An Invitation to Knot Theory

Virtual and Classical
1. Auflage 2016
ISBN: 978-1-4987-0164-8
Verlag: CRC Press

Buch, Englisch, 288 Seiten, Format (B × H): 178 mm x 259 mm, Gewicht: 680 g

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory

An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra.

The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.

Autoren/Hrsg.

Dye, Heather A

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Populäre Darstellungen der Mathematik

Inhaltsverzeichnis

Knots and crossings. Knot polynomials. Algebraic structures. Appendices.

Über Autor(innen)

Heather A. Dye is an associate professor of mathematics at McKendree University in Lebanon, Illinois, where she teaches linear algebra, probability, graph theory, and knot theory. She has published articles on virtual knot theory in the Journal of Knot Theory and its Ramifications, Algebraic and Geometric Topology, and Topology and its Applications. She is a member of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA).