Fall 2001

Lectures: |
MWF 9:00-9:50am, Wellman 109 |

Discussion section: |
T 9:00-9:50am, Wellman 111 |

Instructor: |
Anne Schilling, Kerr Hall 578, phone: 754-9371, anne@math.ucdavis.edu |

Office hours: |
Monday, Wednesday 10-11, Friday 11-12 |

Text: |
D. S. Dummit and R. M. Foote, Abstract Algebra, second edition, published by John Wiley & Sons, 1999. |

Problem Sets: |
There will be weekly homework assignments, handed out on Tuesdays. We will discuss the homework problems in the discussion section the following Tuesday. You are expected to present some of your solutions in the discussion section. Your grade for the discussion section will be based on your participation and your presentation of the homeworks. |

Exams: |
Midterm on November 5; Final exam during final exam period (December 10-15) |

Grading: |
The final grade will be based on: Discussion section 20%, Midterm 30%, Final 50% |

Web: |
http://www.math.ucdavis.edu/~anne/FQ2001/250A.html |

The

Definition of a group

Groups as symmetries

Examples: cyclic, dihedral, symmetric, matrix groups

Homomorphisms

Subgroups and quotient groups

Cosets

Conjugacy classes

Normal subgroups

Lagrange's theorem

The isomorphism theorems

Actions of groups on sets

Symmetric group and alternating group

Cayley's theorem

Groups of symmetries of plactonic solids

Direct products of groups

Group automorphisms

Sylow's theorem

Applications: classification of groups of small order

The alternating group is simple

Classification of finite abelian groups, finitely-generated abelian groups

Time permitting:

Composition series

Jordan-Hoelder theorem

Nilpotent and solvable groups

Free groups

Definition and examples

Ring homomorphisms

Ideals

Chinese Remainder Theorem

anne@math.ucdavis.edu