Mathematical Sciences: The Probabilistic Method

该奖项支持斯宾塞教授从事组合学的研究。具体地说，斯宾塞教授正在开发概率方法，用于处理组合学中的问题。离散数学和计算机科学之间的相互作用提出了一种算法观点。许多存在的概率证明立即为相应的算法问题提供了有效的随机化程序，在某些情况下，这些程序可以被随机化并转换为确定性程序。这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散的集合。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，如电话系统，以及计算机科学中的算法设计，都涉及离散对象，这利用了组合研究。

This award supports the research of Professor Spencer to work in combinatorics. Specifically, Professor Spencer is developing the Probabilistic Method for use in dealing with problems in combinatorics. The interplay between discrete mathematics and computer science suggests an algorithmic viewpoint. Many probabilistic proofs of existence supply immediately efficient randomized procedures for the corresponding algorithmic problems, and in some cases these procedures can be derandomized and converted into deterministic ones. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections can be organized. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, as in telephone systems, and the design of algorithms in computer science all deal with discrete objects, and this makes use of combinatorial research.