- Problem Set 1, due 1/20/06, Solutions
- Problem Set 2, due 1/30/06 Solutions
- Problem Set 3, due 2/8/06 Solutions
- Problem Set 4, due 2/15/06 Solutions
**Midterm on Monday February 20 (in class)**Solutions- Problem Set 5, due 3/8/06 Solutions
- Problem Set 6, due 3/20/06 Solutions
- Problem Set 7, due 3/29/06 Solutions
- Problem Set 8, due 4/10/06 Solutions
- Problem Set 9, NOT TO BE HANDED IN Solutions
- final exam

Instructor: | Harm Derksen |

office: | 3067 East Hall |

email: | hderksen@umich.edu |

phone: | (734) 763 2309 |

webpage: | http://www.math.lsa.umich.edu/~hderksen/math594.w06/index.html |

office hours: | MW 1-2pm, F 3-4pm. |

Book: | David S. Dummit, Richard M. Foote, Abstract Algebra, third edition, John Wiley & Sons, Inc., 2004. |

Topics:
The course consists of two parts, Group Theory
and Field/Galois Theory.

Topics in Group Theory include:

Topics in Group Theory include:

- group actions on sets and permutation representations
- the Sylow theorems
- the Jordan-Hölder theorem
- simplicity of the alternating group
`A`for_{n}`n`at least 5 - nilpotent groups and solvable groups

- field extensions
- splitting fields, algebraic closures
- separable and inseparable extensions
- cyclotomic polymomials
- finite fields
- the Galois correspondence
- solving equations by radicals, insolvability of the quintic

Other resources are:

- Lang, Algebra.
- Artin, Algebra.
- MacLane, Birkhoff, Algebra.
- Van der Waerden, Modern Algebra, vol I.
- Hungerford, Algebra.
- Jacobson, Basic Algebra.

Homework/Exams: Yes, both. About 10 homework
assignments and 2 or 3 exams are planned.