Explore the intricacies of combinatorial optimization in this comprehensive two-part lecture by Hamoon Mousavi from Columbia University. Delve into the concepts of noncommutativity and rounding schemes as they apply to quantum optimization problems. Gain insights from the Rounding Schemes for Quantum Optimization Workshop hosted by the Simons Institute. Over the course of 87 minutes, examine advanced mathematical techniques and their applications in solving complex optimization challenges in the quantum realm.