10/11/2020 | We kick off the academic year with some competition-style problems gathered from AMC, AIME, and Olympiads. [Show less] |

10/18/2020 | We will introduce Gaussian integers in order to decide which prime numbers can be written as a sum of two squares. [Show less] |

10/25/2020 | We will wrap up the discussion of Gaussian integers and prove which prime numbers are the sum of two squares. [Show less] |

11/1/2020 | We will study the limitations of polynomials as prime generating functions. [Show less] |

11/8/2020 | We will study recursive formulas for generating primes. [Show less] |

11/15/2020 | We will take our first peak into algorithms, with the goal of discussing the P vs NP problem the following week. [Show less] |

11/22/2020 | We continue our unit on algorithms by discussing the most famous open problem in the field, P vs NP. [Show less] |

12/6/2020 | The Fundamental Theorem of Algebra... Everyone's heard of it. If it's so fundamental then why haven't we seen a proof?! Look no further, we consider complex polynomials and graphing techniques to prove that every complex polynomial has a root. [Show less] |

1/10/2021 | To start off the new year we are going to split the class into two competing groups. There will be a variety of problems to work on and it will be up to the teams to organize how they feel is best. [Show less] |

1/17/2021 | We start our unit on graphs with a dive into planar graphs and the Euler characteristic. [Show less] |

1/24/2021 | We continue our unit on graph theory with a handout on graph colorings. We will define what it means to color a graph, connect this to coloring maps (geographically speaking), and prove some bounds on how many colors are needed. [Show less] |

1/31/2021 | We continue with a proof of the 5-color theorem and some Ramsey theory. [Show less] |

2/7/2021 | We look at continued fractions and their relation to rational and irrational numbers. [Show less] |

2/21/2021 | We introduce the concept of metrics using a motivating example: the taxicab metric. This worksheet is especially useful for all those of you who are part time students and part time taxi drivers in New York City. [Show less] |