Translation Groups on [0,1]Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.
Signal Processing FundamentalsExplores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.
Quantum Mechanics PostulatesExplains the postulates of quantum mechanics, including system description, evolution, measurement, composite systems, and examples with qubits.
Dual Space and Weak ConvergenceExplores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.
States of Composite SystemsCovers the states of composite systems in Hilbert space, including operators, observables, tensor products, eigenvalues, and partial measurements.
Normed SpacesCovers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Quantum Field Theory: AQFTCovers Advanced Quantum Field Theory with a focus on spinors, wave functions, rotations, and constraints.