Number Theory

General Information | Syllabus | HW Assignments | Course Resources |
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## Syllabus

The following is a**tentative**syllabus for the course. This page will be updated irregularly.

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

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

9/16 | 1.1, 1.2 | Introduction, Division and Euclidean Algorithms |

9/18 | 1.2, 1.3 | Bezout's identity, least common multiples |

9/21 | 1.3, 1.4 | LCMs, Linear Diophantine Equations |

9/23 | 2.1, 2.2 | Fundamental Theorem of Arithmetic, Distribution of primes |

9/25 | 2.2, 2.4 | Distribution of primes, primality testing |

9/28 | 3.1 | Modular arithmetic |

9/30 | 3.2 | Linear Congruences |

10/2 | 3.3, 3.4 | Chinese remainer theorem |

10/5 | 3.4, 4.1 | Polynomials and polynomial congruences |

10/6 (x-hour) | 4.1 | The Arithmetic of ${\mathbb Z}_p$ |

10/7 | Midterm I | In class part; all material through 10/2; takehome part due 10/9 |

10/9 | 4.2 | Pseudoprimes and Carmichael Numbers |

10/12 | class notes | Strong pseudprimes and Miller's test |

10/14 | 5.1, 8.1 | Euler's function |

10/16 | 5.2, class notes | Multiplicative functions;
Euler's function, General remarks about cryptography and public key cryptosystems, signatures, authentication |

10/19 | class notes | Cryptography review, RSA |

10/21 | 6.1, 6.2 | $U_n$ and primitive roots |

10/23 | 6.3-6.5 | Primitive roots for composite moduli, indices |

10/26 | 6.6, 7.1 | Indices, applications of primitive roots, quadratic residues |

10/28 | Midterm II | In class part; all material through 10/23 |

10/30 | 7.1, 7.2 | Quadratic residues |

11/2 | 7.3 | The Legendre symbol and properties |

11/4 | 7.4 | Quadratic reciprocity and Fermat numbers |

11/6 | 7.4, 7.5 | Mersenne numbers, Pepins' test, quadratic residues mod $p^e$ |

11/9 | 8.2-8.6, class notes | Perfect, abundant, deficient numbers; Mobius inversion |

11/11 | 8.2-8.6 | Mobius inversion; Dirichlet convolution |

11/13 | Chapter 10 | Sums of squares |

11/16 | Chapter 10 | Sums of squares |

11/20 | Final Exam | 8-11am |

T. R. Shemanske

Last updated October 28, 2015 16:09:43 EDT