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. 

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 time-invarying systems. The slides are available here


Dr. Amar Bose of MIT, a signal processing expert, the Founder of Bose (sound) Corporation (source)

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

  • Robbins-Monro Algorithm

  • Kiefer-Wolfowitz Algorithm

  • The ODE approach to Stochastic Approximation

  • Stochastic Approximation: two time scale