This is the third course in a “capstone” sequence of mathematics courses for those mathematics majors who intend to pursue licensure to teach secondary school mathematics. It is a slash course since the MS degree program for licensure draws students from other bachelor’s degree programs and those students may wish to take this course.
In this term the focus is on the application of geometric transformations in the formal mathematical study of symmetry. That might sound dry, but it provides an opportunity to use mathematics in highly visual media, including art. There turn out to be exactly 7 mathematical groups (a technical term) that completely categorize structurally “strip” patterns (like one might see adorning the frieze of a building) and exactly 17 mathematical groups that completely categorize repeating two-dimensional planar patterns, the so-called “wallpaper” groups. The study of these groups lies at the heart of the course, combined with some additional topics that extend to 3 dimensions, or relax some of the strictly repeating conditions on 2-dimensional patterns. My experience has been that students leave the course with a heightened awareness and appreciation for symmetry in the world around them (new eyes, so to speak).
I found this to be an especially attractive candidate for a hybrid course, since the online features would lend themselves to students posting photographic examples of patterns exhibiting the symmetries under study. Also, dynamic geometry environments provide powerful tools that beg to be used in a course like this.
