The Second Midterm

This week has been interesting at my Senior Research Project site. I spent most of my time studying for differential geometry instead of looking at nim since we had a midterm this week. For nim, this week, I primarily looked at trying to convert general theorems about impartial games into nim as well as trying to look at theorems about other games and how they would translate into nim. I had a lot of general hunches about different games, but proving things has been harder than I originally expected. With a lot of proofs I've attempted, the intuition for the general outline of the proof has been there, but I have been largely unsuccessful at converting these ideas into rigid proof-writing. Theorems such as the Sprague Grundy theorem that make statements of different games often dont provide very simple proofs. Rather than showing directly that a certain aspect of a game holds, the theorems use proofs like contradiction, induction, and casework. Some of the proofs also seem to follow a circuitous path only to get a nice proof at the end. Thats been nim research for me.

Now for most of the week, I have been frantically cramming differential geometry. After falling behind a bit in the past few weeks, I caught up this week and felt somewhat ready for the midterm. Thankfully, this was not actually for a grade. I took the practice midterm and was able to solve about three of the five problems. With the book, I could solve four of them. But one problem took me too long to solve. It wasn't too long, but it just had a proof that went in a direction that I never bothered to look at ( like all the game theory proofs I had been reading).

I kept studying for the midterm, thinking that I wasn't prepared. Suprisingly, the midterm went well (at least for my standards) and I got four of the five problems. The last problem seemed obvious from reading it and turned out to have a simple proof. I just overthought it.

So now I feel like I'm back on track (for real this time) with differential geometry. I've really enjoyed the college experience and schedule. It has taught me to manage my time better, study independently, and read higher level textbooks better. The class has definitely taught me skills I'll need in college next year.

As for nim... I'm a bit behind. I've hit a few roadblocks, but I'm ready to keep trying to solve some of the cool problems I have.

That is all for now. Thanks for reading~