In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…

Large real-world graph (a.k.a network, relational) data are omnipresent, in online media, businesses, science, and the government. Analysis of these massive graphs is crucial, in order to extract descriptive and predictive knowledge with many commercial, medical, and environmental applications. In addition to its general structure, knowing what…

Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrix-vector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific…