Graduate Algebra I

General Information | Syllabus | HW Assignments |
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On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures | Sections in Text | Brief Description |
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Week 1 | Chapter 0, 1.1-1.6, 2.1, 2.2, 2.4, 3.2 | Groups, examples, homomorphisms, cosets, Lagrange |

Week 2 | Chapter 2.3, 3.1, 3.3, 3.4 | Cyclic groups, standard isomorphism theorems, solvable groups, composition series |

Week 3 | Chapter 3.4, 4.1, 4.2, 4.3 | Jordan-Hölder theorem, Group actions, G-set structure theorem, class equation, symmetric group |

Week 4 | Chapter 4.3, 4.5, 4.6, 5.1, 5.4, 5.5 | Conjugacy classes in S_n, Sylow theorems, Semidirect Products |

Week 5 | Chapter 5.5, 5.2, class notes | Semidirect Products, split extensions, direct sums, free abelian groups, finitely-generated abelian groups |

Week 6 | Appendix II, Chapter 6.3, 7.1-7.4 | Basic category theory (products, coproducts, functors). free groups, introduction to rings |

Week 7 | 7.4, 7.5, 7.6, 15.4 | Prime and maximal ideals, localization, Chinese Remainder Theorem |

Week 8 | 9.1, 9.6, 10.1, 15.4, 8.3 | polynomial rings, group rings, modules, localization of modules, irreducibles and primes in rings |

Week 9 | 8.1, 8.2, 8.3, 9.1, 9.2, 9.3 | UFDs, PIDs, Euclidean rings, polynomial rings |

Week 10 | 9.3, 9.4, 9.5, 9.6(HBT) | Gauss' Lemma and applications, Irreducibility Criteria, Hilbert Basis Theorem, algebraic geometry in 30 minutes |

T. R. Shemanske

Last updated August 02, 2011 13:48:37 EDT