Courses
MATH 506
Development and analysis of numerical methods for ODEs, an introduction to numerical optimization methods, and an introduction to random numbers and Monte Carlo simulations. The course starts with a short survey of numerical methods for ODEs. The related topics include stability, consistency, convergence and the issue of stiffness. Then it moves to computational techniques for optimization problems arising in science and engineering. Finally, it discusses random numbers and Monte Carlo simulations. The course combines the theory and applications (such as programming in MATLAB) with the emphasis on algorithms and their mathematical analysis.
PHYS 510
Classification of solids. Theory of harmonic crystals. Phonons and phonon dispersion relations. Anharmonic effects in crystals. Phonons in metals. Dielectric properties of insulators. Semiconductors. Diamagnetism and paramagnetism. Electron interactions and magnetic structure. Magnetic ordering. Superconductivity.
PHYS 509
Free electron theory of metals. Crystal lattices. Reciprocal lattice. Classification of Bravais lattices. X-ray diffraction and the determination of crystal structures. Electrons in a periodic potential. Tight binding method. Band structures. Semi-classical theory of conduction in metals. Fermi surface. Surface effects.