I. COURSE INFORMATION

• Meeting Time & Place: CE 104, Monday and Wednesday, 5:30-6:45 PM
• Instructor: Dr. George D. Tintera
• Office: Seabreeze 211
• Office Hours: To Be Announced
• Phone: (361) 825-6028, FAX: (361) 825-5848
• Internet: tintera@falcon.tamucc.edu
• Class Website: http://www.tamucc.edu/~tintera/f00/5354

II. COURSE DESCRIPTION

Basic structure theorems for groups, rings, and fields. Additional topics selected from Sylow's theorem, symmetry groups, algebraic coding theory, and Galois theory.

III.PREREQUISITES

MATH 4306 (Modern Algebra)

IV.TEXT AND OTHER SUPLIES REQUIRED

Students will be assigned readings from the following texts

• Algebra, Michael Artin, Prentice Hall, 1991.
• Algebra I, Kostrikin and Shavarevich (eds), Springer Verlag, 1990

V.COURSE OBJECTIVES

After completing the course, a student should be able to

• Understand the role of sets and mappings in the study of algebraic systems,
• Recognize the properties of important algebraic structures,
• Provide proofs of relevant theorems,
• Solve direct application problems as well as problems requiring generalization and synthesis,
• Investigate the literature for problems related to algebra,
• Study symmetry of a mathematical object using group theory,
• Apply the methods of abstract algebra to solution of polynomial equations.

VI. INSTRUCTIONAL METHODS AND ACTIVITIES

The class uses lecture format. Students are expected to read the text before class as directed and be prepared to participate in the class by calculating and evaluating models. A significant portion of the class time will be available for students to present their solutions of homework assignments.

VIII. EVALUATION AND GRADE ASSIGNMENT

Grades: Students will demonstrate their knowledge and use of definitions, relationships and theorems in both written assignments (homework sets), a midterm and a final exam and an in-class presentation. The presentation will be a report on the finding of an article in the mathematics literature and a summary of the algebra used in it.

• A grade of A will be assigned to students who use definitions, ideas, terminology and symbols effectively to create solutions of non-routine problems and to give clear and coherent explanations of the reasoning that underlies such solutions.
• A grade of B will be assigned to students who can demonstrate understanding of basic definitions, ideas and relationships in the solving of problems, and can supply relevant reasons and calculations without prompting. Explanations may not always be clear and correct, but are substantially so.
• A grade of C will be assigned to students who can demonstrate knowledge of basic definitions, ideas and relationships and use them to start solutions to problems or complete solutions to problems whose outlines are given. Substantial gaps in reasoning may be present.
• A grade of D will be given to students who present incoherent, incomprehensible solutions and meaningless and incorrect calculations of most work.

Homework: The homework exercises will be listed in the course schedule (below). It is due the Thursday after it is assigned. Completion of most problems should give students a chance to demonstrate their accomplishment consistent with earning an A. At least one problem in every section should give a chance for a student to demonstrate his/her accomplishment consistent with earning a C.

Exams: The midterm and final exams will be chance to demonstrate their knowledge of the abstract algebra. The level of problems will range from elementary to non-routine problems requiring clear and coherent solutions.

Presentations: The presentations will be based on articles found in journals of the Mathematical Association of America or the Society for Industrial and Applied Mathematics, all available in the Mary and Jeff Bell Library and its website Portal. Students should present a list of 10 articles incorporating abstract algebra from several different journals by the midterm. The instructor and student will choose one article to review. The student will prepare a four to six page typed paper reviewing the article and a 5-10 minute presentation to be delivered to the class starting November 13.

VIII. TENTATIVE COURSE SCHEDULE

It is attached

IX. CLASS POLICIES

Attendance: I will expect all students to attend all class meetings and I will take attendance. If you miss any class meetings without an excused absence, you must submit a written claim (e-mail is OK) to that effect. Do not assume that I have acknowledged your excuse until you have your claim returned with my approval.

Late Homework: In general, I accept homework after deadlines without penalty until such time as I have graded the homework of your classmates. After that time, I will continue to accept late homework, but with an increasing penalty as its lateness increases. Homework turned in more than 1 week after the due date will receive no credit. I also reserve the right to enforce exact deadlines on particular assignments if I feel it is important.

Registration: You are the only person responsible for your registration in this class. If for some reason you decide not to continue with the course, you will need to see your advisor or the registrar to drop the course. If you quit coming to class and do not drop, I will be forced to assign you a grade based on the work you have completed, usually an F. Please don't make me do that.

Last Revised September 6, 2000