Computational Discovery on Jupyter
Neil J. Calkin, Eunice Y. S. Chan, Robert M. Corless · Society for Industrial and Applied Mathematics eBooks · 2023
The authors have been using a largely algebraic form of "computational discovery" in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational mathematics.This paper describes what we mean by "computational discovery," what good it does for the students, and some specific techniques that we used.1 Setting the stage "The imparting of factual knowledge is for us a secondary consideration.Above all we aim to promote in the reader a correct attitude, a certain discipline of thought, which would appear to be of even more essential importance in mathematics than in other scientific disciplines."Pólya & Szegő vol I. [28, p. VII]The preface quoted above from the classic book cited, which is nearly a hundred years old now, opens with an epigraph which we further paraphrase, as follows: "What is good education?Giving students systematic opportunities to discover things for themselves."Indeed, Computational Discovery, also called "Experimental Mathematics," is also very familiar to the research mathematician, not just mathematics educators: nearly everyone uses it (even if they say that they don't, or don't say that they do).There can be no shame in it, if the likes of Gauss and Euler used the technique [6,7].See also the excellent book [14].The most basic idea is, after all, very simple: one computes a few cases, tries to guess a pattern, and if successful,