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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




there are also knotted proteins, although they are rarer:

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


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.


After 15 years of doing math, I've decided that, for myself, the best introduction isn't the one that's "rigorous" or "in-depth", it's the one the leaves you wanting to learn more. For me, that was Colin's book. I wish more topics in math had entry-level books that explicitly helped contextualize why certain questions were being asked, rather than defining undergraduate simply by what material is covered/how things are proved (of course, I ended up as an applied mathematician, so it could just be me).


I had a class with Adams while at Williams (multivariable Calculus, never got to take his Knot Theory class). He was a great teacher, and excellent about teaching students why they should care.




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