Topics in Algebra

The following is a **tentative** schedule for the course. Sections in text refer Pinter's book.
Please check back regularly for updates as the term progresses.

Day | Date | Sections in Text | Brief Description |
---|---|---|---|

1 | 13 Sep (M) | 1 | Why Abstract Algebra? |

2 | 15 Sep (W) | 2 | Operations (and Appendix A: Set Theory) |

3 | 17 Sep (F) | 3 | The Definition of Groups |

4 | 20 Sep (M) | 4 | Elementary Properties of Groups |

5 | 22 Sep (W) | 5 | Subgroups |

6 | 24 Sep (F) | 6 | Functions |

7 | 27 Sep (M) | 7 | Groups of Permutations |

8 | 29 Sep (W) | 8 | Permutations of a Finite Set |

9 | 2 Oct (M) | 9 | Isomorphism |

10 | 4 Oct (M) | 10 | Order of Group Elements |

11 | 6 Oct (W) | Exam 1 | |

12 | 8 Oct (F) | 11 | Cyclic Groups (and Appendix B: Integers) |

13 | 11 Oct (M) | 12 | Partitions and Equivalence Relations |

14 | 13 Oct (W) | 13 | Counting Cosets |

15 | 15 Oct (F) | 14 | Homomorphisms |

16 | 18 Oct (M) | 15 | Quotient Groups |

17 | 20 Oct (W) | 16 | The Fundamental Homomorphism Theorem |

18 | 22 Oct (F) | 17 | Rings: Definitions and Elementary Properties |

19 | 25 Oct (M) | 18 | Ideals and Homomorphisms |

20 | 27 Oct (W) | Exam 2 | |

21 | 29 Oct (F) | 19 | Quotient Rings |

22 | 1 Nov (M) | 20 | Integral Domains |

23 | 3 Nov (W) | 21 | The Integers (and Appendix C: Induction) |

24 | 5 Nov (F) | 22 | Factoring Into Primes |

25 | 8 Nov (M) | 24 | Rings of Polynomials |

26 | 10 Nov (W) | 25 | Factoring Polynomials |

27 | 12 Nov (F) | 26 | Substitution in Polynomials |

28 | 15 Nov (M) | Wrap-up | |

TBD |
Final Exam |