Knot Theory Intersession 2014

MATH 494 Knot Theory (3) Intersession 2014

CRN 48
M-F 1 – 3:50 p.m. SH-155
Hoffoss, D.

A knot is a closed loop of string; two knots are equivalent if one can be wiggled around, stretched, tangled and untangled until it coincides with the other. Knot theory is the mathematical study of knots and their equivalence. It has connections to several different branches of topology, geometric group theory, and abstract algebra. Even DNA, molecules, and viruses have connections to knotting, and their knot type has relevance to the underlying biology.

In this course we will formalize knots mathematically, and learn techniques to distinguish them from one another. Some topics we may discuss include 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. This course will have an emphasis on careful proof writing. The course will count as an upper division elective in the math major. Prerequisite: Math 320 (in particular, you will want to be familiar with rank, nullity, determinant, and eigenvalues of a matrix), but students may be admitted with Math 160 plus permission of instructor. Please see Dr. Hoffoss if you would like to take this course but do not have the necessary prerequisite. Limit 20



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