About the Course
Mathematicians have studied games for over a century. How do they analyze them? In this course, we'll learn combinatorial game theory pertaining to games of perfect information, such as Go and chess. In these games, there are no dice or hidden cards; all game information is known to players except their individual strategies. In this introduction to combinatorial game theory, we'll learn mathematical concepts such as disjunctive sum and Grundy numbers, and use them to explore winning strategies in games such as Nim, Domineering, and Hackenbush. Between class meetings, students will also explore optional readings and resources, and dive deeper into the history and application of combinatorial game theory.
Learning Objectives
- Define games of perfect information and their main types: impartial games and partizan games
- Apply basic terms and concepts in combinatorial game theory to games of perfect information
- Develop winning strategies for games of perfect information
- Identify winning and losing positions in impartial games such as Nim Distinguish between different types of positions in partizan games such as Domineering and Hackenbush
- Compute winners of simple disjunctive sums using Grundy numbers
- Test your strategies by playing games with classmates, family members, and friends
About Advanced Enrichment courses
These courses offer above-grade-level material that is presented in a novel context, explored with other advanced learners, and guided by a CTY educator to help prepare students for higher-order thinking and college-style academic challenges. Students work individually and may finish the course early if they complete all requirements before the course end date.
Requirements
CTY courses have grade-level requirements and most require minimum test scores. Some courses may also have prerequisites.
Identification DetailsDates and Tuition
Online
You will be asked to join or sign in first.
Days: Every Tue for 6 weeks
Times: 7 - 8:30 p.m. (Eastern time)
Register by: August 11, 2026
Time Commitment:
Important Information
Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
Families will be notified by email of any required materials one week prior to the course start date.
Time Commitment: 2.5-3.5 hours per week (1.5 hours of class time, 1-2 hours of independent work). Course will include 6 sessions over 6 weeks.
All online course times are Eastern time.
Technical Requirements
This course requires a computer with high-speed Internet access and an up-to-date web browser such as Chrome or Firefox. You must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.
You will be asked to join or sign in first.
Days: Every Wed for 6 weeks
Times: 7 - 8:30 p.m. (Eastern time)
Register by: September 15, 2026
Time Commitment:
Important Information
Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
Families will be notified by email of any required materials one week prior to the course start date.
Time Commitment: 2.5-3.5 hours per week (1.5 hours of class time, 1-2 hours of independent work). Course will include 6 sessions over 6 weeks.
All online course times are Eastern time.
Technical Requirements
This course requires a computer with high-speed Internet access and an up-to-date web browser such as Chrome or Firefox. You must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.
Registration Fee and Financial Aid
Tuition and fees will be waived or reduced for students who qualify for financial aid.
Learn more about Financial Aid