The final mark will be rounded to a half-integer not equal to 5.5. The final mark may be rounded up by at most one point depending on the average mark for the homework assignments.

The marks are available on Blackboard.

Date | Material | Keune | Homework |
---|---|---|---|

September 2 | Recap of field theory: field extensions, algebraic and transcendental elements, homomorphisms of field extensions | The non-asterisked parts of these exercises | |

September 9 | Adjoining roots of polynomials, splitting fields of polynomials, properties of Hom-sets of such extensions | end of chapter 1, first half of chapter 4 | These exercises |

September 16 | normal extensions, Galois extensions | second half of chapter 4, most of chapter 3 | These exercises |

September 23 | normal extensions, separable extensions, Galois extensions and groups | These exercises | |

September 30 | separable extensions, primitive element theorem | These exercises | |

October 7 | properties of separability, fundamental theorem of Galois theory, cyclotomic extensions | The non-asterisked parts of these exercises | |

October 14 | Galois group of cyclotomic fields | The non-asterisked parts of these exercises | |

October 21 | proof and historical motivation of the fundamental theorem | These exercises | |

November 11 | No lecture! | No Exercise class! | |

November 18 | Symmetric polynomials and their use in constructing Galois extensions | The non-asterisked parts of these exercises | |

November 25 | Radical extensions and solvable groups | These exercises | |

December 2 | non-solvability of the general quintic equation, Galois groups of extensions of Q, reductions mod p |
These exercises | |

December 9 | small degree extensions of Q, Kummer theory, normal basis theorem |
The non-asterisked parts of these exercises | |

December 16 | Last part of exam material, first part of infinite Galois theory | The non-asterisked parts of these exercises | |

January 6 | |||

January 13 |

English | Dutch |
---|---|

algebraic closure | algebraïsche afsluiting |

compass and ruler | passer en liniaal |

constructible | construeerbaar |

cubic | derdegraads |

cyclotomic polynomial | cyclotomisch polynoom, cirkeldelingsveelterm |

extension | uitbreiding |

field | lichaam (Nederland), veld (Vlaanderen) |

polynomial | polynoom, veelterm |

quadratic | tweedegraads |

quartic | vierdegraads |

root | nulpunt; wortel |

solvable | oplosbaar |