Have you ever looked at your knotted up headphones or tangled shoelaces and thought to yourself, I wonder about the math behind those knots? This fall, join Dr. Carolyn Otto to learn about the history and future implications of knot theory in the honors colloquium, Knot Theory and Its Applications.
Otto completed her undergraduate mathematics degree at the University of Wisconsin-Eau Claire, where she was introduced to knot theory through a summer internship. She liked the idea of stepping away from the normal “rigidity” of math: “it didn’t feel like math; it has this creative avenue to it,” she tells us. Soon, Otto was hooked. Because UWEC didn’t offer a knot theory-specific course, Otto had to search out more information on her own, but she eventually went on to obtain her masters and PhD at Rice University, where she studied knot and link theory.
Otto explains that “knots are curves that are all tangled up and live in three-dimensional space. You can think about tying your shoestrings and then fusing the ends together so you cannot untie them…that is a mathematical knot.” When it comes to knots, as well as to knot theory, there are many applications in a variety of disciplines: “it turns out knots show up in nature all the time. By knowing about them we can learn about other things.”
Students from many majors beyond math have found interesting points of entry into knot theory through this course. Sydney Dame, a senior biochemistry and molecular biology major, applied knot theory to protein folding and DNA repair processes and began to understand these processes from a mathematical perspective. She writes, “knot theory and topology have applications to so many other fields of study, especially other STEM fields, and they show students a lesser-known side of mathematics. Non-math majors can learn a lot from this course and shouldn't be intimidated!” Sydney is now working with Dr. Otto, completing research that applies knot theory to protein folding.
Tyler Gonzalez, a senior mathematics major, enjoyed knot theory because of its interdisciplinary approach and varied applications. He was particularly interested in learning about the more artistic side of math: “the beautiful thing about this course is that the mathematics is so visual, and you can literally see the mathematics move through the diagrams you draw. This is a great course for people who want to be able to learn new ways to visualize mathematics.”
For students who are interested in Knot Theory and Its Applications, Otto clarifies that the course’s prerequisite, MATH 114, should not discourage students. She explains, “we don’t do a lot of computations, but there are still some. I do expect a level of abstract thinking and creativity—the epitome of an honors course. A MATH 114 prerequisite helps with that.” Students should expect to approach mathematics in a different way than typical math courses. Instead of memorizing equations and doing computations, Knot Theory and Its Applications uses a discussion-based approach, creating space for students to share insights from their different backgrounds.
Otto is excited for the opportunities this course brings, especially as she will be incorporating a new unit on protein folding based on her research in collaboration with Sydney Dame. Not only does this course present novel opportunities for students to expand their knowledge in math, but it can help expand their understanding of their specific area of study. Knot theory is becoming frequently used in disciplines ranging from chemistry and molecular biology to art and graphic design. So, the question is, what might knot theory do for you?
For more information about the course, check out our Fall 2021 course catalog, or contact us at honors@uwec.edu. Knot Theory and Its Applications (HNRS 368) meets Mondays, Wednesdays, and Fridays, 10-10:50 am.
