Topics in Geometry: Introduction to Knot Theory

Math 309

Winter 2019

This is a math class about knots. While these are objects that arise relatively naturally in a variety of day-to-day and scientific settings, our challenge will be to carefully sort out how to describe, and ultimately study, knots using mathematical tools.

Here are some further remarks about this class:

  • In a mathematical context, the study of knots falls into a broader area of research called topology, which is a branch of geometry (in a broad sense). However, topology (Math 426, for instance) is not a prerequisite for this course and as such we won't really take this point of view; our course will be more combinatorial in nature, building from the ground up.

  • The course does, on the other hand, have prerequisites in the form of linear algebra (Math 221/223 or similar) and mathematical proof (Math 220 or similar). We will rely on both.

  • This course will take the point of view that knots are a naturally occurring objects, and hence these objects are worthy of study in their own right. While I will draw on examples found "in nature" from time to time, this won't be the main emphasis of the course. In particular, if you are the sort of student who does not find it motivating to study and/or think about something for its own sake, this might not be the course for you!

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