This is the homepage for Math 145-02, Abstract Algebra, taught by Prof. Moon Duchin. Note that section 01 is taught by Prof. Montserrat Teixidor and follows a different schedule and assignments!

Syllabus/course info sheet: here.

Here is a rough layout of topic timing. Obviously, real timing may vary from this plan. As you can see, it roughly follows the book, but the symbol * means that there is substantial extra material planned besides what you can find in the text.

date | topic | text | |

1 | Tue Sep 3 | Intro to course; intro to proofs; intro to groups | |

2 | Thu Sep 5 | Ch 1 – the cyclic groups Z/nZ (cf Math 63) | 1 |

3 | Tue Sep 10 | Ch 2 – injection, surjection, bijection, permutation (Math 61) | 2 |

4 | Thu Sep 12 | Ch 1-2 wrapup | 1-2 |

5 | Tue Sep 17 | What is a group? discrete groups Z^d, Z[i], SLnZ, Fn, plus continuous versions | 3.1* |

6 | Thu Sep 19 | generators and relations; Cayley graphs; subgroups | 3.2* |

7 | Tue Sep 24 | examplepalooza: isometry (eg, dihedral) groups, fundamental groups, and more | 3.3* |

8 | Thu Sep 26 | homomorphism and isomorphism | 3.4,3.7 |

9 | Tue Oct 1 | cyclic, abelian, nilpotent groups | 3.5* |

10 | Thu Oct 3 | symmetric groups; permutations as matrices | 3.6* |

11 | Tue Oct 8 | cosets | 3.8 |

12 | Thu Oct 10 | normality and the magic of quotient groups | 3.8 |

Tue Oct 15 | TUFTS MONDAY | ||

Thu Oct 17 | Midterm 1: Groups | ||

13 | Tue Oct 22 | What is a ring? Z/pZ, matrices, R[x] | |

14 | Thu Oct 24 | polynomials and their roots | 4.1 |

15 | Tue Oct 29 | factorization and extensions | 4.2 |

16 | Thu Oct 31 | arithmetic in R[x]/I | 4.3 |

17 | Tue Nov 5 | more generalities on rings, ideals, fields, vec sps, modules | 5.1 |

18 | Thu Nov 7 | ring homomorphisms | 5.2 |

19 | Tue Nov 12 | PIDs and quotients | 5.3 |

20 | Thu Nov 14 | quotient fields | 5.4 |

21 | Tue Nov 19 | Chapters 4-5 review | |

Thu Nov 21 | Midterm 2: Polynomials, Rings, Fields | * | |

22 | Tue Nov 26 | topics: free groups and quotients, free groups and paradoxes | * |

Thu Nov 28 | THANKSGIVING | ||

23 | Tue Dec 3 | worksheet on free groups | * |

24 | Thu Dec 5 | wrap-up of Banach-Tarski paradox | |

Mon Dec 16 | Final Exam: Cumulative |