General Information | Syllabus | HW Assignments |

The Homework Assignments page will always be accurate.

Lectures | Sections in Text | Brief Description |
---|---|---|

9/24 | 1.1 | Introduction to groups |

9/26 | 1.3 | Cyclic groups |

9/29 | 1.2 | Homomorphisms, Dihedral groups |

10/1 | 1.4 | Quaternion groups, cosets, Lagrange and related topics |

10/3 | No class today | |

10/6 | 1.5 | Normality, quotient groups, isomorphism theorems |

10/8 | 1.5, 2.4 | Isomorphism Theorems, Group Actions |

10/10 | 2.4 | Group Actions |

10/13 | 2.4, 1.6 | Group Actions, Permutation groups |

10/15 | 1.6, 2.5 | Permutation Groups, Cauchy's Theorem |

10/17 | 2.5 | Sylow Theorems |

10/20 | 2.5, 1.7 | Applications of Sylow theorems, category theory |

10/22 | 1.7, 1.8 | Direct products, coproducts |

10/24 | class notes | semidirect products |

10/27 | class notes, 2.2 | Semidirect products, split extensions, free groups, fundamental theorem for finitely generated abelian groups |

10/29 | 2.2, 2.7 | FTFGAB (continued), nilpotent groups, normal series |

10/31 | 2.7, 2.8 | solvable groups, composition series, Jordan Holder, group extensions and the classification problem for finte groups |

11/3 | 3.1 | Intro to rings, homomorphisms, characteristic, integral domains, ideals |

11/5 | 3.1, 3.2 | Operations on ideals, isomorphism theorems, prime and maximal ideals |

11/7 | 3.2 | Zorn's lemma, maximal ideals exist, characterization of prime and maximal ideals via quotients, examples |

11/10 | 3.2, 3.4 | Chinese Remainder Theorem, localization |

11/12 | 3.4, 3.3 | Localization, Factorization in commutative rings |

11/14 | 4.1 | Modules, torsion |

11/17 | 4.1 | Localization of modules |

11/19 | 8.1, 8.4, 3.3 | Noetherian integral domains, UFDs, PIDs |

11/21 | 3.6 | Division algorithms over commutative rings |

11/24 | 3.6 | Irreducibility criteria in polynomial rings |

11/26 | Thanksgiving break: 11/26 - 11/30 | |

12/1 | Introduction to Algebraic varieties | |

12/3 | Introduction to Algebraic varieties |

Thomas R. Shemanske

Last updated May 31, 2008 12:23:58 EDT