Teaching numerical methods with IPython notebooks and inquiry-based learning

Abstract

A course in numerical methods should teach both the mathematical theory of numerical analysis and the craft of implementing numerical algorithms. The IPython notebook provides a single medium in which mathematics, explanations , executable code, and visualizations can be combined, and with which the student can interact in order to learn both the theory and the craft of numerical methods. The use of notebooks also lends itself naturally to inquiry-based learning methods. I discuss the motivation and practice of teaching a course based on the use of IPython notebooks and inquiry-based learning, including some specific practical aspects. The discussion is based on my experience teaching a Masters-level course in numerical analysis at King Abdullah University of Science and Technology (KAUST), but is intended to be useful for those who teach at other levels or in industry. Index Terms-IPython, IPython notebook, teaching, numerical methods, inquiry-based learning Teaching numerical methods Numerical analysis is the study of computational algorithms for solving mathematical models. It is used especially to refer to numerical methods for approximating the solution of continuous problems, such as those involving differential or algebraic equations. Solving such problems correctly and efficiently with available computational resources requires both a solid theoretical foundation and the ability to write and evaluate substantial computer programs. Any course in numerical methods should enable students to: 1) Understand numerical algorithms and related mathematical concepts like complexity, stability, and convergence 2) Select an appropriate method for a given problem 3) Implement the selected numerical algorithm 4) Test and debug the numerical implementation In other words, students should develop all the skills necessary to go from a mathematical model to reliably-computed solutions. These skills will allow them to select and use existing numerical software responsibly and efficiently, and to create or extend such software when necessary. Usually, only the first of the objectives above is actually mentioned in the course syllabus, and in some courses it is the only one taught. But the other three objectives