Combinatorics of Convex Polytopes/Teaching with Technology

这个职业奖支持陈淑芬教授的研究和专业发展。陈将调查多面体代数及其连接代数的分段多项式函数和上同调环面品种。她还将继续她的工作立方多面体。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，特别是在离散数学领域。 该项目的研究部分是在组合数学的一般领域。组合数学试图找到有效的方法来研究如何安排离散的对象集合。离散系统的行为对现代通信极为重要。例如，大型网络的设计，如电话系统中的网络设计，以及计算机科学中的算法设计，都要处理离散的对象集，这就需要使用组合研究。

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.