![]() ![]() Students with disabilities need to also contact Disability Support Services in the Ley Student Center. All discussions will remain confidential. Your grade in the class will be based on the following weights:Īny student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first week of class. 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 (use your netid to log in). If you haven't taken necessary prerequisite but would still like to take the course, please talk to me. In particular, one should be familiar the rank, nullity, determinant, and eigenvalues of a matrix. The suggested prerequisite is a course in linear algebra or a course that discusses matrices and some of their properties: Math 221, Math 354, Math 355, or permission of instructor. The course will be mostly self-contained and will have an emphasis on careful proof writing. Some topics we may discuss are 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, slightly 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) Teaching Assistant: Taylor Martin (taylor.martin at rice dot edu) Math 304: Elements of Knot Theory | Spring 2012Ĭlass meets: MWF 10am - 10:50am in HB 427Īll homework and reading assignments can be found on OWL-Space COMPOSITE KNOT DETERMINANTS Contents 1.Math 304: Elements of Knot Theory - Spring 2012.Periodic Projections of Alternating Knots.Minimal Unlinking Pathways As Geodesics in Knot Polynomial Space ✉ Xin Liu 1, Renzo L.KNOTS and KNOT INVARIANTS: an INTRODUCTION Contents 1.Total Linking Numbers of Torus Links and Klein Links.Knots, Reidemeister Moves and Knot Invariants.On Homology 3-Spheres Defined by Two Knots 3.Grade 7/8 Math Circles Knot Theory What Are Mathematical Knots?.The Kauffman Bracket and Genus of Alternating Links Bryan M.Unexpected Ramifications of Knot Theory. ![]()
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