Wish I knew.
The Attempt at a Solution
Like I said, totally baffled.