General Information | Syllabus | HW Assignments |

On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

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

9/22 | 1.2, 1.4, and parts of 3.1, 3.4 | Induction, Divisibility, Fundamental Theorem of Arithmetic |

9/24 | 3.1 | Primes: Euclid's and Euler's Proofs of Infinitude, Chebyshev's Estimates |

9/27 | 3.2, beginning of 3.4 | GCDs, the Fundamental Theorem Revisited |

9/29 | 3.3, remainder of 3.4 | Uses of the Fundamental Theorem, the Euclidean Algorithm |

10/1 | 3.6, 13.1 | Some Diophantine Equations: Linear Equations, Pythagorean Triples |

10/4 | 13.1, 13.2, 4.1 | Pythagorean Triples (cont.), a Special Case of Fermat's Last Theorem, Intro to Congruences |

10/6 | 4.1 | Intro to Congruences (cont.) |

10/8 | 4.2 | Primes in Progressions, Linear Congruences |

10/11 | 4.3 | Chinese Remainder Theorem |

10/13 | Supplemental and 4.4 | Reclusive Primes, Solving Polynomial Congruences |

10/15 | 4.4 | Hensel's Lemma |

10/18 | 5.1, 5.2 | Applications of Congruences: Divisibility Tests, The Perpetual Calendar |

10/20 | 5.2, 5.5 | The Perpetual Calendar (cont.), Check Digits |

10/22 | 6.1 and Supplemental | Wilson's Theorem, Formula for the nth Prime Number |

10/25 | 4.6, 6.1 | Fermat's Little Theorem, Pollard Rho and Pollard p-1 Factorization |

10/27 | 6.2 | Primality Tests, Pseudoprimes and Carmichael Numbers |

10/28 (x-hour) | 6.2, 6.3 | Miller's Test and Rabin's Probabilistic Primality Test, Euler's Theorem |

11/1 | 8.1, 8.2 | Intro to Cryptography: Character and Block Ciphers |

11/3 | 4.5, 8.2 | Hill Ciphers and Systems of Linear Congruences |

11/5 | Supplemental | A Little Bit of Cryptanalysis |

11/8 | 8.2, 8.3 | Cryptanalysis Continued, Stream Ciphers, Exponentiation Ciphers |

11/10 | 8.4 | Public Key Cryptography and RSA, Cryptographic Protocols and Applications |

11/12 | Supplemental | Arithmetic Functions, Dirichlet Convolutions, Formal Dirichlet Series |

11/15 | 7.1, 7.2 | Euler's Phi-function, Sum and Number of Divisors |

11/17 | 7.3, 7.4 | Perfect Numbers, Mersenne Primes, Lucas-Lehmer Test, Mobius Inversion |

11/19 | Supplemental | Average Orders of Multiplicative Functions, Counting Square-Free Integers, Farey Fractions |

11/22 | 11.1 | Quadratic Residues, the Legendre Symbol |

11/29 | 11.2 | Quadratic Reciprocity |

12/1 | Supplemental | Wrap up |

Ryan Daileda

Last updated May 31, 2008 12:24:21 EDT