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

[509581]巴拉斯在过去的半个世纪里，人们越来越多地使用计算机来解决现代社会中出现的复杂决策问题。解决这些问题所需的方法融合了数学、计算机科学和运筹学、线性规划、整数规划和组合优化的思想，这些技术在当今世界被广泛使用。生产、分配和分配的问题通常以这种方式建模。从这三个学科的发展中汲取的新技术需要解决在技术发达的社会中出现的更大的问题。此外，新的应用领域不断涌现。例如，最近在计算分子生物学领域兴起的活动在很大程度上依赖于离散数学来解开它抛出的棘手的排序问题。解决这些问题所需的知识超越了现代大学的传统界限。数学、运筹学和计算机科学系的研究人员经常发现自己在研究类似的问题。另一方面，同时在这三个领域培养研究生的想法起步缓慢。卡耐基梅隆大学几年前就认识到了这一点。利用它在这三个领域的国际公认的优势，它设立了算法、组合学和优化博士课程。该项目的一个独特之处在于，在开始他们的研究之前，学生们将在这三个领域的基础上获得全面的基础。现在已经有近30名学生参加了这个项目。学生质量优良，第一批毕业生已在各大高校和研究实验室任职。这个项目启发了其他机构提供类似的课程。这笔资金将用于支持研究生，并为他们提供一个环境，使他们能够在这三个领域获得知识和研究技能。

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.