Mathematics 216 — Abstract Algebra

Spring 2007
Alan H. Stein

This course studies fundamental algebraic systems in mathematics, selected from groups, rings, fields, and modules. Examples of groups include the invertible matrices with a fixed size and the roots of unity. Rings are illustrated by integers, polynomials, and modular arithmetic. Complex numbers, rational numbers, and rational functions are examples of fields. (There are also finite fields, which are used all the time in computer science.) Finally, ordinary vectors in space and any lattice in the plane are examples of modules. The concern with these algebraic systems is not simply the study of individual systems, but also of functions between systems which carry one operation into the other. For instance, the determinant not only converts matrices into numbers, but it sends a product of matrices into a product of numbers. The level of attention given to such operation-preserving transformations (putting them on an equal footing with the algebraic systems they transform) is one of the characteristic features of abstract algebra, and also one of the algebraic ideas which have reached into other areas of mathematics. Math 213 and a linear algebra course are prerequisites.

This web site is adapted from the sites used for other courses; since this course is being taught on an independent study basis, some of the material may appear to be irrelevant. If you notice anything like that, please let your instructor know.

Contents

• Meeting Times
• Textbook
• Listserv Mailing List
• Notes for Mathematics 216 -- These will be created during the course of the course and organized along the lines of this course.
• Problem Sets, Quizzes and Examinations
• Final Examination

Links

• — These are organized by topic.

Meeting Times

This course is being taught on an independent study basis. We meet at 2:00 pm on Wednesdays. We will not meet Wednesday, April 4, but will arrange another meeting time for that week.

Textbook

We will probably use Abstract Algebra: A First Course, by Dan Saracino.

Listserv Mailing List

The class has a listserv mailing list set up. The name of the list is WMA216-L and it is hosted on listserv.uconn.edu. Every member of the class will be automatically signed up for the list upon filling out the and is expected to participate in the discussions.

Posting a Message to the Mailing List

To post a message to the mailing list, simply address it to WMA216-L@listserv.uconn.edu. Other than that, it may be handled in the same way as any other email message.

Notes for This Course

Notes

There are a number of sets of available. The following sets of slides specific for this class are also available. Each set is available in a normal size text format as well as the slides used in class.

These slides will be created as the semester progresses.

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Problem Sets, Quizzes and Examinations

Since this course is being taught on an independent study basis, this is subject to negotiation.

Final Examination

The final examination will be comprehensive, although more emphasis will be placed on the material covered later in the course and which was not included in any earlier exam than in the earlier material.