A project in algorithms based on a primary historical source about catalan numbers

Abstract

We discuss a project based on an original source from 1838 by Gabriel Lamé, which was used to teach dynamic programming in an Algorithms and Data Structures course for junior level computer science students. The project was developed as part of a group effort at New Mexico State University on using original historical sources in teaching. The project is based on an excerpt from a letter of Monsieur Lamé to Monsieur Liouville on the question: Given a convex polygon, in how many ways can one partition it into triangles by means of diagonals? A variety of tasks in the project, which includes reading, writing, proving statements by mathematical induction, deriving formulas, writing computer programs and analyzing and comparing them for efficiency, help students to develop verbal, analytical and discrete mathematics skills necessary for computer science. We also discuss student reactions to the project and to learning from historical sources.