General Information | Syllabus | HW Assignments | Links | Exams |

The following is a tentative syllabus for this course, which will be
ammended as necessary.

Lectures | Sections in Text | Brief Description |
---|---|---|

9/26 | 1.3, 1.4 | Introduction, Induction and Fibonacci numbers |

9/28 | 1.5, 3.1 | Divisibility, Prime numbers |

10/1 | 3.1, 3.2 | Distribution of primes |

10/3 | 3.3, 3.4 | Greatest Common Divisor, Euclidean Algorithm |

10/5 | 3.4, 3.5 | Extended Euclidean Algorithm, Fundamental Theorem of Arithmetic |

10/8 | 3.5, 3.6 | Factorization and Fermat numbers |

10/10 | 4.1 | Introduction to congruences, Modular arithmetic |

10/12 | 4.2, 4.3 | Linear congruences, Chinese Remainder Theorem |

10/15 | 4.6, 5.1 | Pollard rho factorization, Divisibility tests |

10/17 | 5.2, 5.5 | Perpetual calendar, Check digits |

10/19 | 6.1 | Wilson's Theorem, Fermat's Little Theorem |

10/22 | 6.2 | Pseudoprimes and Carmichael numbers |

10/24 | 6.3, 7.1 | Euler's phi function, Euler's theorem |

10/26 | 7.2, 7.3 | Totient and divisor functions, Perfect numbers |

10/29 | 7.3, 7.4 | Mersenne primes, Mobius inversion |

10/31 | 8.1, 4.5 | Introduction to cryptography, Linear systems of congruences |

11/2 | 8.1, 8.2 | Character ciphers and Block ciphers |

11/5 | 8.4 | Public Key Cryptography (RSA) |

11/7 | 8.5, 8.6 | Knapsack cipher, Cryptographic protocols |

11/9 | 11.1 | Quadratic residues |

11/12 | 11.2 | Quadratic reciprocity |

11/14 | 11.2 | Quadratic reciprocity, Pepin's test |

11/16 | 11.3, 11.4 | Jacobi symbol, Euler pseudoprimes |

11/19 | 3.7, 13.1 | Diophantine equations |

11/21 | NO CLASS | Thanksgiving break |

11/23 | NO CLASS | Thanksgiving break |

11/26 | 13.2 | Fermat's Last Theorem |

11/28 | 13.3 | Sums of squares |

11/30 | Supplement | Introduction to partitions |

12/3 | Supplement | Partitions |

Stephanie Treneer

Last updated June 25, 2009 14:49:07 EDT