  Topology at the undergraduate level is often a theoretical mathematics
course, introducing concepts from point-set topology or possibly algebraic
topology. However, the last two decades have seen an explosion of growth in
applied topology and topological data analysis, which are topics that can be
presented in an accessible way to undergraduate students and can encourage
exciting projects. For the past several years, the Topology course at
Macalester College has included content from point-set and algebraic topology,
as well as applied topology, culminating in a project chosen by the students.
In the course, students work through a topology scavenger hunt as an activity
to introduce the ideas and software behind some of the primary tools in
topological data analysis, namely, persistent homology and mapper. This
scavenger hunt includes a variety of point clouds of varying dimensions, such
as an annulus in 2D, a bouquet of loops in 3D, a sphere in 4D, and a torus in
400D. The students' goal is to analyze each point cloud with a variety of
software to infer the topological structure. After completing this activity,
students are able to extend the ideas learned in the scavenger hunt to an
open-ended capstone project. Examples of past projects include: using
persistence to explore the relationship between country development and
geography, to analyze congressional voting patterns, and to classify genres of
a large corpus of texts by combining with tools from natural language
processing and machine learning.
