This course will cover the mathematical theory and analysis of simple games without chance moves.
Week 1: What is a Combinatorial Game?
Hello and welcome to Games Without Chance: Combinatorial Game Theory! The topic for this first week is Let's play a game: Students will learn what a combinatorial game is, and play simple games.
Week 2: Playing Multiple Games
The topics for this second week is Playing several games at once, adding games, the negative of a game. Student will be able to add simple games and analyze them.
Week 3: Comparing Games
The topics for this third week is Comparing games. Students will determine the outcome of simple sums of games using inequalities.
Week 4: Numbers and Games
The topics for this fourth week is Simplicity and numbers. How to play win numbers. Students will be able to determine which games are numbers and if so what numbers they are.
Week 5: Simplifying Games
The topics for this fifth week is Simplifying games: Dominating moves, reversible moves. Students will be able to simplify simple games.
Week 6: Impartial Games
The topics for this sixth week is Nim: Students will be able to play and analyze impartial games.
Week 7: What You Can Do From Here
The topic for this seventh and final week is Where to go from here.