This text gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research, covering virtual knots, counted invariants, Jones polynomial, algebraic invariants, and applications of virtual knots. 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.
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