Does anyone have any recommendations for books on knot theory, by any chance? I'm taking 4TT3 in the Fall and the topic will be knot theory, which I don't know too much about but sounds really interesting.

Originally Posted by oranges

Does anyone have any recommendations for books on knot theory, by any chance? I'm taking 4TT3 in the Fall and the topic will be knot theory, which I don't know too much about but sounds really interesting.

I'll be taking it too; apparently it will mainly be about algebraic topology, plus some knot theory. There's a good amount of algebraic topology in Munkres, I think. I don't know enough knot theory to recommend anything for that; if Incognitus comes around he'll be able to help more.

Originally Posted by Mahratta

I'll be taking it too; apparently it will mainly be about algebraic topology, plus some knot theory. There's a good amount of algebraic topology in Munkres, I think. I don't know enough knot theory to recommend anything for that; if Incognitus comes around he'll be able to help more.

Algebraic topology, eh? I guess it's going to be quite interesting to take this course and 3T03 concurrently. But anyway, thanks for the suggestion.

Originally Posted by oranges

Algebraic topology, eh? I guess it's going to be quite interesting to take this course and 3T03 concurrently. But anyway, thanks for the suggestion.

Well, at least from what I've seen of knot theory, its ideas are motivated by those of algebraic topology. You find particular algebraic properties which are invariant under "tying". For instance, two knots with equivalent diagrams can be related by 3 tying moves (Reidemeister moves).

What are some examples of invariants?

1. Tricolourability -- how you do this is explained better by a picture than words:
In particular, note that this distinguishes any nontrivial knot (i.e. knot which cannot be deformed to the unknot, or circle), from the unknot.

2. Knot polynomials. Here's the simplest example.

Originally Posted by Mahratta

Well, at least from what I've seen of knot theory, its ideas are motivated by those of algebraic topology. You find particular algebraic properties which are invariant under "tying". For instance, two knots with equivalent diagrams can be related by 3 tying moves (Reidemeister moves).

What are some examples of invariants?

1. Tricolourability -- how you do this is explained better by a picture than words:
In particular, note that this distinguishes any nontrivial knot (i.e. knot which cannot be deformed to the unknot, or circle), from the unknot.

2. Knot polynomials. Here's the simplest example.

Interesting stuff. I remember reading briefly about the Reidemeister moves and invariants like the Alexander-Conway polynomial, but I haven't delved too much into the subject. I'm really looking forward to this course.

Prob offtopic but for those who have done reading course, can you describe process how it is done? thanks

Originally Posted by Differential

Prob offtopic but for those who have done reading course, can you describe process how it is done? thanks

If a prof's research area interests you, email them and ask about a reading course. Provide a good description of your own interests. Math profs are very flexible in general. Unless you know the professor well, email as early as possible.

For those who don't know, you can buy any Springer book at flat rate 25$(no tax and free shipping) if McMaster has e-copy of the book through McMaster Springerlink and you will paperback version of the book. For example, math 3b03 book costs ~60$ with tax and it's paperback so double profit.

Obviously you can use e-copy but if you hate pdf's like me this is pretty good deal.