Algebra (groups and rings)

General Information | Syllabus | HW Assignments |
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Lectures | Sections in Text | Brief Description |
---|---|---|

9/15 | 0.1 - 0.3 | Equivalence relations, partitions, $\mathbb Z/n \mathbb Z$ |

9/17 | 0.1 - 0.3 | Equivalence relations, partitions, $\mathbb Z/n \mathbb Z$ |

9/19 | 1.1 | Definition of groups; examples; begin dihedral group |

9/22 | 1.2 - 1.3 | Dihedral and Symmetric groups |

9/24 | 1.4 - 1.5, start 1.6 | Matrix Groups, Quaternions, Isomorphism |

9/26 | 1.6, 2.1 | Homomorphisms and subgroups |

9/29 | 2.3 | Cyclic groups |

10/1 | 2.3, 2.4 | Subgroups generated by a set; cosets |

10/3 | 3.1 | Cosets and homomorphisms; quotient groups |

10/6 | 3.1 | Lagrange's theorem. More on cosets |

10/8 | 3.2 | First isomorphism theorem |

10/9 | First midterm | In-class part; take-home part due in class Friday |

10/10 | 3.3 | Other isomorphism theorems |

10/13 | 3.5, 1.7, 4.1, 4.2 | the alternating group; Group Actions and Cayley's theorem |

10/15 | 4.2 | Group actions continued |

10/17 | 4.3 | Groups acting by conjugation; the class equation |

10/20 | 3.4, 4.5 | Holder program; Sylow theorems |

10/22 | 5.2, 5.4 | Fundamental theorem of finite abelian groups; recognizing direct products; applications of the Sylow theorems |

10/24 | 7.1, 7.2 | Rings (basic definitions and examples); Polynomial rings |

10/27 | 7.3 | Homomorphisms; quotient rings |

10/29 | 7.4 | Quotient rings and properties of ideals |

10/30 | Second midterm | In-class part; take-home part due in class Friday |

10/31 | 8.1, 9.1 | Euclidean domains; Polynomial rings |

11/3 | 8.2, 9.2 | PIDs |

11/5 | 8.3 | gcds; irreducibles; primes |

11/7 | 8.3 | Unique Factorization Domains |

11/10 | 9.3 | Gauss's lemma and consequences |

11/12 | 9.4 | Irreduciblity criteria |

11/14 | 9.4 | Extension Fields |

11/17 | Wrap it up |

T. R. Shemanske

Last updated July 18, 2017 09:28:24 EDT