GIG: Algorithms, Combinatorics & Optimization: An Interdisciplinary Ph.D. Program

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9509581 Balas The last half century has seen an increasing use of computers insolving the complex decision problems that arise in a modern society.The methods needed to solve many of these problems are a fusion of ideas from Mathematics, Computer Science and Operations Research, Linear Programming, Integer Programming and Combinatorial OptimizationTechniques are widely used in today's world. Problems of production, distribution, and allocation are routinely modeled in this way. New techniques drawing from developments in all three disciplines are needed to solve the ever larger problems that arise in a technologically advanced society. In addition, new areas of application emerge repeatedly. For example, the recent upsurge of activity in Computational Molecular Biology relies heavily on Discrete Mathematics to untangle the knotty sequencing problems that it throws up. The knowledge needed to solve such problems transcends the traditional boundaries of a modern university. Researchers in Mathematics, Operations Research and Computer Science Departments often find themselves working on similar problems. On the other hand the idea of training graduate students simultaneously in all three areas has been slow to get off the ground. Carnegie Mellon recognized this several years ago. Using it's internationally recognized strengths in all three areas it responded by setting up the Ph. D. program in Algorithms, Combinatorics and Optimization. A unique feature of the program is that students are given a thorough grounding in the foundations of all three areas before they embark on their research. Now nearly 30 students have taken part in the program. The quality of the students has been excellent and the first crop of graduates have taken up positions in major universities and research laboratories.The program has inspired other institutions to provide similar courses.The money from this grant will be used to support graduate students and to provide t hem with an environment in which they can acquire knowledge and research skills in all three areas.