A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

This course is an introduction to statistical data analysis. Topics are chosen from applied probability, sampling, estimation, hypothesis testing, linear regression, analysis of variance, categorical data analysis, and nonparametric statistics.

Estimation and control of dynamic systems. Brief review of probability and random variables. Classical and state-space descriptions of random processes and their propagation through linear systems. Frequency domain design of filters and compensators. The Kalman filter to estimate the states of dynamic systems. Conditions for stability of the filter equations.

This course is an introduction to epistemology: the theory of knowledge. We will focus on skepticism—that is, the thesis that we know nothing at all—and we will survey a range of skeptical arguments and responses to skepticism.

This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.