**Introduction to Abstract Algebra**

Mathematics 566: Fall 2003

** Lecture:** MWF 11:00-11:50, Engineering 105.

**Course description:**
In this course, we will study groups and rings. These are abstract
algebraic structures mostly developed in the 1800s in Europe which are
useful for studying many natural questions.
For the most part we will follow the
Course syllabus, including the following major topics: examples and
basic properties of groups; homomorphisms and quotient groups; group actions;
examples and basic properties of rings; and ideals and unique factorization
in rings. After completing the course, everyone should have a passing grade
for the 566 portfolio requirement.
Beyond this, the material is fundamental to the study of mathematics
in general and to the areas of combinatorics, algebraic geometry,
and number theory in particular.
This course will be primarily theoretical, but
if time permits we will investigate applications, such as the applications
of group theory to chemistry, coding theory, and cryptography.

**Prerequisite:**
Math 466 or an equivalent undergraduate abstract algebra course,
or permission of professor.

**Homework:**
Homework is the most important part of this class.
It should demonstrate your knowledge of the material,
your investigation of open ended questions, and your skill at
writing proofs. Homework is divided into easy, medium, and difficult
problems; depending on your plans for graduate study, you will either
hand in the easy or the difficult problems, along with the medium problems.
Homework is due every Friday afternoon.
Homework must be neat, legible, and stapled in order to receive credit.
I encourage you to brainstorm the problems in groups and write up your
solutions independently.

**
Detailed information on homework and exams **

**Text:**
Abstract Algebra (Second Edition), by Dummit and Foote,
Wiley Press.

**Examinations:**
There will be a midterm given
in class on Friday, October 24th.

There will be a final examination
Tuesday, December 16 from 7-9 am whose location will be announced.

**Grading: **The course grades will be computed approximately
as follows.

50% Homework; 5% Class Participation;
15% Midterm; 30% Final.

There will be no class on Monday 9/8.

**Help:** Help is always available if you have trouble with homework
or lecture material. If your classmates can't answer your question,
come ask me! Office hours are 1-2 pm Wednesday and Thursday or by
appointment.