MTH-315 Knot Theory

Prerequisite: MTH-160 Vectors and Matrices and MTH-260 Transition to Higher Mathematics
An introduction to knot theory, a subfield of topology where two knots are considered equivalent if there exists an ambient isotopy between them in three-dimensional space, or more intuitively, two knots are the same if one can be continuously deformed to the other without letting a knot cut through itself. Topics to be examined include knot equivalence and Reidemiester moves, knot composition and prime knots, Seifert surfaces and the genus of a knot, different families of knots and links, Thurston’s classification of knots, combinatorial knot invariants, and knot polynomials. Additional topics may include games on knot diagrams, hyperbolic knots, mosaic knot theory, and/or knots in topological graph theory. 4 credits.