Inspiration from Science Fair

So this week at ASU was pretty standard. I'm falling a bit behind in differential geometry again. It looks like I gotta hit the books hard this weekend. We've been learning really cool and general theorems about surfaces like Isometries and the Theorema Egregium, which literally translates to " The Remarkable Theorem" (it is actually very cool). Surprisingly this week, there was a lot of computation in proving various theorems, which was something I had not seen too much of in Differential Geometry previously. The lecturer actually took time out of the lecture to tell us the importance of computation. A lot of the theorems we had this week, including the Theorema Egregium, had very computational proofs that ultimately led to a beautiful and abstract statement. This weekend really opened me up to the possibility that sometimes the ugly road in math can lead to the best results.

Another cool thing I did was visit the Arizona Science and Engineering fair this week. I got to see the cool high school projects, which as always were super awesome. I also got to see the middle schoolers and the lower schoolers from our school. Seeing the younger kids projects was cool, since I got to see how developed their creative thinking skills in math already are. I visited a lot of my friends from science fair last year and saw how they've been doing in life and research. The most interesting part, however, was seeing a friend (Abi) and his project. He worked on the secretary problem (https://en.wikipedia.org/wiki/Secretary_problem). Also Wikipedia is not very bad for math so its ok that I used a wikipedia link. In his paper, he tackled different variations of the secretary problem similarly to how I was solving different variations of nim. On his poster, he had fairly complicated looking recursive equations that allowed for picking the optimal secretary in certain cases. One neat trick he did, however, was to convert some of his summations into integrals. This not only made his equations look much less intimidating, but also gave some intuition in his equation. Another point he focused on was looking at the results as the number of candidates in his problem got larger.

I now have a couple of things that I want to try to do to my equations. Maybe this will give the nice results I've been looking for all this time. Maybe it wont ( like all the other things I've tried). I'll keep you updated with how my equations look next week.

Thanks for reading~