This week's C&P set was...interesting. It decided to throw a bunch of problems at me that did not exactly fit with my normal approach to attacking math problems. It's good for me, but can be frustrating when I am not allowed to discuss them with people. Despite this I still found myself presenting a solution (despite having told myself that I was not going to this week). The set that is currently out seems to fit my style (which I would have no idea how to characterize) better.
The set theory prof is out of town, so we did not have class this week.
Geometric graph theory never fails to amaze me. This week we talked about rigidity of graphs and why infinitesimal motions (not just physical) motions are important to engineers. We had proofs in terms of engineering concepts. Prior to this class I knew math had applications in physics and engineering, but I would not have guessed that physics and engineering had applications in math.
I absolutely love Topics in Geometry. The material in the class itself is fascinating to me and is making me look at algebra differently...there is a lot more of algebra that can be visualized than I thought there was. I think my favorite part though is the "office hour". Every Friday we have class as normal for the first hour and then have an hour where we can get questions answered and such. We never have enough questions to fill a whole hour, so Gábor tells us about all kinds of cool geometric things that we are not going to get to in class. This morning he explained how you can use geometry to analyze topological properties of some algebras and how number theory can be used in geometric arguments. Seeing all of the connections is both exciting and frustrating. It is amazing that they exist and you can prove really cool things by drawing the connections, but at the same time it means you never know what kind of math will be used in the nicest proof of any given statement and there are currently so many branches of math and so much in each branch that is no way to know if you have the right background and certainly no way to know everything that could possibly be useful.