Spring 2005

Lectures: |
MWF 2:10-3:00pm, Hart 1128 |

Discussion section: |
T 2:10-3:00pm, Hart 1128 |

Instructor: |
Anne Schilling, Kerr Hall 578, phone: 754-9371,
anne@math.ucdavis.edu
Office hours: most weeks Mondays 4-5pm, Fridays 3-4pm |

T.A.: |
Christopher Bumgardner, Kerr Hall 480,
quillbone@math.ucdavis.edu
Office hour: Tuesdays 3-4pm, Wednesdays 1-2pm |

Pre-requisite: |
MAT 150B with a C- or better or consent of the instructor |

Text: |
Michael Artin, Algebra, published by Prentice Hall, 1991. |

Problem Sets: |
There will be weekly homework assignments, handed out on Wednesday, due
the following Wednesday.
You are encouraged to discuss the homework problems with other students. However, the homeworks that you hand in should reflect your own understanding of the material. You are NOT allowed to copy solutions from other students or other sources. No late homeworks will be accepted.
Solutions to the problems will be discussed in the discussion section.
This is also a good forum to get help with problems and to ask
questions! |

Exams: |
Midterm May 6, Final exam on Tuesday June 14, 10:30am - 12:30pm
There will be no make-up exams! |

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

Web: |
http://www.math.ucdavis.edu/~anne/SQ2005/150C.html |

Solutions by Chris: pdf

Solutions by Chris: pdf

Solutions by Chris: pdf

Solutions by Chris: pdf

Solution to 12.4.3 should be Q=[[-1,2],[4,7]], P^{-1}=[[0,1,17],[1,0,-10],[0,0,1]], QAP^{-1}=[[1,0,0],[0,2,0,]]

Midterm Solution: pdf

Solutions by Chris: pdf

Solutions by Chris: pdf

Solutions by Chris: pdf

Solutions by Chris: pdf

The final will cover the same topics as the midterm and in addition chapters 12.5, 12.6, 12.7, 13.1, 13.2, 13.3, 13.5, 13.6, 14.1 and Homeworks 1-8.

Final Solution: pdf

Factorization of integers and polynomials

Unique factorization domains, principal ideal domains and Euclidean domains

Gaussian integers

Primes

Ideal Factorization

Definition of modules

Matrices, free modules and bases

Diagonalization of integer matrices

Generators and relations for modules

Structure theorem for Abelian groups

Application to linear operators

Examples

Algebraic and transcendental elements

Field extensions

Finite fields

Function fields

Algebraically closed fields

Fundamental theorem of Galois theory

Cubic equations

Primitive elements

Cyclotomic extensions

anne@math.ucdavis.edu