MS 131. Structure and Bonding in Materials. 9 units (3-0-6); first term, 2025-26. Prerequisites: graduate standing or introductory quantum mechanics. Electronic states in atoms and molecules. Born-Oppenheimer approximation. Crystal structure, including databases and visualization. Reciprocal space and Brillouin zone. Band theory using tight binding and plane waves. Introduction to density functional theory. Bonding and electronic structure in metals, semiconductors, ionic crystals, and complex oxides. Symmetry in materials: point groups, space groups, and time-reversal symmetry. Physical properties of crystals and their tensor representation. Introduction to correlated and topological quantum materials.
Instructor: Bernardi

APh/MS 141. Introduction to Computational Methods for Science and Engineering. 9 units (3-0-6); third term, 2025-26. Prerequisites: graduate standing or instructor's permission. A broad introduction to scientific computing using Python. Introduction to Python and its packages Numpy, SciPy, and Matplotlib. Numerical precision and sources of error. Root-finding and optimization. Numerical differentiation and integration. Introduction to numerical methods for linear systems and eigenvalue problems. Numerical methods for ordinary differential equations. Finite-difference methods for partial differential equations. Discrete Fourier transform. Introduction to data-driven and machine learning methods, including deep learning using Keras and Tensorflow. Introduction to quantum computing using Qiskit and IBM-Q. Students develop numerical calculations in the homework and in midterm and final projects.
Instructor: Bernardi