Redesigning interactive educational modules for combinatorial scientific computing.

Abstract

Combinatorial scientific computing refers to the field of using combinatorial algorithms to solve problems in computational science and data science. Teaching even elementary topics from this area is difficult because it involves bridging the gap between scientific computing and graph theory. Furthermore, it is often necessary to understand not only the methodologies from mathematics and computer science, but also from different scientific domains from which the underlying problems arise. To enrich the learning process in combinatorial scientific computing, we designed and implemented a set of interactive educational modules called EXPLAIN. The central idea behind EXPLAIN is its focus on describing the equivalence of a problem in terms of scientific computing and graph theory. That is, in EXPLAIN, the scientific computing problem and its graph theoretical representation are treated as two sides of the same coin. The process of solving a problem is interactively explored by visualizing transformations on an object from scientific computing, simultaneously, with the corresponding transformations on a suitably defined graph. We describe the redesign of the EXPLAIN software with an emphasis on integrating a domain-specific scripting language and a hierarchical visualization for recursively defined problems.