Combinatorics of Convex Polytopes/Teaching with Technology

凸多面体组合学/技术教学

• 批准号: 9502455
• 负责人: Clara Chan
• 金额: $ 4.19万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-15 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9502455&HistoricalAwards=false
• 关键词: Combinatorics; Convex; Polytopes; Teaching; Technology

This CAREER award supports the research and professional development of Professor Clara Chan. Chan will investigate the polytope algebra and its connections to the algebra of piecewise polynomial functions and cohomology of toric varieties. She will also continue her work on cubical polytopes. The main focus of the educational plan is to bring more advanced technology into undergraduate mathematics courses at Virginia Tech, especially in the area of Discrete Mathematics. The research component of this project is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.

该职业奖支持 Clara Chan 教授的研究和专业发展。陈将研究多面体代数及其与分段多项式函数代数和环面簇上同调的联系。她还将继续研究立方体多面体。该教育计划的主要重点是将更先进的技术引入弗吉尼亚理工大学的本科数学课程，特别是离散数学领域。 该项目的研究部分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排列离散的对象集合。离散系统的行为对于现代通信极其重要。例如，大型网络的设计（例如电话系统中的网络）以及计算机科学中处理离散对象集的算法设计，都利用了组合研究。