The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

I worked from this book extensively during my undergraduate thesis, and it was an absolute joy to read and learn from. Compared to Lickorish ("An Introduction To Knot Theory"), the explanations were easy even if you hadn't had 3 semesters of graduate abstract algebra.

If you want a fun application of where knot theory can be used "in the real world" there are some interesting applications to DNA untangling and the function of DNA Topoisomerase - e.g.:

https://sinews.siam.org/Details-Page/untangling-dna-with-kno...

http://matwbn.icm.edu.pl/ksiazki/bcp/bcp42/bcp4216.pdf

Re: The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

#5

Post by pbk1 » Thu, Feb 07, 2019, 3:42 PM UTC

Wow - I took introductory topology with Colin just a few years ago. He wove in a few examples from OP's book and I had several friends who took his knot course - excellent resource for anyone interested and he is an amazing person/mathematician.

Readers here might appreciate one of my favorite homework "problems" from his topology course- it's a simple but counter-intuitive mathematical result that's easy to replicate even for young children. Rip a sheet of paper (8.5x11 will do) in two long strips. Take the strips and tape them so that one is a ring and the other is a Moebius strip.

Here's where the magic happens: make a guess about what happens when you cut each object long-ways, then cut both objects with a pair of scissors. Won't give any spoilers but the result may surprise you :)

EDIT: also forgot to mention the knot book and his topology book are great at highlighting open/outstanding problems that precocious undergrads could tackle. I definitely wish more authors of math texts went out of their way to point out avenues for exploration like this.

Re: The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

#6

Post by _emacsomancer_ » Thu, Feb 07, 2019, 3:52 PM UTC

Puts me in mind also of The 85 Ways to Tie a Tie [https://en.wikipedia.org/wiki/The_85_Ways_to_Tie_a_Tie].

Re: The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

#7

Post by lumberjack » Thu, Feb 07, 2019, 4:03 PM UTC

dannykwells wrote: post #4

I worked from this book extensively during my undergraduate thesis, and it was an absolute joy to read and learn from. Compared to Lickorish ("An Introduction To Knot Theory"), the explanations were easy even if you hadn't had 3 semesters of graduate abstract algebra. If you want a fun application of where knot theory can be used "in the real world" there are some interesting applications to DNA untangling and the fu…

I found this book a bit too informal. A very easy introduction to Knot Theory, that is still mathematically rigorous is Cromwell's, one of the few books written explicitly for undergraduates. After you are about 1/3 of the way through, you can start using Lickorish. Combined they make the best introduction, by far.

Re: The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

#8

Post by gilleain » Thu, Feb 07, 2019, 4:16 PM UTC

dannykwells wrote: post #4

I worked from this book extensively during my undergraduate thesis, and it was an absolute joy to read and learn from. Compared to Lickorish ("An Introduction To Knot Theory"), the explanations were easy even if you hadn't had 3 semesters of graduate abstract algebra. If you want a fun application of where knot theory can be used "in the real world" there are some interesting applications to DNA untangling and the fu…

there are also knotted proteins, although they are rarer:

https://en.m.wikipedia.org/wiki/Knotted_protein

Re: The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

#9

Post by posterboy » Thu, Feb 07, 2019, 4:21 PM UTC

pbk1 wrote: post #5

Wow - I took introductory topology with Colin just a few years ago. He wove in a few examples from OP's book and I had several friends who took his knot course - excellent resource for anyone interested and he is an amazing person/mathematician. Readers here might appreciate one of my favorite homework "problems" from his topology course- it's a simple but counter-intuitive mathematical result that's easy to replicat…

I will get two entangled moebius strips, right!?

Re: The Knot Book: Introduction to the Mathematical Theory of Knots (1994) [pdf]

#10

Post by jlv2 » Thu, Feb 07, 2019, 4:25 PM UTC

case_of_snakes wrote: post #2

No joke, I've been wanting an introductory book on this.

Knot jokes, page 276.