Posts Tagged ‘Knot Theory’

180px-Four_Colour_Map_Example.svgDon’t let the title mislead you, coloring isn’t kid’s stuff.  Coloring of graphs is a rich mathematical area of research which young mathematicians will encounter frequently.

Mr. Maier is going to talk about coloring arguments and some of their applications to combinatorial problems, especially problems from the theory of plane tilings, but also from knot theory, probability, and some popular puzzles.  Is it possible to cover an eight-by-eight inch chessboard with two-by-one inch dominos? Is it possible to cover the remainder with dominos? If so, how, and if not, why not?

If you’d like to learn more about coloring the following links may be useful:

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rh-trefoil-knotUnfortunately, due to state MATHCOUNTS and other activities, many students missed Dr. Razvan Gelca’s excellent talk on Invariants and Knot Theory.  Thankfully Dr. Gelca has made his slides available for these important topics.

You will find several interesting problems and solutions in this first deck:  Razvan Gelca – Invariants1

The second set of slides deals with Knot Theory.  Knot Theory is a good illustration of the importance of pure math and the topics explored through math circles.  For hundreds of years mathematicians explored the various ways that a string or rope could be twisted around itself motivated by little more than intellectual curiosity.  Today, however, we are finding that the principles of Knot Theory are critical to some of the most important applied sciences such as molecular biology.  Razvan Gelca – Knots

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