Here’s the independent research I produced during my final year at Northwestern. It’s based on the absolutely fantastic text: Winning Ways for Your Mathematical Plays. I can’t recommend this text highly enough.
In my thesis, the first 40 pages or so are an alternate presentation of the relevant ideas from WW: that text isn’t written formally, so I first present a definition-theorem-proof style presentation of the ideas I’d need for my original work. Then, I apply the WW framework to analyze some very simple King and Pawn Endings on a chessboard.