Computational Activities for a Sophomore-Level Mathematical Methods Course

This talk describes a series of more than ten computational activities developed and adapted for a sophomore-level Mathematical Methods course. These activities reinforce course topics including: algebraic operations on real and complex numbers, numeric solving of ordinary differential equations, symbolic computation (integration, differentiation, and matrix operations), Fourier Series/Transforms, Monte Carlo methods, and numerical methods for partial differential equations. Activities are written in python using Jupyter Notebooks due to their free availability, flexibility, and growing popularity in physics research. We discuss how free computing resources provided through the Ohio Supercomputer Center's Classroom OnDemand system allow students to remotely connect to a cloud-based Jupyter environment on laptops, tablets, and Chromebooks. We also briefly discuss complementary efforts to add computation throughout the physics major.