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Knot Theory

Is a donut the same as a coffee cup? From a topological perspective, the answer is ''yes.'' The mathematical field of topology is concerned with properties of geometric structures that are preserved when the structure is deformed by stretching and bending without cutting or gluing. In this way, a coffee cup can be topologically transformed into a donut where the handle of the cup becomes the hole of a donut. This course introduces basic concepts from the field of topology, first through the study of knots. For most people, knots are about shoelaces, fishing line, ribbons and ropes, but not about mathematics. However, knot theory is a very important branch of mathematics that is a subfield of topology. Furthermore, knot theory is an area of current mathematical research, and it has applications in physics, chemistry and biology. Beginning with the study of knots, and leading to the study of surfaces, this course will cover topics such as Reidemeister moves, graphs and networks, Euler characteristic, homeomorphism, and classifications of knots and surfaces.

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Session One
Applications are Closed
at the time of application
on the first day of session

Completion of an algebra course.