The author taught two courses on cryptography, one at Duke University aimed at non-mathematics majors and one at Rose-Hulman Institute of Technology aimed at mathematics and computer science majors. Both tried to incorporate technical and societal aspects of cryptography, with varying emphases. This paper will discuss the strengths and weaknesses of both courses and compare the differences in t...

Lurch is a free word processor that can check the mathematical reasoning in a document.1 Although it would be easy to make a word processor that could check simple arithmetic, or even algebra, Lurch aims to do much more than that. It can check the steps of a mathematical proof, even a proof not written in a formal style. The current version works best for introduction-to-proof courses, covering...

The discussion of models and modeling in this chapter is based, in part, on the results of research on students’ understanding of quantum mechanics (Gardner, 2002) and research designed to probe students’ ability to visualize the rotation of organic molecules (Briggs, 2004). Our perspective on models and modeling has also been influenced by work in both physics education (Halloun, 1996) and mat...