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Games without Chance

Combinatorial Game Theory

Dr. Tom Morley

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

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What's inside

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.

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.

Resources

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops mathematical theory for games without chance moves

Taught by an expert in game theory, Dr. Tom Morley

Covers topics relevant to industry and academia

Provides hands-on labs and interactive materials

Requires extensive background knowledge in mathematics

Does not cover applications of game theory in real-world scenarios

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Reviews summary

Thought-provoking combinatorial game theory

Learners say Games without Chance: Combinatorial Game Theory provides an engaging, thought-provoking analysis of combinatorics from a unique perspective. Engaging lectures are delivered in a somewhat unconventional yet approachable classic mathematic style, with lectures presented by Prof Morley who is praised for adding some sense of humour. Though a few learners noted some disorganization and unexplained gaps, several stated that they were intrigued by the subject matter and found the course valuable.

Despite being presented in a somewhat old-fashioned style, learners found lectures engaging and humorous, praising the instructor.

"Prof Morley does very well in keeping things engaging and adding some sense of humour into his lectures."

Course provides an engaging, thought-provoking analysis of combinatorics.

"very interesting analysis of "

Some learners noted that the course's organization and presentation could use improvement, with some unexplained gaps and disorganization.

"The content of the course jumps back and forwards very rapidly: some weeks some knowledge is assumed and then the next week the lecturer explains it."

"Even then there are some reasonably large gaps and 'obvious' questions unanswered."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Games without Chance: Combinatorial Game Theory with these activities:

Introduction to Combinatorial Game Theory

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Explore and understand the fundamental concepts of combinatorial game theory.

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Watch a video tutorial on combinatorial game theory.
Read an introduction to combinatorial game theory.
Identify the key ideas and principles in combinatorial game theory.

Review Set Theory

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Review essential concepts from set theory to enhance your understanding of the foundations of combinatorial game theory.

Browse courses on Set Theory

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Identify different types of sets and their properties
Practice operations on sets, including union, intersection, and complement

Organize and Review Course Resources

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Enhance your learning by organizing and reviewing key resources, including lecture notes, assignments, and readings, to ensure a comprehensive understanding of course materials.

Browse courses on Resource Management

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Gather all relevant course materials, such as lecture notes, slides, and readings
Organize these materials into a logical structure, using folders or digital tools
Review and summarize the materials on a regular basis to reinforce your understanding

Nine other activities

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Read 'Winning Ways for Your Mathematical Plays, Volume 1'

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Delve into a seminal work on combinatorial game theory, providing a comprehensive foundation for understanding the principles and strategies of these games.

View Winning Ways for Your Mathematical Plays:... on Amazon

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Acquire a physical or digital copy of the book
Read through the chapters sequentially, taking notes and highlighting key concepts
Work through the examples and exercises to reinforce your understanding

Analyzing Simple Games

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Practice analyzing and evaluating simple combinatorial games.

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Play a simple combinatorial game.
Identify the winning strategy for the game.
Analyze the game using combinatorial game theory concepts.
Repeat the process with another simple game.

Peer Review and Discussion

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Engage with peers to discuss and exchange ideas on combinatorial game theory concepts.

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Find a study partner or group.
Discuss and present your understanding of a particular combinatorial game theory concept.
Exchange feedback and insights with your peers.

Explore Online Combinatorial Game Tutorials

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Supplement your learning by exploring online tutorials that provide step-by-step guidance on combinatorial game strategies and concepts.

Browse courses on Game Theory

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Find reputable websites or platforms offering video or written tutorials
Select tutorials that cover specific topics you want to enhance your understanding of
Follow the tutorials actively, taking notes and trying out examples

Engage in Study Group Discussions

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Foster collaborative learning by joining or forming study groups to discuss course concepts, work on assignments, and reinforce your understanding.

Browse courses on Game Theory

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Find or create a study group with fellow students who share your interests
Establish regular meeting times and discuss a schedule for covering the course material
Actively participate in discussions, ask questions, and share insights

Solve Combinatorial Game Puzzles

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Reinforce your understanding by engaging in practice drills that challenge your ability to analyze and solve combinatorial game puzzles.

Browse courses on Game Theory

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Find online or printed sources that provide a collection of puzzles
Select puzzles that align with your current level of understanding
Spend dedicated time attempting to solve the puzzles

Design a Combinatorial Game of Your Own

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Apply your knowledge by designing a new combinatorial game, considering its rules, strategies, and implications within the framework of game theory.

Browse courses on Game Design

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Brainstorm ideas for a novel game concept and its underlying rules
Develop a prototype of the game, including a description of its mechanics and gameplay
Test your game with others and gather feedback to refine its design

Attend Combinatorial Game Theory Workshops

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Enhance your practical skills and knowledge by attending workshops led by experts in combinatorial game theory, offering hands-on learning experiences and opportunities for interaction.

Browse courses on Game Theory

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Research and identify upcoming workshops on combinatorial game theory
Register for workshops that align with your interests and learning goals
Actively participate in the workshops, asking questions and engaging in discussions

Design a Combinatorial Game

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Create your own combinatorial game to represent and analyze a real-world problem or scenario.

