The goal of this course is to expose students to modern and fundamental developments of optimization theory, algorithms and applications in computer science.  The course focus is on various topics including the conceptual and algorithmic sides of convex optimization as well as dynamic programming.  We will cover cone programming including linear, quadratic and semidefinite programming, geometric programming and dynamic programming whose rich expressive power makes it suitable for a wide spectrum of important optimization problems arising in mathematics and computer science.  On the algorithmic side, the course covers efficient methods including optimization decomposition, convex relaxation and iterative methods, e.g., proximal algorithms, to address large-scale problems and non-convex problems.  Emphasis will also be placed on the software aspect of convex optimization and dynamic programming.  A variety of applications in computer science will be selectively drawn from combinatorial graph problems, Internet and wireless networks, online social networks, machine learning, statistical inference, compressed sensing and artificial intelligence.