# CTYI Game Theory

## Basic Information

Here is the Grade Game Handout that we spoke about in class (the one from Yale).

Here is the mixed strategies handout that we spoke about in class (the one from Yale).

Here's the Game Theory Handout regarding mixed strategy Nash equilibria & how to calculate them.

Finally, here's a blank Hex board courtesy of Wikipedia.

## Games

When we spoke about the game *Order and Chaos*, we used the following material:

The *Order and Chaos* Wikipedia page.

*Solving Order and Chaos*, a paper demonstrating from an empty board, perfect play on both sides leads to an Order win.

The *Order and Chaos* webapp, giving the strategy for an Order win.

The mathematical theory for the game of Nim.

When we spoke about the game *Bagh-Chal*, we used the following material:

The Wikipedia page for Bagh-Chal, also known as *Tigers and Goats*.

*Computing Tigers and Goats*, a paper claiming "partial results show that Tigers appears to have the better part of the opening, but Goats may catch up in the long run."

Play against a computer Tiger in this online game of *Tigers and Goats*.

## Maths

When we spoke about the Hex Theorem, we used the following material:

*An Inductive Proof of Hex Uniqueness* by Samuel Clowes Huneke; a proof that there can be no more than one winner in a game of Hex.

*Some Games and Machines for Playing Them* by John Nash, talking a bit about Hex.

*The Hex Theorem and Brouwer's Fixed Point Theorem* - proof the theorems are equivalent (and more proofs involving the Hex Theorem).

## Econ 159

Finally, this is a link to Econ 159, a game theory course taught at Yale University by Professor Ben Polak. I encourage you to continue your study of game theory by watching his lectures!

## Links for Online/Hybrid Game Theory Class

For 2020, here is the Game Theory handbook, with accompanying course outline. These are an abridged set of notes, based on the 2019 Game Theory course.

For 2021, here is the Game Theory handbook and the course summary. These are an abridged set of notes, based on the above 2019 Game Theory course. Here is an additional worksheet on *Werewolf* and *Conway's Game of Life*.

Below are some links useful to the teaching of the course.

# CTYI Mathematics

# "The Maths Experience".

## Basic Information

Here is the Maths Experience handbook used for the 1 week long CTYI course in 2020.

Here is the outline for this course.

Going forward, here are some good resources:

Introduction to University Mathematics by Professor Richard Earl.

How to Solve it by George Pólya.

Bridging the gap between secondary school and university.

On Youtube: Oxford Mathematics, Numberphile, Crash Course.

# Maths with Applications + ML

## Basic Information

I designed and taught a 5 weekend course on ''Maths with Applications'' as part of the Online Spring 2021 CTYI experience. The goal of this course was to outline 5 different topics in mathematical applications: probability, computability theory, astrometry, machine learning, and game theory.

Here is the outline for the course, and here is the full Handbook. Also see this short intro to machine learning designed for advanced primary school children.

One website I found especially useful for teaching primary school children was machinelearningforkids.co.uk.