Syllabus 150A: Modern Algebra
Fall 2003

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Lectures: MWF 10:00-10:50am, WELLMN 229   crn: 79210
Discussion section: T 10:00-10:50am, WELLMN 229
Instructor: Monica Vazirani, Kerr Hall 579, phone: 752-2218, vazirani@math.ucdavis.edu OR mjvazirani@ucdavis.edu
Office hours: Monday 1pm-2pm; 11am-noon Friday. unless you hear otherwise
T.A.: Jaejeong Lee zlee@ucdavis.edu
Office hours: 472 Kerr Tuesdays 11-12, Wednesdays 3:10-4pm and click here for an announcement about extra office hours.
Text: Michael Artin, Algebra, published by Prentice Hall, 1991. This is on reserve in Shield library.
Problem Sets: There will be weekly homework assignments, generally 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. If you do collaborate with students on a problem, please write their names at the end of your homework (collaborators: Alice, Bob, Carol, etc.). 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 October 31, Friday.

Final exam: Tuesday, December 09 - 4:00-6:00 pm, in 229 Wellman (NOT 148 Phy. Science)
There will be no make-up exams!
Grading: The final grade will be based on: Problem sets 25%, Midterm 25%, Final 50%
Prerequisites: A proof-writing class (such as 108), and a good linear algebra class (such as 22A or 167).
Web: http://www.math.ucdavis.edu/~vazirani/F03/150A.html

Online resources

Peter Scott's group theory tutorial. Each subsection has a quiz at the bottom of the page.

Introduction to permutations, a pdf file, especially the first 10 pages.

Introduction to group theory


Random other .pdf files available: hw0--symmetries of square and hexagon , comments on hw0 , handout2, on homo-(iso, auto) morphisms , and solutions to handout2 , handout on basis notation like [T]_B^B ,

Problem sets

Homework 0: , a handout from class, due Sept 29

Homework 1: , due October 3
Solutions by Jaejeong: pdf

Homework 2: , due October 8
Solutions by Jaejeong: pdf

Homework 3: , due October 15
Solutions by Jaejeong: pdf

Homework 4: , due October 22
Solutions by Jaejeong: pdf

Homework 5: , due October 29
Solutions by Jaejeong: pdf

Midterm!!! was: October 31

Solutions by MV: pdf
A practice exam is available. You can obtain it from Jaejeong in section, and discuss it in his section and office hours (T 11-12, W 3-4). You can also discuss it in the online discussion group through MyUCDavis.

Homework 6: , due November 5
Solutions by Jaejeong: pdf

Homework 7: , due November 12
Solutions by Jaejeong: pdf


Homework 8: , due November 19
Solutions by Jaejeong: pdf

Homework 9: , due November 26
Solutions by Jaejeong: pdf

Homework 10: , due December 3
Solutions by Jaejeong: pdf



Final Exam: Tuesday, December 09 - 4:00-6:00 pm, 229 Wellman (NOT 148 Phy. Science)
Practice Final: pdf; with solutions; the actual final will have similar format, but also have definitions, as on your midterm.
also, for you to practice, here are copies of your midterm and practice midterm.

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
Diagonalization

If there is time, we will cover select parts of Chapters 5 and 9.