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Games without Chance: Combinatorial Game Theory

Approx. 14 hours to complete

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Course Summary

Learn about the mathematical study of combinatorial games and its applications in real-world situations through this course. Discover various strategies and techniques used in combinatorial game theory to analyze and solve games.

Key Learning Points

Understand the fundamentals of combinatorial game theory and its applications
Learn about different types of games and their strategies
Explore the mathematical study of game theory through various examples and case studies

Learning Outcomes

Develop analytical thinking and problem-solving skills
Learn to apply game theory concepts to real-world situations
Understand the mathematical foundations of combinatorial game theory

Prerequisites or good to have knowledge before taking this course

Basic knowledge of algebra and calculus
Familiarity with programming languages such as Python or Java

Course Difficulty Level

Intermediate

Course Format

Self-paced
Online

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Related Education Paths

Notable People in This Field

John Nash
John von Neumann

Related Books

Description

This course will cover the mathematical theory and analysis of simple games without chance moves.

Outline

Week 1: What is a Combinatorial Game?
Introduction to Two Players Left and Right
What is a Combinatorial Game?
Example Problem
Example Problem Solution
Start Here
Consent Form
Syllabus
Course Logistics
About The Instructor
Get More From Georgia Tech
Start Here (Week 1)
Game Rules
Week 1 Lecture Slides
Extra Problems

Week 2: Playing Multiple Games
Cutcake and Adding Games
The 0 Game
Adding Games
Quiz Problems
Week 2 Quiz Review
Start Here (Week 2)
Game Rules
Week 2 Lecture Slides
Earn a Georgia Tech Badge/Certificate/CEUs
Extra Problems
Quiz Week 2
Mid-Course Survey 1

Week 3: Comparing Games
Ordering Games
Example and a Problem
Problem Solution
Ski Jumps
Games That Are Not Numbers
Proof and Quiz
Start Here (Week 3)
Game Rules
Week 3 Lecture Slides
Week 3 Quiz Solutions
Extra Problems
Quiz Week 3

Week 4: Numbers and Games
Some Numbers Are Games
Some Games Are Numbers
Simplicity
More Numbers
Quiz Preview
Start Here (Week 4)
Game Rules
Week 4 Lecture Slides
Week 4 Quiz Solutions
Extra Problems
Quiz 4
Mid-Course Survey 2

Week 5: Simplifying Games
New Ways of Simplifying Games
Examples From Nim
General Reversible
Toads and Frogs
Start Here (Week 5)
Game Rules
Week 5 Lecture Slides
Week 5 Quiz Solutions
Extra Problems
Quiz 5

Week 6: Impartial Games
Nim and How to Win
Impartial Games, Reversible Moves
Examples, Mex
All Impartial Games Are Equivalent to Nim
Start Here (Week 6)
Game Rules
Week 6 Lecture Slides
Week 6 Quiz Solutions
Extra Problems
Quiz 6

Week 7: What You Can Do From Here
Infinite Games
Loopy Games
Mean Values, Hot, Cold, Sente, Gote
Atomic Weights
Start Here (Week 7)
Game Rules
Week 7 Lecture Slides
Week 7 Quiz Solutions
Bonus Quiz
Final Week Survey

Resources
Game Rules

Summary of User Reviews

Explore the fascinating world of combinatorial game theory with this comprehensive course on Coursera. Students have found the course to be highly engaging and informative, with a strong emphasis on practical applications. One key aspect that many users thought was good was the clear and concise explanations of complex concepts.