xii Prefac e
matics and t o proceed t o such topics a s topology, algebra, differential ge -
ometry, and algebraic topology.
Unfortunately, mathematic s i s often taugh t a s if the only goal were t o
pass a body o f information fro m on e person t o the next. Although thi s is
certainly an important goal , it is essential to teach an appreciation fo r th e
beauty o f mathematic s an d a sense of th e excitemen t o f doing mathemat-
ics. Once readers ar e hooked, the y wil l fill i n th e detail s themselves , an d
they will go a lot farther and learn a lot more.
Who, then , i s thi s boo k for ? It i s aime d a t anyon e wit h a curiosit y
about mathematics. I hope people will pick up this book and start readin g
it on their own. I also hope that they will do the exercises: the only way to
learn mathematic s i s to d o it . Som e o f th e exercise s ar e straightforward ;
others tak e som e thought . Th e ver y hardes t ar e starre d an d ca n be a bi t
Scientists wit h primar y interest s i n physic s o r biochemistr y shoul d
find th e applications of knot theory to these fields particularly fascinating .
Although thes e application s hav e onl y bee n discovere d recently , alread y
they have had a huge impact.
This boo k ca n b e an d ha s bee n use d effectivel y a s a textboo k i n
classes. With the exception of a few spots , the book assumes only a famil -
iarity with hig h schoo l algebra. I have als o given talk s on selecte d topic s
from thi s book to high school students and teachers , college students, and
students as young as seventh graders.
The first si x chapters of the book are designed t o be read sequentially .
With the exception that Section 8.3 depends o n Section 7.4, the remainin g
four chapter s ar e independen t an d ca n b e rea d i n an y order . Th e topic s
chosen fo r thi s book ar e no t th e standar d topic s tha t on e would se e in a
more advance d treatis e o n kno t theory . Certainl y th e mos t glarin g omis -
sion i s any discussio n o f th e fundamental group . My desir e t o make thi s
book mor e interestin g an d accessibl e t o a n audienc e withou t advance d
background has precluded such topics.
The choice of topics has been made by looking for area s that ar e eas y
to understan d withou t muc h background , ar e exciting , an d provid e op -
portunities for new research. Some of the topics such as almost alternatin g
knots ar e s o ne w tha t littl e researc h ha s ye t been don e o n them , leavin g
numerous open questions.
Although I dre w o n man y source s whil e writin g thi s book , I relie d
particularly heavil y on the writings and approache s o f Joan Birman, John
Conway, Camero n Gordon , Vaugha n Jones , Loui s Kauffman , Raymon d
Lickorish, Ke n Millett , Joze f Przytycki , Dal e Rol f sen , Dewit t Sumners ,
Morwen Thistlethwaite, and William Thurston.
I would lik e to thank all the following colleagues , who contributed in -
numerable comment s an d suggestion s durin g th e writin g o f thi s book ,
and correcte d man y of the mistakes therein: Daniel Allcock, Thomas Ban -