WHY KNOT? An Introduction to the Mathematical Theory of Knots by Colin Adams
Key College Publishing, 2004 ISBN 1-931914-22-2
For those of us who feel that perhaps we ought to know some formal [mathematical] knot theory, this is a user-friendly starter kit in a cartoon format of 4 sections and 3 appendices, devoid of any real algebra, giving us enough data to decide if we would like to pursue the subject further … or stop (but with minds widened by some useful new concepts).
Section 1 A brief introduction to knots, real and theoretical
Section 2 Mathematical knot types and tools: trivial, prime and composite knots; chirality (handedness); crossing, linking and unknotting numbers; the 3 Reidemeister moves; and the Dowker notation.
Section 3 A brief history of knot theory, with its relevance to knotted DNA and molecules,
Section 4 A look into the Future
Appendix 1 Extra fun
Appendix 2 Prime knots through 8 crossings
Appendix 3 Prime links through 7 crossings
Further reading
The author, Colin Adams, is a Professor of Mathematics, who has (twice) won teaching awards, and is the author of an earlier, more detailed, introduction of knot theory, The Knot Book, Prentice Hall, 2004.
The hefty price of this later publication unfortunately reflects its limited target market, because it is a slim product (a mere 62 pages), although it does punch above its weight with 39 brain-stretching practical exercises (labelled Experiments), and answers to the 25 needing them after Appendix 3.
To reproduce and manipulate the many knot diagrams (I counted around 200), this booklet comes with an articulated plastic worm, 1-metre long by 8mm diameter, of 50 pop-jointed segments (© Richard X Zawitz 1981). This orange-&-purple creature – trade name ‘the Tangle® – was too wriggly for me and so I resorted to a piece of cord instead, but others may like it.
Geoffrey Budworth