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Identify a problem or scenario that can be represented as a combinatorial game.
Design the rules and mechanics of the game.
Write a description of the game, including its rules and objectives.
Test and evaluate the game with others.

Career center

Learners who complete Games without Chance: Combinatorial Game Theory will develop knowledge and skills that may be useful to these careers:

Game Theorist

Game Theorists are professionals who use mathematical models to analyze and predict the outcomes of strategic interactions. This course, Games without Chance: Combinatorial Game Theory, can help you build a foundation in the mathematical theory and analysis of simple games without chance moves. You will learn how to model games, analyze their outcomes, and develop strategies for winning. This knowledge can be applied to a variety of fields, including economics, finance, and computer science. If you are interested in a career as a Game Theorist, this course is a great place to start.

See salaries and explore the career path for Game Theorist

Game Designer

Game Designers create and design games. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to design engaging and challenging games. You will learn how to model games, analyze their outcomes, and develop strategies for winning. This knowledge can be applied to a variety of game genres, including board games, card games, and video games. If you are interested in a career as a Game Designer, this course is a great way to get started.

See salaries and explore the career path for Game Designer

Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to solve complex problems in a variety of industries. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to model problems, analyze data, and develop solutions. This knowledge can be applied to a variety of industries, including manufacturing, transportation, and healthcare. If you are interested in a career as an Operations Research Analyst, this course is a great way to get started.

See salaries and explore the career path for Operations Research Analyst

Data Scientist

Data Scientists use data to solve problems and make decisions. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to collect, analyze, and interpret data. This knowledge can be applied to a variety of industries, including finance, healthcare, and marketing. If you are interested in a career as a Data Scientist, this course is a great way to get started.

See salaries and explore the career path for Data Scientist

Software Engineer

Software Engineers design, develop, and maintain software systems. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to design, implement, and test software systems. This knowledge can be applied to a variety of industries, including technology, finance, and healthcare. If you are interested in a career as a Software Engineer, this course is a great way to get started.

See salaries and explore the career path for Software Engineer

Financial Analyst

Financial Analysts use financial data to make investment recommendations. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to analyze financial data, make investment recommendations, and manage risk. This knowledge can be applied to a variety of industries, including investment management, banking, and insurance. If you are interested in a career as a Financial Analyst, this course is a great way to get started.

See salaries and explore the career path for Financial Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to develop and implement mathematical models, analyze financial data, and make investment recommendations. This knowledge can be applied to a variety of industries, including investment management, banking, and insurance. If you are interested in a career as a Quantitative Analyst, this course is a great way to get started.

See salaries and explore the career path for Quantitative Analyst

Actuary

Actuaries use mathematical and statistical models to assess risk and uncertainty. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to develop and implement mathematical models, analyze data, and make risk assessments. This knowledge can be applied to a variety of industries, including insurance, healthcare, and finance. If you are interested in a career as an Actuary, this course is a great way to get started.

See salaries and explore the career path for Actuary

Economist

Economists study the production, distribution, and consumption of goods and services. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to analyze economic data, develop economic models, and make economic forecasts. This knowledge can be applied to a variety of industries, including government, business, and academia. If you are interested in a career as an Economist, this course is a great way to get started.

See salaries and explore the career path for Economist

Statistician

Statisticians collect, analyze, and interpret data. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to design and conduct surveys, collect data, and analyze data. This knowledge can be applied to a variety of industries, including healthcare, marketing, and public policy. If you are interested in a career as a Statistician, this course is a great way to get started.

See salaries and explore the career path for Statistician

Market Researcher

Market Researchers study the market for goods and services. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to conduct market research, analyze data, and make marketing recommendations.

See salaries and explore the career path for Market Researcher

Business Analyst

Business Analysts study the needs of businesses and develop solutions to improve their performance. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to analyze business data, identify business needs, and develop solutions.

See salaries and explore the career path for Business Analyst

Management Consultant

Management Consultants advise businesses on how to improve their performance. This course, Games without Chance: Combinatorial Game Theory, can help you develop the skills you need to be successful in this field. You will learn how to analyze business data, identify business needs, and develop solutions.

See salaries and explore the career path for Management Consultant

Teacher

Teachers educate students in a variety of subjects. This course, Games without Chance: Combinatorial Game Theory, may help you develop the skills you need to be successful in this field. You will learn how to develop lesson plans, teach lessons, and assess student learning. This knowledge can be applied to a variety of teaching positions, including elementary school teacher, secondary school teacher, and college professor.

See salaries and explore the career path for Teacher

Librarian

Librarians help people find and access information. This course, Games without Chance: Combinatorial Game Theory, may help you develop the skills you need to be successful in this field. You will learn how to organize and catalog books, assist patrons with research, and promote literacy. This knowledge can be applied to a variety of library positions, including children's librarian, school librarian, and academic librarian.

See salaries and explore the career path for Librarian

Reading list

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Games without Chance: Combinatorial Game Theory .

Winning Ways for Your Mathematical Plays

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The book covers various topics in game theory and it is useful for background knowledge.

Games without Chance

Combinatorial Game Theory

What's inside

Syllabus

Good to know

Save this course

Reviews summary

Thought-provoking combinatorial game theory

Activities

Career center

Reading list

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