Description: Pre- requisite(s): MATH 209A, MATH 209B, MATH 209C, MATH 228; or consent of instructor. Foundations of quantum theory together with the relevant mathemat- ics. Probabilistic interpretation of quantum mechanics, self-adjoint operators and physical observables, non- commutativity and the uncertainty principle. Spectral theory for (unbounded) self-adjoint operators. Stone’s theorem and other topics.