10/8/2017 | Attached are the test from the lesson, the homework that was due on 10/08/17 and the problems from the contest held during the second part of the lesson. Homework for 10/15/17 are problems 1c and 4b from the contest, as well as problem 4 from the previous homework. [Show less] |

10/15/2017 | Problems on tilings and the relation of grid colorings to solving them. Handout and homework for 10/22/17 attached. [Show less] |

10/22/2017 | More tilings and colorings, factorization of polynomials. [Show less] |

10/29/2017 | Today we start a block on Number Theory. First topic: remainders. We have all seen them before, but how can we use them, and why do they even exist? Also: integral points on graphs of linear functions and an interesting system of equations. [Show less] |

11/5/2017 | Continuing the topic from last week, remainders and divisibility. [Show less] |

11/12/2017 | We introduce the concept of the greatest common divisor and prove some basic statements about it. [Show less] |

11/19/2017 | We formulate the Euclidean algorithm and use it to prove some important number-theoretic lemmas. [Show less] |

12/3/2017 | We further use the Euclidean algorithm to investigate some linear diophantine equations. [Show less] |

12/10/2017 | [Show less] |

1/14/2018 | Introduction to graph theory and geometry. [Show less] |

1/21/2018 | [Show less] |

1/28/2018 | Continuation of graphs and geometry [Show less] |

2/4/2018 | Eulerian graphs and patallelograms. [Show less] |

2/11/2018 | Eulerian paths and parallelograms. [Show less] |

2/25/2018 | First lesson on game theory and continuation of geometry. [Show less] |

3/4/2018 | Winning/losing positions and circles. [Show less] |

3/11/2018 | Stealing strategies and relative positions of 2 circles. [Show less] |

3/18/2018 | Stealing strategies continuation, along with central angles and arcs on a circle. [Show less] |

4/8/2018 | Today we start learning a new powerful proof technique -- induction. [Show less] |

4/15/2018 | We proceed by applying induction to problems in combinatorics. [Show less] |

4/22/2018 | We proceed by applying induction to problems in algebra. Also: more inscribed angles. [Show less] |

4/29/2018 | This week, we look at applications of induction to arithmetic. Also: more inscribed angles [Show less] |

5/6/2018 | We introduce bipartite graphs, as well as continue with cyclic quadrilaterals. [Show less] |

5/13/2018 | We continue with bipartite graphs and geometry. [Show less] |

5/20/2018 | We use the framework of bipartite graphs to investigate the Stable Marriage Problem. [Show less] |