Abstract Algebra

General Information | Syllabus | HW Assignments | Course Resources |
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## Syllabus

The following is a**tentative**syllabus for the course. This page will be updated irregularly.

On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

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

9/12 | 1.1, 1.2 | Introduction, sets and equivalence relations |

9/14 | 2.1, 2.2 | Properties of $\mathbb Z$: induction, division and Euclidean algorithm |

9/16 | 3.1, 3.2 | $\mathbb Z_n$: Integers modulo $ n$, Symmetric groups, Dihedral groups $ D_3$, $ D_4$, matrix groups, Quaternion group |

9/19 | 3.2, 3.3 | Simple properties of groups, subgroups and characterization |

9/21 | 4.1, 4.2 | Cyclic groups, multiplicative group of $\mathbb C$ |

9/23 | 5.1, 5.2 | Symmetric groups, cycle notation, general dihedral groups |

9/26 | 6.1, 6.2, 6.3 | Cosets; Lagrange's theorem, applications |

9/28 | 9.1, 9.2 | Isomorphism; direct products |

9/30 | 10.1, 10.2 | Normal subgroups; factor groups; the alterating group |

10/3 | 11.1, 11.2 | First Isomorphism theorem |

10/5 | Midterm Exam I | |

10/6 (x-hour) | 11.2 | The other isomorphism theorems |

10/7 | 14.1 | Groups acting on sets; Cayley's theorem |

10/10 | 14.2 | The class equation and applications |

10/12 | 15.1, 15.2 | The Sylow Theorems |

10/14 | 13.1 | Fundamental theorem of finite abelian groups; recognizing direct products |

10/17 | 13.2 | Solvable groups; Simple Groups and the Hölder prgram |

10/19 | 16.1, 16.2 | Rings; integral domains |

10/21 | 16.2, 16.3 | Integral domains, homomorphisms, ideals |

10/24 | 16.3, 16.4 | Maximal and prime ideals |

10/26 | Midterm Exam II | |

10/27 (x-hour) | 17.1 | Rings, Polynomial Rings, Finite Fields |

10/28 | 17.2 | The Division Algorithm |

10/31 | 17.3 | Irreducibility, Rational root test, Gauss's lemma |

11/2 | 17.3 | Gauss's lemma, Eisenstein's criterion |

11/4 | 18.1 | Integral domains and fields of Fractions |

11/7 | 18.2 | PIDs are Unique Factorization domains |

11/9 | 18.2 | $D$ UFD implies $D[x]$ UFD |

11/11 | 18.2 | Detecting multiple roots, irreducibility in $\mathbb Q[x,y]$ |

11/14 | Cyclotomic polynomials | |

11/18 | Final Exam | 8-11am |

T. R. Shemanske

Last updated November 10, 2016 10:33:19 EST