Mathematical Game Theory: Analyzing Games of Pure Strategy

How do mathematicians analyze strategic games where nothing is left to chance? Combinatorial game theory provides the elegant mathematical framework needed to dissect two-player games of perfect information. This written course guides you from the fundamental principles of game states to advanced strategies for classic impartial and partisan games. You will develop the analytical skills to break down complex positions, assign mathematical values to game states, and systematically determine winning moves. What you'll learn: - Understand the foundational definitions of combinatorial games, including impartial and partisan game rules. - Analyze game positions mathematically using the Sprague-Grundy theorem and nim-values. - Calculate winning strategies for classic games such as Nim, Hackenbush, and Domineering. - Evaluate game additions and combinations to find optimal moves in compound game states. - Explore modern computational perspectives on game theory, including the basic algorithmic complexity of finding winning strategies. You will begin by learning core terminology and basic game structures before progressing to algebraic notations and strategic calculations. Through clear written explanations and step-by-step mathematical breakdowns, you will master the theory behind perfect-information gameplay. This course is designed for beginners in mathematics, computer science, or logic, requiring no prior background in game theory. Start exploring the fascinating mathematics of pure strategy today.