This course provides necessary mathematical background that is useful to students engaging in research in the field of signal processing. The subjects of the course are also relevant to digital communications and machine learning. The topics include: singular value decomposition, projection, Perron-Frobenius theorem, convex analysis, Karush–Kuhn–Tucker conditions for optimization, discrete Fourier transform and implementation via fast Fourier transform, sparse signal recovery, almost sure convergence, Markov chains and random walks, renewal processes, queueing theory, and random matrix theory.