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.
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