Master of Mathematics in Combinatorics and Optimization - Continuous Optimization in Waterloo Canada | University of Waterloo

Combinatorics examines discrete structures and their characteristics. Contemporary scientific progress frequently utilizes combinatorial models to represent physical phenomena, with computational advancements enabling practical research in this field. Given that computers handle discrete data, combinatorics has become essential to computer science. Optimization, or mathematical programming, focuses on maximizing or minimizing functions while adhering to defined constraints. The rise of computing technology spurred significant theoretical growth in optimization, enriching both combinatorics and classical mathematical analysis. These optimization functions find applications in engineering, physical sciences, management disciplines, and various mathematical fields. The MMath program includes approximately one year of graduate-level coursework followed by either a research project or thesis under faculty supervision.

Continuous optimization serves as the foundational mathematical approach for solving real-world challenges, from biomolecular design to investment portfolio management. It involves determining the minimum or maximum values of functions with real variables, subject to equation or inequality constraints. Mathematicians have studied continuous optimization since the era of Newton, Lagrange, and Bernoulli. At Waterloo, the continuous optimization research group particularly emphasizes convex optimization—where both the objective function and feasible set exhibit convexity. Convex optimization problems have broad practical applications and possess unique characteristics that enable advanced analysis and efficient algorithmic solutions. Group members have contributed groundbreaking work in this area, developing improved convex optimization algorithms and investigating fundamental properties of convex sets, including those related to positive semidefinite matrices.