10/7/2018 | We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares. [Show less] |

10/14/2018 | We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares. [Show less] |

10/21/2018 | We introduce the Gini index, an economic metric to measure wealth inequality. [Show less] |

10/28/2018 | We introduce Legendre symbols and quadratic reciprocity to study residues modulo primes. [Show less] |

11/4/2018 | We explore applications of quadratic reciprocity. [Show less] |

11/11/2018 | Instead of our typical definition of addition and multiplication, tropical arithmetic looks at minimum and addition operations. We will graph and find roots of tropical polynomials. [Show less] |

11/18/2018 | We will continue our study of tropical arithmetic by proving a version of the Fundamental Theorem of Algebra for tropical quadratic polynomials. [Show less] |

12/2/2018 | Given a ruler, how many inch markings can you remove and still measure each increment between 1 and 12 inches? Is there some way to construct a 12-inch ruler such that each increment from 1 to 12 can be measured in a unique way? [Show less] |

12/9/2018 | [Show less] |

1/13/2019 | We will introduce continued fractions and learn how to calculate them. We will also investigate the relationship between the irrationality of a number and properties of its continued fraction expansion. [Show less] |

1/20/2019 | We will continue our study of continued fractions with an imporant application in number theory: Given an irrational number, how efficiently can it be approximated by rational numbers? Continued fraction expansions play an important role in solving this problem. [Show less] |

1/27/2019 |
In this power-point presentation, we will address the following questions: Why do some musical intervals sound pleasant, while others do not? Why do we have exactly 12 notes in an octave of a piano? Why aren't distances between frets on a flute or a guitar equal to each other? The answers, surprisingly, involve deep mathematical analysis involving continued fractions, the problem of doubling the cube, and rational approximations.
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2/3/2019 | We will introduce the formal defnition of a limit of a sequence and develop basic properties. [Show less] |

2/10/2019 | We will continue our practice with formally proving limits of sequences and we will prove some additional properties of sequence limits. [Show less] |

2/24/2019 | We characterize all polynomials that have integer outputs for integer inputs. [Show less] |