Math 5-282 announcement

Course Announcement Fall 1998 Math 5-282 (Fundamental Structures of Algebra)

Math 5-282 (Fundamental Structures of Algebra)
MWF 9:05 AM
Vincent 207

Instructor: Professor Joel Roberts

Course objectives:

The sequence Math 5282/3/4 satisfies the Algebra requirement for the Mathematics major in either IT or CLA, and is also designated as an honors course in the requirements for graduation with honors in mathematics.
There is more emphasis on theory than there is in the sequence Math 5245/6/7 (Introduction to Modern Algebra I-II-III.)
In the present implementation, we will also study a more extensive range of examples than in the other sequence. Indeed, this is the main reason for choosing the particular textbook that we will be using.

Text:

Subject matter:

Group theory and linear algebra, corresponding to chapters I through V of the text. (Certain sections of some chapters will be omitted.)
Besides learning the basic theory about groups, we will also study various instances of matrix groups and groups of geometric transformations and/or symmetry groups.
Learning the material in this course includes learning to read and understand proofs and to write proofs of propositions in algebra. This can be difficult for students who have not previously taken abstract math courses, and we will try to facilitate the process of learning to do this. It is appropriate to assume that this learning process will also require significant effort from the students.

Winter Quarter: (Math 5283)

Planned topics include selected parts of Chapters VI, VII, and VIII of the text (more group theory, bilinear forms, and linear groups), and most of Chapter X (ring theory)

Spring Quarter: (Math 5284)

Planned topics include factorization, modules, and fields (corresponding to chapters XI, XII, and XIII of the text).

Prerequisite: The prerequisite is a sophomore math sequence, including linear algebra.
Possibilities for this sequence include:

Math 3262 can be helpful, whether taken previously or concurrently.

Required work:

Grading policies:

Comments and questions to: roberts@math.umn.edu Back to the class homepage.