The mathematical field of topology is concerned with properties that are preserved by stretching and bending without cutting or gluing. For example, a coffee mug and a donut are considered the same topologically: the handle of the mug can be stretched into the hole of the donut. Similarly, the way a string tangles with itself in a knot is a topological property. Studied since the late 19th century, knot theory (a subfield of topology) is an area of current mathematical research, with applications in physics, chemistry and biology.
This course introduces the basic ideas and techniques of topology, with a focus on the study of knots. It covers knot theory basics like knot diagrams, isotopy, and Reidemeister moves, as well as classical and modern knot invariants. Additional topics (depending on student interest) include the topology of graphs and surfaces and applications of knot theory. In the process, students are exposed to the techniques and ideas of mathematical research.