MATH 055. Intermediate Topics in Geometry

Knot Theory: Tie a knot in a string then glue the ends together. Can this knot be untangled without cutting it open? This question and many others relating to these “mathematical knots” have increasingly been studied by mathematicians, with many breakthroughs occurring in the past 20 years. In this course we will discuss methods of knot tabulation, invariants (properties) of knots such as the bridge-number, surfaces associated to knots, ties to Hyperbolic Geometry, Physics, Chemistry, Molecular Biology, and other sciences, as well as open problems in the field. While our proof-based approach will heavily feature drawing, artistic skill is not a prerequisite.
Prerequisite: Credit for, or placement out of, one of MATH 027 or MATH 028 and also one of MATH 033 , MATH 034 , or MATH 035, along with a grade of C or better in at least one of the two previously mentioned math courses; or permission of the instructor.

Natural sciences and engineering.
1 credit.
Catalog chapter: Mathematics and Statistics
Department website: https://www.swarthmore.edu/mathematics-statistics

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