*Knots Unravelled* is a guide to the fascinating world of knots, from the familiar realm of knotted string to the less familiar branch of mathematics known as knot theory.

- Are two given knots the same or different?
- How many knots are there?
- Can knots be classified?

Questions like this are easily asked, but finding answers requires more effort. Mathematical ideas help to put the study of knots on a firm footing, and also either answer such questions, or explain why an answer cannot be found. The core chapters of *Knots Unravelled* lead the reader through this mathematics, from the basics to the frontiers of current work in knot theory.

Between the main chapters, the ‘interludes' reveal some of the rich variety of ways in which knots appear throughout human culture, drawing attention to related mathematics and making connections with other material in the book.

A key feature of the text is the range of tasks and activities for the reader to work through---with string, rope, or pencil and paper to hand! Complete solutions are provided at the back of the book.

The book makes full use of clear diagrams, and a table of knots, a glossary and an index are included.

Sample pages can be seen in the Book Gallery.

Reviews of *Knots Unravelled* appear in:

*The European Mathematical Society Book Reviews*(January 2012)*Mathematical Digest*(January 2012)*MAA Reviews*(April 2012)*Mathematics in School*(May 2012)*Zentralblatt MATH*(Springer)*Mathematical Reviews*(January 2013)*The Mathematical Gazette*(March 2014)

- European Mathematical Society Book Review (PDF)
- Mathematical Digest (PDF)
- MAA Reviews
- Mathematics in School (PDF)
- Zentralblatt MATH
- Mathematical Reviews (PDF)
- The Mathematical Gazette (PDF)
- Book Gallery
- Order
- Order form (PDF)

“It is a very attractive presentation of elementary knot theory and I shall have no hesitation in recommending it to any beginner wondering how to start thinking about knots.” Raymond Lickorish

In all but the last chapter of the book the mathematical methods involved are not advanced and should be accessible to any enquiring reader, from around age 12 or 13. The final chapter is more demanding, requiring some familiarity with negative powers and the idea of polynomials. Throughout the book the reader is required to follow careful reasoning and some of the ideas are quite sophisticated.

For the teacher, *Knots Unravelled* is a useful classroom resource, either for individual study, or as the basis for investigative work.

Meike Akveld has taught mathematics at school (for 10 years) and university and currently teaches at ETH Zürich, Switzerland. Andrew Jobbings taught mathematics at secondary school in England (for 28 years) before founding Arbelos.

Both authors first came across mathematical knot theory during their studies in topology, and both are keen to bring mathematics to a wider audience. They met in Minsk in 2009 as part of their voluntary work for the Kangourou sans Frontières.

- Introduction
- Knots everywhere
- Knots in rope
- Knot science
- History

*Interlude* Knots in paper

- Working with diagrams
- Describing knots
- Mathematical knots
- Projections and knot diagrams
- Knotted or not? The same or different?
- Reidemeister moves

*Interlude* Celtic knots

- Counting crossings
- Telling knots apart
- The crossing number
- Which crossing numbers are possible?
- Does the crossing number classify knots?
- Crossing number 5
- Classifying knots

*Interlude* Tie knots

- New knots from old
- Mirror images
- Combining knots
- Changing crossings

*Interlude* The figure of eight

- Using colours
- Knot invariants
- Three-colourability

*Interlude* Hunter's bend

- Links
- What is a link?
- The Borromean rings
- Components
- The linking number
- Three-colourability

*Interlude* Torus knots

- Knot polynomials
- The bracket polynomial
- The writhe
- The
*X*-polynomial - The Jones polynomial

*Postlude* A special trefoil

Solutions

Bibliography

Table of knots and links

Glossary

Index

© A K Jobbings 2004–2018

Clicking a link will scroll the page to the relevant section.

“What a gorgeous book! Congratulations!” Jeffrey Weeks

More testimonials“*Knots Unravelled* is a beautiful introduction to the world of knots at a basic level.” EMS Book Review

Soft bound

17.0 cm by 24.6 cm

viii + 121

Over 250 high quality black and white

978 0 9555477 2 0

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