Abstract Algebra I
Mathematics 566: Fall 2015
Lecture: MWF 1:00-1:50, Engineering E206.
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. 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 qualifying exam requirement. Beyond this, the material is fundamental to the study of mathematics in general and to the areas of algebraic geometry, combinatorics, number theory, and topology in particular. This course will be primarily theoretical, but if time permits we will investigate some 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 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 problems to do on your own and problems to turn in.
Homework is due every Friday afternoon.
Homework must be neat, legible, stapled, with skipped lines, in order to receive credit.
I encourage you to brainstorm the problems in groups and write up your solutions independently.
Abstract Algebra (third edition), by Dummit and Foote, Wiley Press.
There will be a midterm given in class on Friday 10/9.
There will be a final examination Wednesday, December 16 from 4:10-6:10 pm.
Grading: The course grades will be computed approximately
40% Homework; 25% Midterm; 35% Final.
Class participation will determine borderline grades.
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 Wed 2-3, Fri 10-11, or by appointment.