Wednesday, 8/31 | Intro to the course, discussion of syllabus, review of Math 243 (Chapter 0) |

Friday, 9/2 | Review (Chapter 0), Symmetries (Chapter 1) Read: Chapters 0 and 1. Chapter 0 is intended mostly to be a refresher, so you can it read it fairly quickly, making sure that the main topics ring a bell: Euclid's Lemma, modular arithmetic, equivalence relations, and the material on functions. In Chapter 1, make sure you understand the example of the symmetries of the square. |

Monday, 9/5 | More on Symmetries (Chapter 1), Definition and Examples of Groups (Chapter 2). Read: Chapter 1 (if you didn't finish before), and Chapter 2, p. 40-48. |

Wednesday, 9/7 | Examples of Groups (Chapter 2) HW #1 due: Chapter 0, #3, 14, 22, 30. Chapter 1, #2, 6, 16, 22. |

Friday, 9/9 | Properties of Groups (Chapter 2), Finite Groups and Subgroups (Chapter 3) Read: Chapter 2, |

Monday, 9/12 | Subgroups (Chapter 3) |

Wednesday, 9/14 | Subgroups (Chapter 3) HW #2 due: Chapter 2, #8, 9 (Hint: one approach is to use the Corollary to Theorem 0.2 on p.5), 16, 18, 26, 29. Chapter 3, #10, 13, 16, 18. |

Friday, 9/16 | Cyclic Groups (Chapter 4) Read: Chapter 4, p.72-77 |

Monday, 9/19 | Cyclic Groups (Chapter 4) Read: Chapter 4, p.77-81 |

Wednesday, 9/21 | Cyclic Groups (Chapter 4) HW #3 due: Chapter 2, Computer exercise #2 (click here for the relevant software). Chapter 3, #26, 29, 36, 52. Chapter 4, #8, 10, 22, 35, 42, Computer Exercise #1. |

Friday, 9/23 | Finish up Cyclic Groups (Chapter 4), start Permutation Groups (Chapter 5)
Read: Chapter 5, p. 95-102 |

Monday, 9/26 | Permutation Groups (Chapter 5) Read: Chapter 5, p. 103-113 |

Wednesday, 9/28 | Permutation Groups (Chapter 5) HW #4 due: Chapter 4, #16, 29, 35, 52, 62, 64. Supplementary exercises to Chapters 1-4 (p. 91-92) #1, 5, 34. Chapter 5, #2. |

Friday, 9/30 | Permutation Groups (Chapter 5) |

Monday, 10/3 | Permutation Groups (Chapter 5), begin Isomorphisms (Chapter 6) |

Wednesday, 10/5 | Isomorphisms (Chapter 6) HW #5 due: First show that the order of an n-cycle is n. Then Chapter 5, #4, 6, 18, 26, 30, 31, 37, 52, 59. |

Friday, 10/7 | Isomorphisms (Chapter 6) |

Monday, 10/10 | No class -- Fall break |

Wednesday, 10/12 | No class -- Fall break |

Friday, 10/14 | No class -- Fall break |

Monday, 10/17 | Automorphisms (Chapter 6). Read: pp. 129-133, 138-141. |

Wednesday, 10/19 | Cosets (Chapter 7) Read: pp. 141-144 HW #6 due: Chapter 6, #8, 10, 22, 24, 32, 38, 39, 42 |

Friday, 10/21 | Lagrange's Theorem (Chapter 7) |

Monday, 10/24 | Applications of Cosets (Chapter 7) |

Wednesday, 10/26 | Midterm 1 |

Friday, 10/28 | Final remarks on cosets (Ch. 7). External Direct Products (Chapter 8). Read: pp. 155-157 |

Monday, 10/31 | External Direct Products (Chapter 8). Normal Subgroups and Factor Groups (Chapter 9) Read: pp. 158-159, 178-179 |

Wednesday, 11/2 | Normal Subgroups and Factor Groups (Chapter 9) Read: pp. 180-185 HW #7 due: Chapter 7, #7, 14, 20, 24, 26, 40. Chapter 8, #5, 9, 29, 32. |

Friday, 11/4 | Factor Groups (Chapter 9) Read: pp. 180-183 First draft of adopt-a-group assignment due. |

Monday, 11/7 | Factor Groups and Applications (Chapter 9) Read: pp. 183-187 |

Wednesday, 11/9 | Factor Groups and Applications (Chapter 9) Read: pp. 187-192 HW #8 due: Chapter 9, #4, 7, 10, 11, 14, 24, 48. |

Friday, 11/11 | More applications of factor groups (Chapter 9), Group Homomorphisms (Chapter 10) Read: pp. 200-203 |

Monday, 11/14 | Group Homomorphisms (Chapter 10). Read: pp. 204-207. |

Wednesday, 11/16 | Group Homomorphisms (Chapter 10). Read: pp. 208-211. HW #9 due: Chapter 9, #27, 31, 34, 50, 65. Chapter 10, #2, 10. . |

Friday, 11/18 | Group Homomorphisms (Chapter 10). |

Monday, 11/21 | Finite Abelian Groups (Chapter 11). Read: statement and consequences of the fundamental theorem of finite abelian groups (you don't need to read the proof). |

Wednesday, 11/23 | No Class -- Thanksgiving |

Friday, 11/25 | No Class -- Thanksgiving |

Monday, 11/28 | Finite Abelian Groups (Chapter 11) |

Wednesday, 11/30 | Midterm 2 |

Friday, 12/2 | Finite Abelian Groups (Chapter 11), Introduction to the Sylow Theorems (Chapter 24) Read: Chapter 24, pp. 403-405. |

Monday, 12/5 | Sylow Theorems (Chapter 24) Read: Chapter 24, pp. 406-410. |

Wednesday, 12/7 | Sylow Theorems (Chapter 24). You are encouraged to hand in HW #10 today, though you may also hand it in on Friday. HW #10: Chapter 10, #18, 30. Chapter 11, #10, 28. Chapter 24, #16, 18, 32 (Hint: Let N be the normal subgroup and consider a Sylow subgroup of G/N. Then use a part of Theorem 10.2.) |

Friday, 12/9 | More Sylow Theorems, course wrap-up. |

Final Exam: Wednesday, 12/14, 11:30-2:00 in usual classroom |