Computational Discovery with Newton Fractals, Bohemian Matrices, & Mandelbrot Polynomials

TL;DR

This paper discusses the use of algebraic computational discovery techniques, including Newton fractals, Bohemian matrices, and Mandelbrot polynomials, to enhance teaching in pure, applied, and computational mathematics.

Contribution

It introduces specific algebraic methods for computational discovery and demonstrates their educational benefits across different mathematics disciplines.

Findings

Enhanced student understanding of complex mathematical concepts

Effective use of Newton fractals, Bohemian matrices, and Mandelbrot polynomials in teaching

Positive impact on student engagement and learning outcomes

Abstract

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.