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

math.harvard.edu

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

#13

Post by pbk1 »

posterboy wrote: post #9
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!?

Only one way to find out!

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

#16

Post by nabla9 »

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…

Additional trick.

Make a Moebius strip that is thick enoug that you can cut it long-ways into three same width strips. But before you cut them completely, twist the middle strip again.

  a-------------d
  b-----b\/c----c
  c-----c/\b----b
  d-------------a

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

#18

Post by dannykwells »

lumberjack wrote: post #7
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.

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).

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

#19

Post by jkingsbery »

dannykwells wrote: post #18
lumberjack wrote: post #7

Earlier quoted context omitted.

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 a…

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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