Title: Knot Invariants and the Pretzel Knot P(k,k,-k)

Adviser: Robb Todd

Description: The Goal is to learn as much about pretzel knots as possible, including studying closed forms of the Jones Polynomial for special families of Pretzel links and studying the zeros of the Jones polynomials for those families pretzel links. If possible we will try and apply or generalize what we learn to the the family of Pretzel Knots P(k,k,-k).

Prerequisites: The student should be comfortable with Calc I,II, and III, Linear Algebra (4050), Abstract Algebra I and II (4110, 4120). The project will be guided reading of research papers and at least weekly discussions.. The student should also be familiar with computing in MAPLE.