Game Numbers, Summer 2020

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Room:
Time: Sunday 11:45AM - 1:00PM
Grades: 8-12
Prerequisites:
Material fee: $0.00

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Description: Mathematical games can be used to define and explore curious new types of numbers; or, to look at it the other way around, one can invent numbers to define and study the nature of mathematical games. In this course we will present, study, and then play a variety of mathematical games; you will compete against your peers, and, at the end of the course, you will - as a team - compete against me. Let's see how much you learn! Prerequisites: students should be comfortable with proofs and mathematical logic, as well as working with sets (for example, union and intersection); students should also know the definition of the following number sets: natural numbers, integers, rational numbers, real numbers. On the first day of class we will define "equivalence relation" - if you want, you can look this up ahead of time.

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Homeworks

These homeworks are copyrighted material, posted here for use by SchoolNova students and parents. Everyone else is welcome to print a copy of these materials for their personal use; any redistribution or commercial use is prohibited

• Assigned on 06/28: Game Numbers 1: A Gamut of Games  |  Nim: Python Program to play Nim  |  Grundy's Game: Python Program to play Grundy's Game  |  
  Welcome to the first week of Game Numbers! Here's a collection of games for you to get started playing! I have included two Python programs to play two of the games on your computers. They are included here as .txt files; I will tell you in class how to use them.
  
• Assigned on 07/5: Game Numbers 2: N & P; Game Addition  |  
  Here is an updated version of the material from July 5th.
  
• Assigned on 07/12: Game Numbers 3: Game Arithmetic  |  Game Numbers 3: Test Equations  |  
  
• Assigned on 07/19: Game Numbers 4: Nim Theorem  |  
  
• Assigned on 07/26: Game Numbers 5: MEX & Nim Addition  |  
  
• Assigned on 08/2: Game Numbers: The Final Game  |