Linknot Knot Theory by Computer - Practical Knot Theory

In this review of LinKnot: Knot Theory by Computer the reviewer finds a focused, hands-on resource aimed at students and researchers who want computational tools alongside classical theory. The book's biggest strength is its practical orientation: it combines clear exposition of knot theory topics with direct access to the LinKnot Mathematica/webMathematica package, making it immediately useful for those who prefer experiment-driven learning and for researchers exploring open problems.

Key Features

• Computational focus: The inclusion of the LinKnot package lets readers perform concrete calculations and test conjectures rather than only reading abstract proofs.
• Broad topic coverage: The book addresses basic notions and advanced themes such as unknotting number, braid family representatives, and amphicheirality to support varied study paths.
• Problem-oriented methods: New approaches for handling open problems are presented, helping researchers approach questions like invertibility and undetectability with computational experiments.
• Cross-disciplinary relevance: Examples and explanations are accessible to readers from chemistry, molecular biology and physics who need mathematical tools for applications.
• Illustrations and examples: Numerous diagrams and worked computations improve intuition for topology concepts that are otherwise hard to visualize.

Who It's For

The book is best for graduate students, research mathematicians, and technically minded readers in related exact sciences who want a practical, computation-ready introduction to knot theory. It particularly suits those who already use or can access Mathematica or webMathematica and wish to run examples themselves.

Readers looking for a purely introductory textbook without software, or casual hobbyists who do not plan to run computations, may find parts of the book too focused on experimental mathematics and implementation details.

Pros & Cons

Pros

• Direct integration with LinKnot software makes experimentation straightforward and reproducible.
• Covers both foundational concepts and contemporary problems, useful for research preparation.
• Clear illustrations and worked examples aid geometric intuition.

Cons

• Reliance on Mathematica/webMathematica means readers without access to those tools get less value.

Specifications

Our Verdict

LinKnot: Knot Theory by Computer is a valuable resource for readers who want to combine theoretical topology with hands-on computation. It offers good value to graduate students and researchers by turning abstract problems into computable experiments, but it is less suitable for readers who cannot run Mathematica or who need only a non-computational introduction.

Frequently Asked Questions

Does the book include software?
The book is written to be used with the LinKnot package for Mathematica and webMathematica and includes examples intended for those tools.

Is prior knowledge required?
Basic background in topology or an undergraduate mathematics level helps, although motivated readers from related sciences can follow the computational examples.

Is this suitable for research work?
Yes; the text emphasizes experimental mathematics and methods that support exploration of open problems useful to researchers.