DESCRIPTION: This course will be an elementary introduction to the mathematical theory of knots with emphasis in some developments that occurred in the last thirty years. We will describe the different classifications of knots, their properties, various ways for measuring their complexity and some applications of knot theory to biology and physics. Since some open problems in this area can be explained at an elementary level, students will also have the opportunity to get a taste of what it is like to do research in mathematics. We expect to cover material from the first eight chapters of the textbook. If time permits, we will also cover chapter nine.
TEXTBOOK: Adams, Colin; The knot book. An elementary introduction to the mathematical theory of knots. Revised reprint of the 1994 original. American Mathematical Society, Providence, RI, 2004. xiv+307 pp. ISBN: 0-8218-3678-1.