Games without Chance: Combinatorial Game Theory

Go to Course: https://www.coursera.org/learn/combinatorial-game-theory

Introduction

### Course Review: Games without Chance: Combinatorial Game Theory If you have ever enjoyed games that challenge your strategic thinking, or if you have a curiosity for mathematics, then the Coursera course **"Games without Chance: Combinatorial Game Theory"** could be the perfect academic venture for you. From diving deep into the principles of games without elements of chance to applying mathematical theories in practical scenarios, this course is a treasure trove for enthusiasts and learners alike. #### Course Overview At its core, this course introduces students to the fascinating world of combinatorial game theory, which is the study of mathematical games that are played with deterministic strategies. Over the span of seven weeks, the curriculum is structured to provide both theoretical insights and hands-on experience with various combinatorial games. Each week covers a different aspect of game theory, from the fundamentals of what constitutes a combinatorial game to advanced strategies like simplifying complex games and analyzing impartial games like Nim. #### Weekly Breakdown - **Week 1: What is a Combinatorial Game?** The course kicks off with an engaging introduction to combinatorial games. Participants will play simple games, learning the foundational concepts while having fun. This interactive start sets a positive tone for the weeks ahead. - **Week 2: Playing Multiple Games** Building on the introductory week, students explore added complexity by analyzing multiple games simultaneously. The concept of combining games and understanding the negative of a game is both insightful and mathematically intriguing. - **Week 3: Comparing Games** In the third week, the focus shifts to comparing games through inequalities. The course will arm you with the tools needed to evaluate the outcomes of game combinations, enhancing your analytical skills. - **Week 4: Numbers and Games** This week dives into how numbers play a vital role in combinatorial games. Students will learn to identify which games can be classified as numbers and unlock the secrets behind "win numbers," adding a crucial layer of strategy. - **Week 5: Simplifying Games** Strategies for simplifying games are tackled in the fifth week. Here, you will discover concepts like dominating moves and reversible moves, which are essential for crafting winning strategies in complex games. - **Week 6: Impartial Games** An exploration of Nim, one of the most famous impartial games, forms the focus of the sixth week. This lesson is pivotal for understanding how game theory applies to games where players have no control over their moves beyond basic strategy. - **Week 7: What You Can Do From Here** The final week serves as a capstone, discussing possible future directions in combinatorial game theory. This wrap-up not only provides closure but also inspires learners to delve deeper into advanced topics in the field. #### Resources This course is structured to ensure students have access to comprehensive resources, including readings, video lectures, quizzes, and community discussions, which foster a supportive learning environment. #### Recommendation **"Games without Chance: Combinatorial Game Theory"** is highly recommended for anyone interested in mathematics, strategy games, and logical problem-solving. Whether you are a student looking to enhance your analytical skills, a teacher seeking resources for your classes, or simply a game enthusiast looking to deepen your understanding, this course offers a rich learning experience. Its hands-on approach, combined with a well-structured syllabus, makes it accessible to beginners while still providing depth for more seasoned participants. Plus, the potential to apply what you learn to real-world scenarios in strategy games can be incredibly fulfilling. Enroll today and embark on a journey through the captivating realm of combinatorial game theory!

Syllabus

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.

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.

The topics for this third week is Comparing games. Students will determine the outcome of simple sums of games using inequalities.

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.

The topics for this fifth week is Simplifying games: Dominating moves, reversible moves. Students will be able to simplify simple games.

The topics for this sixth week is Nim: Students will be able to play and analyze impartial games.

The topic for this seventh and final week is Where to go from here.