![]() ![]() Good mathematical exposition will be counted on both exams. There will be one midterm (the date to be determined) and a final exam. Your homework grade will consist of two scores: one for correctness and one for exposition. Late homework will receive at most 1/2 credit. You must show all of your work for full credit. Homeworks will be assigned every Wednesday and will be due the following Wednesday in class (or before class) unless otherwise stated they will be posted on OWL-Space. If you haven't taken the necessary prerequisite but would still like to take the course, please talk to me. In particular, one should be familiar with the rank, nullity, determinant, and eigenvalues of a matrix. The prerequisite is a course in linear algebra or a course that discusses matrices and some of their properties: Math 221, Math 354, Math 355, CAAM 335, or equivalent. The course will be mostly self-contained and will have an emphasis on careful proof writing. Here are some of the topics that we will discuss: Reidemeister moves, mod-p colorings, knot determinants, knot polynomials, Seifert surfaces, Euler characteristic, knot groups, and untying knots in 4-dimensions. We will also discuss open problems in knot theory. We will learn how to formalize knots and learn techniques to distinguish them from one another. The purpose of this course is to learn the basics of knot theory. It is an essential tool in the study of 3 and 4-dimensional manifolds. Knot theory is a large and active research area of mathematics that employs advanced techniques of abstract algebra and geometry. Knot theory is the study of smooth simple closed curves in 3-dimensional space. Knot Knotes by Justin Roberts (notes found at, more advanced than Livingston or Adams) The Knot Book by Colin Adams (book, includes a lot of open problems) Other useful references in Knot Theory (not required) Knot Theory by Charles Livingston (required) Homework and reading assignments will be posted on OWL-Space Office Hours: Mon 11am-12pm, Tues 1-2pm, Thurs 1-2pm Math 304: Elements of Knot Theory | Spring 2014Ĭlass meets: MWF 10am - 10:50am in HB 453 I included the original plaster trefoil sculpture which turned out to be the only one I’ve produced.Math 304: Elements of Knot Theory - Spring 2014 All the others had broken or went wrong, but I mounted fragments of the failures on the wall. Five sets of manilla and cotton rope were used to do a translation of real world knots into mathematical versions. The usual knots were mounted on the wall. The large unknot took up one end of the space and cast some very nice shadows.īelow each one was a cotton rope of the same knot with the ends taped together which the viewer was encouraged to pick up and play. This piece seemed to be most interesting to the audience. I think it’s size coupled with the surprising news that it was really just a circle helped to bring attention to it. Overall the show was fairly successful from my point of view. I conveyed most of what I had intended with the work, and the interest level was higher than I had expected. ![]() One of the shelves fell off the wall, and the manipulative objects were not as clearly labeled as I had hoped. I may need to do a planned presentation at the next event. Speaking of which, my intentions with the beginning of the new year will be to make more work based on knots and have one more gallery show. I’ll be bringing the plaster trefoil to the JMM Art Exhibit in Seattle in a couple of weeks. I’m typing this a bit after the fact, but here is an update! As the end of the semester approached, I worked to put together a gallery style exhibition of knot theory. My plan was to have “real world” knots and their mathematical counterparts, along with some larger more sculptural examples of a few of the knots. I wanted some hands-on aspect to the show, as well as some sculptures in more of a museum artifact type of situation. I also planned on having an example of the application of knot theory which was inspired by this paper: Knots and braids on the Sun. I hadn’t tried to make a spherical object from plaster yet, but I had thought about it before. I emulated an approach I had seen in a globe making video somewhere a couple of years ago. It worked pretty well and was a lot of fun. Sun sculpture in progressĪfter getting this initial hemisphere, I added tubes filled with plaster as I had made in an earlier project. The plaster helped them to hold a certain curvature. I then colored everything sorts of orange and yellow. It was supposed to be an abstract representation of solar ejections coming out of the sun in a braid-like pattern. It was interesting, but I did not include it in the final show. I may consider it again, however, if I ever make a series of playground equipment. ![]()
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