An Invitation to Knot Theory ─ Virtual and Classical

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.

Heather A. Dye is an associate professor of mathematics at McKendree University, where she regularly teaches a wide range of undergraduate courses. She has mentored students' theses in mathematics and has co-directed a summer research program in knot theory. She is an active researcher in virtual knot theory and shares this interest with her undergraduate students.