Topics, Fall 2003

The text is Hungerford, Abstract Algebra, 2^{nd} edition.
Topics to be covered, in order:

Sections | Topics |

1.1-1.3 | Arithmetic in Z |

2.1-2.2 | Congruence classes, Z_{n} |

2.3 | Z_{p}, p prime |

3.1-3.2 | Rings and fields |

3.3 | Isomorphism and homomorphism |

4.1, 4.4 | Polynomial rings, divisibility, roots |

4.2-4.3 | Divisibility and unique factorization |

4.5 | Eisenstein's test, Fundamental Theorem |

5.1-5.2 | Quotient rings |

6.1-6.2 | Ideals and homomorphisms |

7.1-7.2 | Groups |

7.3 | Subgroups and congruences |

9.1 | Euclidean domains |

9.2-9.3 (survey) | Application to number theory |

10.1 | Vector spaces |

10.2 | Fields |

15 | Application to Euclidean geometry |

7.4 | Group isomorphisms, automorphisms |

7.5 | The Lagrange theorem |

7.9 | The symmetric and alternating groups |

11.3 (part I) | Solvable groups |

11.1 | The Galois group |

11.3 | Solvability by radicals |

Main page, 351.