10/6/2019 | What kinds of patterns can be used as wallpaper? What are their groups of symmetries, and how can we classify them? How many are there? We will attempt to answer some of these questions and learn how to use Thurston's "orbifold notation" for wallpaper patterns.
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10/13/2019 | We will continue to answer some of the questions posed about wallpaper symmetries. For those that finish the worksheet on wallpaper symmetries, we started discussing the origins and early properties of the p-adic numbers.
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10/20/2019 | We will study the symmetries of frieze patterns, especially those of unimodular frieze patterns. We work toward an interesting result proved by Conway and Coxeter about polygonal structures in frieze patterns.
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10/27/2019 | We continue our study of the symmetries of unimodular frieze patterns with some challenge problems. We introduce the result proved by Conway and Coxeter connecting polygonal triangulations to frieze patterns.
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11/3/2019 | We work in groups to write rigorous proofs of statements from number theory, graph theory, combinatorics, set theory and other topics. [Show less] |

11/10/2019 | We work in groups to write rigorous proofs of statements from number theory, graph theory, combinatorics, set theory and other topics. [Show less] |

11/17/2019 | We work on Olympiad style problems about Combinatorics, Number Theory, Probability, Geometry, and basic Set and Function Theory. [Show less] |

11/24/2019 | We do further Olympiad style problems about Combinatorics, Number Theory, Probability, Geometry, and basic Set and Function Theory. [Show less] |

12/8/2019 | [Show less] |

1/12/2020 | We motivate the study of metrics by introducing the taxicab metric (the distance traveled by a taxi in a city with a grid layout). How would you define a circle, line segment between points, or a parabola with a new notion of distance? [Show less] |

1/19/2020 | Using the taxicab metric as a guide, we define the general notion of metric and give numerous examples. [Show less] |

1/26/2020 | We can extend the integers by including square roots of integers like -1 or 3. Can we predict which prime integers remain prime in the extension? [Show less] |

2/2/2020 | Happy Groundhog Day! With the help of famous results about quadratic reciprocity we will classify primes in most quadratic extensions of the integers. [Show less] |

2/9/2020 | We will introduce the generating function, a creative, combinatorial tool that can simply solve many interesting problems. By the end, we will have used generating functions to study the Fibonacci sequence, dice games, and ways to pay the unlucky cashier with coins. [Show less] |

2/23/2020 | In the first week of a three week sequence, we introduce basic probability concepts such as conditional probability, Bayes' Rule, and tower property [Show less] |

3/1/2020 | We will continue our study of probability by introducing random variables and distributions. [Show less] |

3/8/2020 | We will continue our study of random variables by introducing the Bernoulli, geometric, and binomial distributions. As a final surprising example, we construct a famous example of a non-measurable set. [Show less] |

3/15/2020 | [Show less] |

4/5/2020 | We review the material from last quarter. [Show less] |

4/12/2020 | [Show less] |

4/19/2020 | [Show less] |

4/26/2020 | [Show less] |

5/3/2020 | [Show less] |

5/10/2020 | [Show less] |

5/17/2020 | [Show less] |

5/31/2020 | [Show less] |

6/7/2020 | [Show less] |