Homework | Problems | Due Date |

HW#1 (Solutions) | Chapter 1: 5.1, 5.3; Chapter 2: 2.4, 2.6, 3.2, 4.3 | Wednesday Sept 20 |

HW#2 (Solutions) | Chapter 2: Write a full proof for Prop. 2.3.8; Exercises: 4.6, 4.7, 4.9, 5.1 | Wednesday Sept 27 |

HW#3 (Solutions) | Chapter 2: Exercises: 5.2, 6.2, 6.7, 6.10 | Wednesday Oct 4 |

HW#4 (Solutions: 1, 2) | Chapter 2: Exercises: 12.1, 12.5, 10.5, 10.2, 9.4 | Wednesday Oct 18 |

HW#5 | Chapter 6: Exercises: 7.1, 7.3, 7.10, 8.2; Chapter 7: Exercises: 1.1, 2.2, 2.8, 2.13, 3.3 | Wednesday Nov 15 |

HW#6 | Chapter 7: Exercises: 6.4, 7.3, 7.4, 7.5(a) | Wednesday Nov 22 |

HW#7 | Chapter 7: Exercises: 7.9(a), 7.10 | Wednesday Nov 29 |

Prove the fixed point theorem

Date | Sections Covered | Practice Problems/ Further reading |

W Sep 6 | 2.1 | Read Chapter 1 and do exercises outlined in class |

F Sep 8 | 2.1, 2.2 started definition and examples of groups | assigned in class (do them, and watch for where you need associativity!) |

M Sep 11 | 2.2, permutation groups, and started 2.3 | Read 1.5 and do exercises from class |

W Sep 13 | 2.4, order of an element and cyclic groups | Chapter 2: 2.1, 2.3 |

F Sep 15 | 2.4, 2.5: cyclic groups, generators of groups, started homomorphisms | |

M Sep 18 | 2.5: some examples of homomorphisms | |

W Sep 20 | 2.5: kernels and normal subgroups | read about generators of S_3 on p42 to be comfortable with symmetric group operations |

F Sep 22 | 2.5: discussion on the symmetric group | |

M Sep 25 | 2.6: isomorphism theorems, Cayely's theorem | Read 2.6; Chapter 2, problems: 6.5, 6.6 |

W Sep 27 | 2.7: partitions and equivalence relations | Read section 2.7 |

F Sep 29 | 2.8: cosets and Lagrange's theorem | Do problem from class and read 2.8 |

M Oct 2 | 2.8: applications of cosets | Read in Section 2.8 about using right cosets |

W Oct 4 | 2.8, 2.12: normal subgroups and beginning of quotient groups | |

F Oct 6 | 2.12: the quotient group | please do problems mentioned in class |

M Oct 9 | THANKSGIVING-- NO CLASS | |

W Oct 11 | 2.12: First Isomorphism Theorem; 2.9 | |

F Oct 13 | 2.9: Modular arithmetic; 2.10 | |

M Oct 16 | 2.10: The correspondence Theorem | |

W Oct 18 | 2.11: Products of Groups | |

F Oct 20 | 2.11: Products of Groups | work out the proof of Prop. 2.11.4 and Prop. 2.11.5 |

M Oct 23 | MIDTERM | |

W Oct 25 | The Dihedral Group | |

F Oct 27 | 6.7: operations of groups on sets, orbits, stabilizers | |

M Oct 30 | 6.7, 6.8: more on orbits and stabilizers; operations on cosets | |

T Oct 31 | [LAST DAY TO DROP WITH W] NO CLASS | |

W Nov 1 | 7.1: The class equation | Read and do details of the class equation for SL_2(F_3) in Section 7.2 |

F Nov 3 | 7.3: p-groups | |

M Nov 6 | STUDY BREAK -- NO CLASS | |

W Nov 8 | STUDY BREAK -- NO CLASS | |

F Nov 10 | STUDY BREAK -- NO CLASS | |

M Nov 13 | REMEMBRANCE DAY -- NO CLASS | |

W Nov 15 | 7.6, 7.7: The normalizer of a subgroup, beginning of Sylow theorems | |

F Nov 17 | 7.7: Classifying groups of order 6 and 15 | Read and try find isomorphism classes of groups of order 21 |

M Nov 20 | Permutation representations and proof of First Sylow Theorem | |

W Nov 22 | Proof of Second and part of Third Sylow Theorem | try exercises in book to classify groups using Sylow theorems, not just homework problems! |

F Nov 24 | ||

M Nov 27 | ||

W Nov 29 | ||

F Dec 1 | ||

M Dec 4 | ||

T Dec 5 | LAST DAY -- MONDAY SCHEDULE |