In the beginning of class today we derived a way to simplify the Jones polynomial, but it's still a very long and complicated process (just slightly less than it was before). It wasn't exceptionally helpful, because the Jones polynomial simplified is still NP-hard, meaning that even computers can't compute it quickly or efficiently. Luckily, she also told us that today would be the last time she'd have us compute a Jones polynomial for a specific knot (no more sitting and cancelling A's for an hour and a half!).
After lunch we learned about braids. According to Alexander's Theorem, any knot can be represented by a braid. A braid is made by crossing any number of strands over and under each other, then connecting the ends. It's hard to visualize knots as braids (unless there's an algorithm she's not telling us to get the braid from the knot, which seems likely), but once they're braids they're easier to talk about, and they can be written down as a simple string of letters (representing different strands going over or under each other).
|I think, therefore it is.|
After class, in the TA session, Jeff did a quick presentation on polynomial long division, and then we talked about a class quote and a class motto for the VSA "termbook." Like a yearbook, but just for these three weeks. Our quote is "Mathematical proverbs: 1) Just because something seems easy, doesn't mean it is. 2) Your teacher may sometimes ask you to prove something that isn't true." Our motto is "It's probably a trefoil..." However, the motto came very close to being what's shown on the board in the picture, a reference to when we were working on finding the two-bridge representation of figure-eight knots. Brenna and Ethan each got very excited when they thought they found it, but I looked over and told them that their knots were trefoils, not figure-eights. Brenna swore that it only turned into a trefoil after I said that, and that beforehand it was clearly a figure-eight knot.
This evening was also Proctor Group Night, which really just meant that each proctor group got dinner together. We went to the Coco Cafe, and I got a grilled cheese sandwich with tomato and pesto, which was amazing. They also had really good peach lemonade as the special of the day. Then we went to Hot & Cold, a dessert place where they specialize in coffees and shaved ice. I ordered a strawberry lemonade shaved ice, which was refreshing and as tasty as it looked. Both cafes were rather far away from each other and the dorms, so we did a lot of walking. On the way, I talked to Kelly about the classes she's taking for her majors and minors (majors in secondary education and math, minor in psychology, previously a minor in sociology). Psychology sounds really fascinating, so now I'm thinking about a minor in that. (Double majoring in math and physics and double minoring in psychology and philosophy is definitely going to be manageable...)