10/7/2018 |
We will start the school year with an an overview of math problems and puzzles involving a chessboard (with and without chess pieces) and solving techniques including tiling, coloring and invariance principle.
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10/14/2018 | In this meeting we will explore the symmetries of different objects like squares, rectangles, and coins. We will see how these symmetries interact with each other to form a structure called a *group.* [Show less] |

10/21/2018 | Having experimented with the groups of symmetries of the rectangle+string model, we will define groups and explore associated concepts such as subgroups, group actions, isomorphisms, orbits, and stabilizers. [Show less] |

10/28/2018 | In this meeting, our goal is to construct a strange new geometry where straight lines are circles and triangles have angles that sum to less than 180. We start with circle inversions and then introduce the Poincaré disc model. [Show less] |

11/4/2018 | We will continue our exploration of the Poincaré disc and prove facts about hyperbolic lines and shapes. [Show less] |

11/11/2018 | We will keep working in the Poincare disc and discover phenomena peculiar to hyperbolic geometry such as AAA congruence, Lobachevskii's Theorem, and Schweikart's constant. [Show less] |

11/18/2018 | We look at more peculiar hyperbolic facts, like the hyperbolic Pythagorean theorem and the angle of parallelism. [Show less] |

11/25/2018 | [Show less] |

12/2/2018 | We will have a short review quiz. Then, Aaron Anderson will talk about how electrical circuits correspond to random walks on the vertices of graphs. [Show less] |

12/9/2018 | We will continue talking about the correspondence between voltage, resistance, and current in circuits with random walks on graphs. [Show less] |

1/13/2019 | We will have a competition to solve problems for prizes! [Show less] |

1/20/2019 | We will start a lesson studying algorithms: what are they, and how do they work? [Show less] |

1/27/2019 | We will learn about more aspects of algorithms, such as efficiency and computational complexity. [Show less] |

2/3/2019 | We're going to look at the famous Cantor set, its construction, and some of its oddities. [Show less] |

2/10/2019 | We will continue studying the Cantor set, invesitgating properties such as its cardinality and "dimension." Once we develop some notions of dimension, as a bonus we will also look at other fractal sets and their dimensions. [Show less] |

2/24/2019 | We’ll explore a measure of economic inequality known as the Gini Index. In particular, we’ll learn what it is, how to calculate it, and what some of its strengths and limitations are.
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3/3/2019 | In this lesson we will do combinatorial weighing and probability problems, with some related problems about information exchange. [Show less] |

3/10/2019 | To celebrate Pi day, we'll look at some probability questions involving pi. For example: suppose you have equally spaced lines and you drop a toothpick. What is the probability that the tootpick crosses a line? [Show less] |

3/17/2019 | We will continue the worksheet on problem related to pi. We will find the probability that two randomly selected integers are coprime and calculate some continued fractions. [Show less] |