Syllabus 150A: Modern Algebra
Fall 2001



Click here for the grades.
Lectures: MWF 1:10-2:00pm, Young 184
Discussion section: T 1:10-2:00pm, Young 184
Instructor: Anne Schilling, Kerr Hall 578, phone: 754-9371, anne@math.ucdavis.edu
Office hours: Monday, Wednesday 10-11, Friday 11-12
T.A.: Maya Ahmed, Kerr Hall 577, ahmed@math.ucdavis.edu
Office hours: Tuesdays 3-4pm, Thursdays 3-4pm
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 November 2, Final exam during the final exam period (December 10-15)
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/FQ2001/150A.html

Problem sets

Homework 1: ps or pdf, due October 10
Solutions by Maya: pdf

Homework 2: ps or pdf, due October 17
Solutions by Maya: pdf

Homework 3: ps or pdf, due October 24
Solutions by Maya: pdf

Homework 4: ps or pdf, due October 31
Solutions by Maya: pdf

Homework 5: ps or pdf, due November 7
Solutions by Maya: pdf

Homework 6: ps or pdf, due November 14
Solutions by Maya: pdf

Homework 7: ps or pdf, due November 21
Solutions by Maya: pdf

Homework 8: ps or pdf, due November 28
Solutions by Maya: pdf

Homework 9: (last one!) ps or pdf, due December 5
Solutions pdf


Practice Final: ps or pdf;
Solutions will be discussed in class on December 7 ps or pdf

Final Exam: Thursday December 13, 10:30am-12:30pm in Young 184

Content of the lectures:

The class is based on Chapters 1-4 of Artin's book. Topics to be discussed include:

1. Preliminaries
Matrices
Permutations and permutation matrices

2. Group Theory
The definition of a group
Subgroups
Homomorphisms
Isomorphisms
Cosets
Products of groups
Quotient groups
Modular arithmetic

3. Vector spaces
Real and complex vector spaces
Abstract fields
Bases and dimensions
Computations with bases
Direct sums

4. Linear Transformations
The dimension formula
The matrix of a linear transformation
Eigenvectors
The characteristic polynomial
Orthogonal matrices and rotation
Diagonalization

anne@math.ucdavis.edu