21-373 Algebraic Structures - Spring 2008 MWF 1:30PM-2:20PM PH A18C

Instructor: Rami Grossberg
Office: WEH 7204
Phone: x8482 (268-8482 from external lines), messages at x2545
Email: Rami@cmu.edu
URL: www.math.cmu.edu/~rami
Office Hours: Immediately after class or by appointment.

Purpose. I found the following excellent discription of what is Algebra on a web page of Texas A&M University: Algebra is one of fundamental disciplines of mathematics and an algebraic way of thinking is pervasive in much of mathematics. Many mathematical and physical phenomenon can be described by one of the many algebraic structures, such as groups, rings, fields, modules and vectorspaces. Applications are numerous and include computer graphics (as an application of algebraic geometry) and coding/cryptography (as an application of number theory).

The goal of this course is to introduce the basic concepts and facts of modern algebra. This should prepare the student to be able to manipulate and understand fairly abstract concepts, and provide the necessary background for a large number of courses in algebra and applications. We will present some of the most useful ideas of algebra, which are of great importance in a large number of subjects within mathematics and outside.

Course description. We will concentrate in the basic properties of groups, and rings. We will cover most of chapters 1-9 (the first half of the book). We will concentrate on chapters 3,4,8 and 9.

Assignments. A list will be posted on a weekly basis. There will be two types of problems: with an asterisk and without. The problems with an asterisk will be collected in class once a week on Wedensdays and will be graded. The homework is an important part of the learning process; you are strongly advised to try all of the assigned problems; in case of difficulties you should consult me.

Text: "Abstract Algebra" by D. S. Dummit & R. M. Foote. current edition Published by John Wiley & Sons. price comparison.

Office Hourse: MWF 2:30-3:30PM or by appointment.

Test Dates: The first test will be held on Friday Feb 29th. The date of the second midterm will be posted.

Evaluation: There will be two one hour tests (in class), weekly homework assignments, and a three hour final. These will be weighted as follows:

• Each of the two midterm tests will make up 20% of the grade
• The final will make up 40% of the grade
• Homework assignments will be collected every Wedensday, they make up 20% of the grade.
The standards of academic honesty as stated in the Student Handbook will be strictly enforced.

Prerequisites. Ability to read and write proofs and little linear algebra.