The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the basics of the subjects to undergraduates without requiring a lot of prerequisite knowledge, and at the same time connect several different areas of mathematics and computer science. Moreover, these are branches of mathematics suitable for undergraduate research. In this article, I will describe how I taught a special topics course on coding theory and cryptography, in a non-traditional way, at a small liberal arts college, the pedagogical aspects and the results and implications of the course. (Contains 3 figures.)