SES # | TOPICS | KEY DATES |
---|---|---|

Group Representations | ||

1 | Group representations | |

2 | Unitary representations | Problem set 1 out |

3 | Characters | |

4 | One-dimensional characters | |

5 | The regular representation |
Problem set 1 due Problem set 2 out |

6 | Characters (cont.) | |

Rings: Basic Definitions | ||

7 | Rings, ring homomorphisms | Problem set 2 due |

8 | Ideals, quotient rings, correspondence theorem | |

9 | Maximal ideals, prime ideals, fractions | Problem set 3 out |

Rings: Factoring | ||

10 | Gauss' Lemma | |

11 | Unique factorization | |

12 | Factoring integer polynomials | Problem set 3 due |

13 | First quiz | |

Quadratic Imaginary Integers | ||

14 | Gauss primes | Problem set 4 out |

15 | Quadratic integers | |

16 | Ideal factorization | |

17 | Prime ideals |
Problem set 4 due Problem set 5 out |

18 | Ideal classes | |

Linear Algebra over a Ring | ||

19 | Integer matrices | |

20 | Free modules | |

21 | Presenting modules | Problem set 5 due |

22 | Hilbert Basis Theorem | Problem set 6 out |

23 | Structure of abelian groups | |

24 | Linear Operators | |

25 | Second quiz | |

Fields: Field Extensions | ||

26 | Algebraic elements, degree | |

27 | Ruler and compass | Problem set 6 due |

28 | Adjoining elements | |

29 | Finite fields | Problem set 7 out |

30 | Primitive elements | |

Fields: Galois Theory | ||

31 | Symmetric functions, discriminant |
Problem set 7 due Problem set 8 out |

32 | Splitting fields, the Galois group | |

33 | Fixed fields, Galois extensions | |

34 | The main theorem |
Problem set 8 due Problem set 9 out |

35 | Cubic and quartic equations | |

36 | Quartic equations (cont.) | |

37 | Third quiz | |

38 | Roots of unity, Kummer extensions | |

39 | Quintic equations | Problem set 9 due |