You should give a look to most of those books during the first weeks of this course, and then pick up the two or three you like most and stick to them. If you need some rest but wish to stay in a number theoretic world, try the novel: Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis. |

Class |
Topic |
Readings |
Exercises |

Sept 3 | Presentation of the course. Overview of Number Theory. Reminder on traces and Norms | [C, chapter 1] | Refresher in algebra |

Sept 10 | Reminder on trace and norms. | [S, chapter 3] or [F, II.1] or [Ma, Chapter 3] or [Mi] or [J] or [L] | |

Sept 12 | The Pell-Fermat equation and quadratic fields. | [S, chapter 5] or [F. III.1] or [Ma] or [Mi] ot [J] or [L] | |

Sept 17 | Dedekind domains: Definition, stability | ||

Sept 24 | Dedekind domains: unique decomposition of ideals, weak Approximation theorem. | ||

Oct 1 | Discrete valuation domain. Decomposition of a prime in an extension. | Exercises set 1 | |

Oct 3 | Decomposition of a prime in an extension | ||

Oct 8 | Exercises set 2 | ||

Oct 10 | Discriminant. | ||

Oct 15 | Decomposition of a prime in a Galois extension. | ||

Oct 17 | Decomposition groups and their structures. Frobenius elements | Exercises set 3 | |

Oct 22 | Cyclotomic fields and the law of quadratic reciprocity | ||

Oct 24 | Geometric methods: discrete subgroup of euclidean spaces | ||

Oct 29 | Geometric methods: Finiteness of the class number | ||

Oct 31 | Geometric methods: Finiteness of the set of number fields with a bounded discriminant. | ||

Nov 5 | Geometric methods: Dirichlet's unit theorem | ||

Nov 7 | Analytic methods: L-functions | ||

Nov 12 | Exercises set 4 | ||

Nov 14 | |||

Nov 19 | |||

Nov 21 | |||

Nov 25 (Monday) | |||

Nov 26 | |||

Dec 3 | |||

Dec 5 | |||