Courses
UCSD ECE 250: Random Processes
This course is the core graduate level course on foundation of random processes. The course notes are available here.
Topics include:

foundation of probability theory,

sum of independent random processes, strong law of large numbers, and central limit theorem,

conditional expectation, martingale theory,

estimation theory,

discrete time homogeneous Markov chains, and

processing of stationary processes.
Joseph Doob and his students, Blackwell, Halmos, and Ambrose
UCSD ECE 272A: Advanced Linear Systems Theory
This course is a first graduate level (core) course on dynamics and control which focuses on theoretical foundation of linear systems theory.
Topics include:

continuous time linear systems,

existence and uniqueness of solutions to LTV systems,

stability of linear systems: direct and indirect Lyapunov method,

controllability and stabilizability of LTI systems, and

observer design for LTI systems.
Roger Brockett, Eduardo Sontag, Mike Warren, and Alberto Isidori (source)
UCSD ECE 101: Linear Systems Theory (Signals and Systems)
This is the main undergrad core course on signals and systems that discusses topics including signals and linear timeinvarying systems. The slides are available here.
UCSD ECE 285: Stochastic Approximation, theory and applications
This course is about a powerful tool in learning theory, random processes, stochastic optimization, adaptive control, etc.
The topics to be covered include:

Motivating Examples:

SGD, Qlearning, Simulated Annealing, Replicator Dynamics, Adaptive Control


Mathematical Preliminaries:

Convergence in metric spaces

Background in Probability

Martingale theory

Ordinary Differential Equations: existence and uniqueness of solutions, stability


RobbinsMonro Algorithm

KieferWolfowitz Algorithm

The ODE approach to Stochastic Approximation

Stochastic Approximation: two time scale