Syllabus 150C: Modern Algebra
Spring 2005

Office Hours during Finals Week: Monday 9-10am (Anne), Monday 3-4pm (Chris)
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,
Office hours: most weeks Mondays 4-5pm, Fridays 3-4pm
T.A.: Christopher Bumgardner, Kerr Hall 480,
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%

Problem sets

Homework 0: Send me an e-mail at and tell me something about yourself, what kind of math you like, what you expect of the class or anything else, so that I can get to know you all a little bit!

Homework 1: ps or pdf, due April 13
Solutions by Chris: pdf

Homework 2: ps or pdf, due April 20
Solutions by Chris: pdf

Homework 3: ps or pdf, due April 27
Solutions by Chris: pdf

Homework 4: ps or pdf, due May 4
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: May 6 in class. The midterm will cover chapters 11.1, 11.2, 11.3, Eisenstein Criterion Proposition 4.5 in chapter 11.4, 11.5, 12.1, 12.2, 12.4 and Homeworks 1-4. No homework is due on May 11.
Midterm Solution: pdf

Homework 5: ps or pdf, due May 18
Solutions by Chris: pdf

Homework 6: ps or pdf, due May 25
Solutions by Chris: pdf

Homework 7: ps or pdf, due June 1
Solutions by Chris: pdf

Homework 8: ps or pdf, due June 8
Solutions by Chris: pdf

Final: June 14 from 10:30-12:30 in Hart 1128
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

Content of the lectures:

The class is based primarily on Chapters 11-14 of Artin's book. Topics to be discussed include:

11. Factorization
Factorization of integers and polynomials
Unique factorization domains, principal ideal domains and Euclidean domains
Gaussian integers
Ideal Factorization

12. Modules
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

13. Fields
Algebraic and transcendental elements
Field extensions
Finite fields
Function fields
Algebraically closed fields

14. Galois Theory
Fundamental theorem of Galois theory
Cubic equations
Primitive elements
Cyclotomic extensions