The Persistence of Mathematics: integrating mathematical problem solving into the first-year engineering curriculum

Mathematics is more than a set of tools. It is a mode of thinking and a powerful and integral way to approach engineering. Over the course of this year, the authors of this paper, with help from our colleagues, were able to integrate multiple courses from the first-year curriculum. We were able to give novel exercises, assessments, and course material that showed the usefulness of mathematics as a way of thought. In this paper, we give the main examples of what we had done throughout the year, connecting calculus and linear algebra with programming, statics, design, and engineering orientation. These are interspersed with the lessons learned in creating these interventions.