Course Overview

• Full Course Description

  Take a piece of string, jumble it up, then seal the ends together. The result is a knot. Notice that you can't untie the knot because you've permanently sealed the ends together. We call two knots equivalent if you can move one jumbled piece of string to look exactly like the other without cutting it open. (Using more technical language, knots are embeddings of the circle into 3-space, considered up to ambient isotopy.) Given two knots, can you determine if they are equivalent? If you suspect that they are not equivalent, can you prove it?
  
  Mathematicians have been studying knots ever since the late 1800's when Lord Kelvin incorrectly theorized that all of matter was made up of knotted ether, where different elements corresponded to different knots. Although his theory of matter was incorrect, the study of knots has turned out to be a very rich field of mathematics, specifically a subfield of low-dimensional topology. While knots are the subject of current research by top mathematicians, there are knot theory topics that can be understood and investigated by students as young as middle school.

  This course will study knot theory without assuming anything beyond high school mathematics.

• Professor Bio
  Constance Leidy is an associate professor of mathematics at Wesleyan. She has taught a variety of math courses from calculus to graduate seminars. Her area of research is knot theory, which is a subfield of low-dimensional topology. She is the author of several published articles in knot theory and has supervised two PhD students. She has experience teaching knot theory in a variety of settings, including at the undergraduate and graduate level. As an instructor at the Rice University Mathematics Institute for Young Women, she taught knot theory to high school students, and has even run short seminars in knot theory for middle school students.