Elementary Number Theory

General Information | Syllabus | HW Assignments |
---|

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

We shall cover chapters 1 - 8 of the text with some additional material on cryptography.

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

9/23 | 1.1, 1.2 | Introduction, Division and Euclidean algoritms |

9/25 | 1.2, 1.3 | Bezout's identity, least common multiples |

9/28 | 1.3, 1.4 | LCMs, Linear Diophantine Equations |

9/30 | 2.1, 2.2 | Fundamental Theorem of Arithmetic, Distribution of Primes |

10/2 | 2.2, 2.3 | Distribution of primes, Fermat/Mersenne Primes |

10/5 | 2.3, 3.1 | Distribution of primes, modular arithmetic |

10/7 | 3.2 | Linear congruences |

10/9 | 3.3 | Chinese Remainder Theorem |

10/12 | 3.1, 3.4 | Polynomials and polynomial congruences mod d |

10/14 | 4.1 | Arithmetic os Z_p |

10/16 | 4.2 | Pseudoprimes and Carmichael numbers |

10/19 | 4.2, classnotes | Pseudoprimes and strong pseudoprimes |

10/20 | First Hour Exam | |

10/20 (x-hour) | In class part with take-home due tomorrow | |

10/21 | classnotes | strong pseudoprimes, Miller's test |

10/23 | 5.1, 81. | Euler's function |

10/26 | 5.2, 8.1 | Multiplicative functions, Euler's function |

10/28 | 5.3, classnotes | Crytpography, RSA |

10/30 | classnotes | Public Key Cryptosystems, signatures, and authentication |

11/2 | 6.1, 6.2 | U_n and primitive roots modulo primes |

11/4 | 6.3, 6.4, 6.5 | primitive roots for composite moduli, indices |

11/6 | 6.6, 7.1 | indices, applications of primitive roots, quadratic residues |

11/9 | 7.1, 7.2 | quadratic residues |

11/10 | Second Hour Exam | |

11/10 (x-hour) | In class part with take-home due tomorrow | |

11/11 | 7.3 | The Legendre symbol and properties |

11/13 | 7.4 | Quadratic Reciprocity, Fermat Numbers |

11/16 | 7.4, 7.5 | Mersenne Numbers, Pepin's Test, quadratic residues mod p and mod p^e |

11/18 | 8.2-8.6, class notes | Perfect, abundant, deficient numbers; Mobius Inversion |

11/20 | 8.2 - 8.6 | Mobius inversions, Dirichlet convolution |

11/23 | 10.1, 10.3, 10.4 | Sums of 2, 3 and 4 squares |

11/25 | Thanksgiving break: 11/25 - 11/29 | |

11/30 | 10.2 | Gaussian integers and sums of two squares |

12/2 | 10.5 | Quaternions and sums of four squares |

T. R. Shemanske

Last updated August 02, 2011 13:48:42 EDT