Advanced Geometry SummaryMonday - Friday, June 26 - June 30, 2006The Advanced Geometry Working Group is really the Knot Theory Working Group. Each afternoon the group attends Colin Adams's course for the Undergraduate Faculty Program from 1 to 2. Then the group discusses ideas, studies examples and works problems from the course during the next hour, 2-3. While an ultimate goal of the group is to consider how knot theory can be brought into the secondary classroom, the first week we devoted ourselves to developing an understanding for ourselves of the math in the course.
Note: There will be no attempt in these notes to explain the contents of the course. For anyone wanting a reference, The Knot Book On Monday, during the course we all formed human figure 8 knots (with about 10 people per knot) and then deformed the knot from one orientation to the opposite orientation by a little "knot dance." In the group time we discussed the meaning of "handedness" in the crossings of a projection of a knot. We also repeated the Figure 8 Knot construction with rope to better understand it in the light of how the crossings change. On Tuesday, the course was treated to a guest lecture by Sir Randolph Bacon III.
He spoke on some knotty nautical problems that arose during his harrowing yachting adventures. In a flashback, Mel Slugbait told us about Reidemeister Moves and Dowker notation for describing crossings. In the group time we had a lot to discuss and figure out about these ideas. On Thursday, we worked more on Reidemeister moves, links, and torus knots, as well as spherical moves. On Friday, we were introduced to stick knots, and the group experimented with knots from coffee stirrers and drinking straws.
This first week our group benefited from the participation of four member of the DIPD group. We will miss them in Week 2. |
by Colin Adams has a lot of the material and a similar point of view.
