# Spring 2018, Math 4581: Abstract Algebra II

## Announcements

Wednesday 28 March: On Monday (2 April) we will work on Homework 10, and on Wednesday (4 April) we will have lecture on the class equation, rather than lecture on Monday and review on Wednesday.

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: work on HW10 | Apr 4: class equation, 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.