Explain the following basic concepts underlying the topics in solid state physics: (1) crystal symmetry, (2) reciprocal lattice and the first Brillouin zone in k-space, and (3) the quantum behavior of electrons, Pauli's exclusion principle, and the Fermi-Dirac distribution function.

Use these basic concepts to explain crystal structure, x-ray diffraction, lattice vibrations, behavior of electrons in metals and semiconductors, and thermal, magnetic, dielectric and optical properties of materials.

Show their understanding of these topics and their underlying concepts by solving problems using a variety of mathematical tools.