Syllabus 150B: Modern Algebra
Winter 2002

The class grades and final scores are listed here under the last 4 digits of your social security number.
Lectures: MWF 1:10-2:00pm, Olson 118
Discussion section: T 1:10-2:00pm, Olson 118
Instructor: Anne Schilling, Kerr Hall 578, phone: 754-9371, anne@math.ucdavis.edu
Office hours: Monday, Friday 2-3:20
T.A.: Sunny Fawcett, Kerr 479, fawcett@math.ucdavis.edu
Office hours: Tuesday 4-5
Pre-requisite: MAT 150A 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 February 8, Final exam on Friday March 22, 1:30-3:30 pm
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/WQ2002/150B.html

Problem sets

Homework 0: Send me an e-mail at anne@math.ucdavis.edu 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 January 16
Solutions: ps or pdf

Homework 2: ps or pdf, due January 23
Solutions: ps or pdf

Homework 3: ps or pdf, due January 30
Solutions: ps or pdf

Homework 4: ps or pdf, due February 6
Solutions: ps or pdf
Sunny figures (no pun intended): ps or pdf

Homework 5: ps or pdf, due February 13
Solutions: ps or pdf

Homework 6: ps or pdf, due February 20
Solutions: ps or pdf

Homework 7: ps or pdf, due February 27
Solutions: ps or pdf

Homework 8: ps or pdf, due March 6
Solutions: ps or pdf

Homework 9: last one! ps or pdf, due March 13
Solutions: ps or pdf

Sample Final Problems: ps or pdf

Content of the lectures:

The class is based primarily on Chapters 5-8 of Artin's book. Topics to be discussed include:

1. Topics in Advanced Group Theory
Group actions
Stabilizers and orbits
The class equation of an action
Applications of G-set to counting
Conjugation
The Sylow Theorems

2. Symmetry
The orthogonal group O_n
Symmetry figures in R^2
The isometry group of R^2
Finite subgroups of Iso(R^2)
Discrete subgroups of Iso(R^2)
Finite subgroups of SO_3(R)

3. Bilinear Forms
Definition of bilinear forms
Symmetric forms: orthogonality
Hermitian forms
The spectral theorem

4. Linear Groups
The classical linear groups
The special unitary group SU_2
The orthogonal representations of SU_2

5. Group Representations
Group representations
G-invariant and unitary representations
Invariant subspaces and irreducibility
Characters
anne@math.ucdavis.edu