Note: Problems marked by a * are optional and do not need to be handed in with the assigned problems. These problems will tend to be (a bit) harder than the average HW problem. If you solve one, write it and let me know so we can talk about it, they are fun to discuss! |

Week 1 |
Class Topic |
Reading For |
Homework From |

9/16 | Set Theory and Induction | Section 0 | 0.1, 0.4, 0.5, 0.7, 0.8, 0.22* |

9/17 (x-hour) | Proof Writing & (Basic) Number Theory | - | Handout |

9/18 | Binary Operations; Introduction to Groups | Section 1 | 1.1a, 1.3(a,c,g), 1.6a |

9/20 | Groups (Con't) | Section 2 | 2.1(a,c,f,h), 2.3, 2.8 |

(Solutions) |

Week 2 |

9/23 | Fundamental Group Theorems | Section 3 | 3.1,6,9,10,14,17* |

9/25 | Powers of an Element | Section 4 (Through Thm 4.4) | 4.3,6,20,22,24 |

9/27 | Cyclic Groups | Section 4 (Remainder) | 4.9,10,13,16,17,22,25* |

(Solutions) |

Week 3 |

9/30 | Subgroups | Section 5 (up to p.48) | 5.1(e,h,i),5,14,16,23,24 |

10/1 (x-hour) | Cyclic Groups and Subgroups | Rest of Section 5 | 5.4,6,7,8,19 |

10/2 | Cyclic Groups and Subgroups; Functions | Section 7 | 6.1(a,b),3,5; 7.4,7 |

10/4 | Bijective Functions; The Symmetric Groups | Section 8 to p71 | 7.9, 7.11 |

(Solutions) |

Week 4 |

10/7 | Symmetric Groups: The Alternating Group | Section 8: p66-71 | 8.1a, 4, 8, 10 |

10/8 (x-hour) | Symmetric Groups | 8.2,3,6,13 | |

10/9 | Symmetric Groups: Dihedral Groups | Section 8: p71-76 | 8.15, 17 |

10/11 | Cosets | Section 9 | 9.5a,18 |

(Solutions) |

Week 5 |

10/14 | Counting and Lagrange's Theorem | Section 10 (to p. 92) | 10.3,6,11,13,15 |

10/15 | Exam #1 (6-10PM) |
-- | -- |

10/16 | Counting and Lagrange's Theorem (Con't) | Section 10 (to p. 92) | 10.5,8,22* |

10/18 | Normal Subgroups | - | 11.3,4,8 |

(Solutions) |

Week 6 |

10/21 | Normal Subgroups | Section 11 | 11.15, 16, 17, 20 |

10/23 | Normal Subgroups and Quotient Groups | 11.22,23,29 | |

10/25 | Homomorphisms & Isomorphism | Section 12 | 12.2, 4(b,g), 5,14 |

(Solutions) |

Week 7 |

10/28 | Homomorphisms & Isomorphisms | Section 12 | 12.4(c,e,f),7,13,15, |

10/29 (x-hour) | Homomorphisms & Isomorphisms (Con't) | Section 12 | 12.20,22,36(see ex. 27) |

10/30 | Fundamental Theorem on Group Homomorphisms | Section 13 | 13.2,4,8,10 |

11/1 | Fundamental Theorem on Group Homomorphisms | Section 13 | 13.15,16,19,20 |

(Solutions) |

Week 8 |

11/4 | Fundamental Theorem on Finite Ablelian Groups | Section 14 | 14.1a,e, 4 |

11/5 | Exam #2 (6-10PM) |
-- | -- |

11/6 | No Class | - | - |

11/8 | Fundamental Theorem on Finite Ablelian Groups | Section 14 | 14.2,6,7,12 |

(Solutions) |

Week 9 |

11/11 | Rings | Section 16 | 16.1, 2(a,c),3,18 |

11/13 | Subrings | - | 16.14,15,24,30 |

11/15 | Ideals and Quotient Rings | Section 17 (skip thm 17.5,6,8) | 17.1(a,c),5,11,18,27,33 |

(Solutions) |

Week 10 |

11/18 |

Final Exam |

11/26 | Final Exam (8-11AM) |
-- | -- |