As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

One module is presented in units 203, 204, and 205, as a guide for students, and presents a general strategy for solving integrals effectively. With this material is a solutions manual to exercises. This document set also includes a unit featuring applications of calculus to geography: 206-Mercator's World Map and the Calculus. Unit 207-Management…