**MATH 3003 - Schedule**

Day | Topics/events | Sections in text |

1/17 | There are infinitely many primes (proof), Prime Number Theorem (discussion) | 1.1.1, 1.2.1, 1.2.5 |

1/19 | GCD, Euclid's theorem, Fundamental Theorem of Arithmetic | 1.1.2, 1.1.3, 1.1.4 |

1/24 | Prime Sieve, Dirichlet's Theorem, zoo of conjectures about primes | 1.2.2, 1.2.3, 1.2.4 |

1/26 | Arithmetic modulo n, groups and rings | 2.1 |

1/31 | Linear congruence, sets of residues | 2.1.1 |

2/2 | Wilson's and Euler's theorems | 2.1.2, 2.1.3 |

2/7 | Euler's phi-function, Chinese remainder theorem | 2.2 |

2/9 | Snow day | N/A |

2/14 | Extended Euclidean Algorithm, computing large powers modulo n | 2.3 |

2/16 | Polynomial equations (modulo n), primitive roots | 2.5 |

2/21 | Existence of primitive roots modulo a prime, review | 2.5 |

2/23 | Test 1 | 1.1 - 2.3 |

2/28 | Primality tests | 2.4 |

3/2 | Simple ciphers, Diffie-Hellman key exchange | 3.2 |

3/7 | RSA | 3.3, 3.4.1, 3.42 |

3/9 | Law of Quadratic Reciprocity (statement and examples) | 4.1 |

3/21 | Euler's criterion and Gauss Sums | 4.2, 4.4 |

3/23 | Proof of the Law of Quadratic Reciprocity using Gauss sums | 4.4 |

3/28 | Gauss' lemma and Euler's version of Quadratic Reciprocity | 4.3 |

3/30 | Second proof of Quadratic Reciprocity | 4.3 |

4/4 | Finding square roots modulo n | 4.5 |

4/6 | Test 2 | 2.5 - 4.4 |

4/11 | Ellipic curves, addition rule | 6.1, 6.2 |

4/13 | Ellipic curves over Z/pZ, examples | 6.2 |

4/18 | Pollard's p-1 method, Lenstra's factorization | 6.3 |

4/20 | Lenstra's factorization examples, Elliptic curve Diffie-Hellman | 6.4 |

4/25 | Congruent numbers | 6.5 |