Games without Chance: Combinatorial Game Theory

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Opleiderscore: starstarstarstar_borderstar_border 6,3 Coursera heeft een gemiddelde beoordeling van 6,3 (uit 4 ervaringen)

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Beschrijving

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

Created by:  Georgia Institute of Technology
  • Taught by:  Dr. Tom Morley, Professor

    School of Mathematics
Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.3 stars Average User Rating 4.3See what learners said Coursework

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

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

Created by:  Georgia Institute of Technology
  • Taught by:  Dr. Tom Morley, Professor

    School of Mathematics
Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.3 stars Average User Rating 4.3See what learners said Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

Help from your peers

Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.

Certificates

Earn official recognition for your work, and share your success with friends, colleagues, and employers.

Georgia Institute of Technology The Georgia Institute of Technology is one of the nation's top research universities, distinguished by its commitment to improving the human condition through advanced science and technology. Georgia Tech's campus occupies 400 acres in the heart of the city of Atlanta, where more than 20,000 undergraduate and graduate students receive a focused, technologically based education.

Syllabus


WEEK 1


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.


4 videos, 10 readings expand


  1. Reading: Start Here
  2. Reading: Consent Form
  3. Reading: Syllabus
  4. Reading: Course Logistics
  5. Reading: About The Instructor
  6. Reading: Get From Georgia Tech
  7. Reading: Start Here (Week 1)
  8. Reading: Game Rules
  9. Video: Introduction to Two Players Left and Right
  10. Video: What is a Combinatorial Game?
  11. Video: Example Problem
  12. Video: Example Problem Solution
  13. Reading: Week 1 Lecture Slides
  14. Reading: Extra Problems


WEEK 2


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.


5 videos, 5 readings, 1 practice quiz expand


  1. Reading: Start Here (Week 2)
  2. Reading: Game Rules
  3. Video: Cutcake and Adding Games
  4. Video: The 0 Game
  5. Video: Adding Games
  6. Reading: Week 2 Lecture Slides
  7. Video: Quiz Problems
  8. Video: Week 2 Quiz Review
  9. Reading: Earn a Georgia Tech Badge/Certificate/CEUs
  10. Reading: Extra Problems
  11. Practice Quiz: Mid-Course Survey 1

Graded: Quiz Week 2

WEEK 3


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.


6 videos, 5 readings expand


  1. Reading: Start Here (Week 3)
  2. Reading: Game Rules
  3. Video: Ordering Games
  4. Video: Example and a Problem
  5. Video: Problem Solution
  6. Video: Ski Jumps
  7. Video: Games That Are Not Numbers
  8. Reading: Week 3 Lecture Slides
  9. Video: Proof and Quiz
  10. Reading: Week 3 Quiz Solutions
  11. Reading: Extra Problems

Graded: Quiz Week 3

WEEK 4


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.


5 videos, 5 readings, 1 practice quiz expand


  1. Reading: Start Here (Week 4)
  2. Reading: Game Rules
  3. Video: Some Numbers Are Games
  4. Video: Some Games Are Numbers
  5. Video: Simplicity
  6. Video: Numbers
  7. Reading: Week 4 Lecture Slides
  8. Video: Quiz Preview
  9. Reading: Week 4 Quiz Solutions
  10. Reading: Extra Problems
  11. Practice Quiz: Mid-Course Survey 2

Graded: Quiz 4

WEEK 5


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.


4 videos, 5 readings expand


  1. Reading: Start Here (Week 5)
  2. Reading: Game Rules
  3. Video: New Ways of Simplifying Games
  4. Video: Examples From Nim
  5. Video: General Reversible
  6. Video: Toads and Frogs
  7. Reading: Week 5 Lecture Slides
  8. Reading: Week 5 Quiz Solutions
  9. Reading: Extra Problems

Graded: Quiz 5

WEEK 6


Week 6: Impartial Games
The topics for this sixth week is Nim: Students will be able to play and analyze impartial games.


4 videos, 5 readings expand


  1. Reading: Start Here (Week 6)
  2. Reading: Game Rules
  3. Video: Nim and How to Win
  4. Video: Impartial Games, Reversible Moves
  5. Video: Examples, Mex
  6. Video: All Impartial Games Are Equivalent to Nim
  7. Reading: Week 6 Lecture Slides
  8. Reading: Week 6 Quiz Solutions
  9. Reading: Extra Problems

Graded: Quiz 6

WEEK 7


Week 7: What You Can Do From Here
The topic for this seventh and final week is Where to go from here.


4 videos, 4 readings, 1 practice quiz expand


  1. Reading: Start Here (Week 7)
  2. Reading: Game Rules
  3. Video: Infinite Games
  4. Video: Loopy Games
  5. Video: Mean Values, Hot, Cold, Sente, Gote
  6. Video: Atomic Weights
  7. Reading: Week 7 Lecture Slides
  8. Reading: Week 7 Quiz Solutions
  9. Practice Quiz: Final Week Survey

Graded: Bonus Quiz

Resources



1 reading expand


  1. Reading: Game Rules

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