Related to the Ph.D. program in operations research, Carnegie Mellon offers an interdisciplinary Ph.D. program in algorithms, combinatorics, and optimization. This program is administered jointly by the Tepper School of Business (operations research group), the Computer Science Department (algorithms group), and the Mathematics Department (discrete mathematics group).
To a great extent, the mathematics used by computer scientists and operations researchers overlap. The boundaries between operations research and computer science have become blurred. Important new theories and whole fields, like polyhedral combinatorics, have been and are being developed jointly by computer scientists, operations researchers, and applied mathematicians (who consider themselves a little bit of both). Presentations of new results on graphs and matroid theory can be heard at operations research conferences, while papers on linear programming, network flows, and matching in graphs are frequently presented at computer science conferences. The mathematical content of the papers has become greater and more diverse. Yet, in spite of this, few Ph.D. students graduate with an equally solid knowledge of all three areas.
The Ph.D. program in algorithms, combinatorics, and optimization is intended to fill this gap. It brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as graph theory, combinatorial optimization, integer programming, polyhedral theory, computational algebra, geometry, and number theory.
The academic requirements are the same for all students in the program. The coordinating committee has established a challenging core curriculum in analysis, algebra, probability, linear and integer programming, graph theory, dynamic programming, convex analysis, algorithms, and complexity theory. For more information, see the separate brochure for the Algorithms, Combinatorics and Optimization program, or go to the ACO homepage.
The program is intended for a small number of students. Students may apply to the Ph.D program in algorithms, combinatorics, and optimization through any of the three participating departments. For this purpose, an application form should be obtained from the admissions secretaries in the Department of Computer Science or the Department of Mathematics. If you are applying through the Tepper School of Business, you should complete an online application. In filling out the application, the student should indicate his or her preference for the program.