Professor:
Dr.
Janet Vassilev

Office: SMLC 324

Office
Hours: MF 1-1:50, W 10 - 10:50 am
and by
appointment.

Telephone:
(505) 277-2214

email: jvassil@math.unm.edu

webpage:
**http://www.math.unm.edu/~jvassil**

Date | Section | Topic | Homework |

1/18 | 10.2-10.4 | Module Review | 10.2 10 10.3 9, 11, 18 10.4 10, 12, 16, 19 |

1/23 | 10.5 | Exact Sequences/Projective Modules | |

1/25 | 10.5 | Injective Modules | 10.5 1, 2, 3, 9, 10, 11, 28a |

1/30 | 10.5/11.3 | Flat Modules/Dual Vector Spaces | |

2/1 | 11.5 | Tensor Algebras | 10.5 4, 6, 15, 16, 21, 26 |

2/6 | 11.5 | Tensor Algebras continued | |

2/8 | 12.1 | Modules over PIDs | 11.3 3, 4 11.5 3, 4, 12, 13 12.1 2, 5 |

2/13 | 12.1 | Fundamental Theorem of f.g. Modules over PIDs | |

2/15 | 12.2 | Fundamental Theorem of f.g. Modules over PIDs continued, Rational Canonical Form | 12.1 8, 9 10, 14, 17, 18, 19 |

2/20 | 12.2 | Rational Canonical Form | |

2/22 | 12.2 | Rational Canonical Form /Exam Review | 12.2 9(1st 2 only), 10, 11, 14,18 |

2/27 | Midterm 1 | ||

3/1 | 12.3 | Jordan Canonical Form | 12.3 2, 5, 6, 9, 10, 18, 21, 26, 37 |

3/6 | 13.1 | Field Extensions | |

3/8 | 13.2 | Algebraic Extensions | 13.1 1, 2, 3, 6 13.2 2, 3, 4, 7, 9, 14 |

3/20 | 13.4 | Splitting Fields | |

3/22 | 13.4-13.5 | Algebraic Closures and Separable Extensions | 13.4 2, 3, 4, 5, 6 13.5 2, 5, 8, 11 |

3/27 | 13.6,14.1 | Cyclotomic Extensions and Field Automorphisms | |

3/29 | 14.2 | Fundamental Theorem of Galois Theory | 13.6 3, 4, 6, 8, 10 14.1 1, 5, 6, 8 |

4/3 | 14.2 | Fundamental Theorem of Galois Theory continued | |

4/5 | 14.3 | Finite Fields | 14.2 2, 3, 4, 5, 9, 12, 13, 114, 16 |

4/10 | 14.4 | Composite and Simple Extensions | |

4/12 | 14.5,14.6 | Abelian Extensions/Galois Groups of Polynomials | |

4/17 | 14.6 | Galois Groups of Polynomials/Exam Review | 14.2 17, 18, 22, 23 14.3 7 14.4 6, 7, 8 |

4/19 | Midterm 2 | ||

4/24 | 14.7 | Solvable and Radical Extensions | |

4/26 | 14.8 | Computation of Galois groups over the rationals | 14.5 5, 12 14.6 2(b,c), 7, 9, 13, 18 14.7 2, 4 |

5/1 | 14.9 | Transcendental Extensions | |

5/3 | Review for Final | ||

5/10 | Final Exam |