General Information | Assignments | Home |
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Date | Sections(s) | Topics covered |
---|---|---|

22 Sep | 0.1 | Equivalence Relations and Partitions |

24 Sep | 0.3 | The definition of Z/nZ |

27 Sep | 1.1 | Definition of groups; examples; begin dihedral group |

29 Sep | 1.2 - 1.3 | The dihedral and symmetric groups |

1 Oct | 1.4 - 1.5, start 1.6 | Matrix groups, Quaternions, isomorphism |

4 Oct | 1.6, 2.1 | Homomorphisms and subgroups |

6 Oct | 2.1 | Subgroups |

8 Oct | 2.3 | Cyclic groups |

11 Oct | 2.4, 3.1 | Subgroups generated by a set, cosets |

13 Oct | 3.1, 3.2 | Cosets and homomorphisms |

15 Oct | 3.2 | More on cosets and Lagrange's theorem |

18 Oct | 3.3, 3.5 | The first isomorphism theorem, and the alternating group |

20 Oct | 1.7, 4.1, 4.2 | Group Actions and Cayley's Theorem |

22 Oct | 4.3 | Groups acting by conjugation; the class equation |

25 Oct | 4.3, 4.5 | Class equation, Sylow Theorems |

27 Oct | 5.4 | Recognizing direct products, applications of Sylow theorems, and fundamental theorem of finite abelian groups |

28 Oct | 7.1 | Rings, basic definitions |

1 Nov | 7.2, 7.3 | Polynomial Rings, homomorphisms |

3 Nov | 7.3 | Homomorphisms and quotient rings |

5 Nov | 7.4 | Quotient rings and properties of ideals |

8 Nov | 8.1, 9.1 | Euclidean Domains, polynomial rings |

10 Nov | 8.2, 9.2 | PIDs |

12 Nov | 8.3 | gcds, irreducibles, primes |

15 Nov | 8.3 | Unique Factorization Domains |

17 Nov | 9.3 | Gauss's lemma and consequences (R UFD => R[x] UFD) |

19 Nov | 9.4 | Irreducibility criteria |

22 Nov | 9.4 | Extension fields |

29 Nov | Albegra in number theory and geometry | |

1 Dec | Albegra in number theory and geometry |

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T. R. Shemanske on 18 Nov 1999

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