Doctor of Philosophy in Combinatorics and Optimization - Discrete Optimization

University of Waterloo

Combinatorics is the study of discrete structures and their properties. Many modern scientific advances have employed combinatorial structures to model the physical world, and recent advances in computational technology have made such investigations feasible. In particular, since computers process discrete data, combinatorics has become indispensable to computer science. Optimization, or mathematical programming, is the study of maximizing and minimizing functions subject to specified boundary conditions or constraints. With the emergence of computers, optimization experienced a dramatic growth as a mathematical theory, enhancing both combinatorics and classical analysis. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. The PhD involves about two years of grad courses followed by research and a dissertation, and typically lasts four years.Discrete or combinatorial optimization embodies a vast and significant area of combinatorics that interfaces many related subjects. Included among these are linear programming, operations research, theory of algorithms and computational complexity. Much of combinatorial optimization is motivated by very simple and natural problems such as routing problems in networks, packing and covering problems in graph theory, scheduling problems, and sorting problems.