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 naturally occurring objects–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. Instead, this course is meant to provide a window to pure mathematics research, and hopefully provide a partial answer to the question "what do mathematicians do?"
A previous (online) version of this course can be found here.
Assignment submission and grading will make use of Canvas. Here are some essential guidelines for assignment submission:
1. Your solutions to assignments must be submitted using canvas. In particular, do not email assignments.
2. Your solutions must be submitted as a single file.
3. The only accepted file type is PDF.
4. Files should be named according to the following convention:
There are free online tools available that will allow you to complete (2) and (3). Due to the volume of data being managed, it is really important that these 4 points be met so that we can grade your work effectively. As a result, if one (or more) of these four points are not met, your assignment will not be accepted/graded.
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