Advanced Mathematics for Signals, Systems, Control and Communications

This is the graduate course that gives you the functional-analysis toolkit underneath everything signals, control, and communications people actually do, Hilbert spaces, projection and orthogonal expansions, dual spaces and Hahn-Banach, distributions, and the Fourier transform treated rigorously rather than as recipes. You work through four problem sets, a midterm and final, and a project that takes a real problem in signal processing or control and reformulates it as optimization (often constrained) over a function space. Following Luenberger's classic, it's the bridge between undergraduate transform-and-system mechanics and the optimization, estimation, and adaptive-filtering literature you'll need for research.