# Spring 2018, Math 4581: Abstract Algebra II

## Announcements

Thursday 25 January: From now on, office hours are changed to Tuesdays 2-5pm.

## Syllabus

There's lots of information on the syllabus.

## Calendar

Jan 8: chapter 1 | Jan 10: chapter 2 | Jan 12: more chapter 2 |

Jan 15: no class | Jan 17: chapter 3, HW1 due | Jan 19: groups, subgroups |

Jan 22: permutations | Jan 24: test review, HW2 due | Jan 26: test on chapters 1--3 |

Jan 29: work on HW3 | Jan 31: orbit/stab thm, HW3 due | Feb 2: Lagrange's thm |

Feb 5: work on HW4 | Feb 7: chapter 5, HW4 due | Feb 9: chapter 6 |

Feb 12: chapter 7 | Feb 14: test review, HW5 due | Feb 16: test on chapter 4 |

Feb 19: F[x]/<p(x)> | Feb 21: min. polyn., HW6 due | Feb 23: p irreducible => field |

Feb 26: work on HW7 | Feb 28: deg. of extensions, HW7 | Mar 2: chapter 9 |

Mar 5: chapter 10 | Mar 7: test review, HW8 due | Mar 9: test on chapter 8 |

Mar 12: spring break | Mar 14: spring break | Mar 16: spring break |

Mar 19: Galois group | Mar 21: Gal. permutes roots | Mar 23: fixed fields |

Mar 26: work on HW9 | Mar 28: Galois fund. thm., HW9 | Mar 30: normal subgroups |

Apr 2: class equation | Apr 4: test review, HW10 due | Apr 6: test on Galois theory |

Apr 9: work on HW11 | Apr 11: quotient groups, HW11 | Apr 13: more quotient groups |

Apr 16: work on HW12 | Apr 18: constructibility, HW12 | Apr 20: solvability by radicals |

Apr 23: test review | | |

Tues May 1: final exam | | |

## Homework

HW1 (due Jan 17): Judson chapter 20 exercises 6, 7, 15, 16.

HW2 (due Jan 24): Solomon ch 2 ex 1; ch 3 ex 1, 2, 6, 7.

HW3 (due Jan 31): Judson ch 3 ex 14, 33, 53; ch 4 ex 30; ch 5 ex 2dfijo, 3bd.

HW4 (due Feb 7): Judson ch 14 ex 2, 3; ch 6 ex 5dfh, 9, 14.

HW5 (due Feb 14): Judson ch 6 ex 11, 12, 17, 18.

HW6 (due Feb 21): Judson ch 14 ex 12, 14.

HW7 (due Feb 28): Judson ch 16 ex 8; ch 17 ex 7, 9, 10; ch 21 ex 1abce, 5.

HW8 (due Mar 7): Judson ch 21 ex 2, 13, 22, 28.

HW9 (due Mar 28): Judson ch 23 ex 1.

HW10 (due Apr 4): Judson ch 21 ex 4; ch 23 ex 6, 9, 22cdef.

HW11 (due Apr 11): Judson ch 10 ex 2 (without factor groups); ch 14 ex 7, 22.

HW12 (due Apr 18): Judson ch 10 ex 1abce, 2, 4.