Math 386, Spring 2005

Advanced Topics in Abstract Algebra


Course description: This course will use what was learned in Math 385 to study some special and beautiful topics. During the first half of the course, we will look at Galois Theory and the amazing correspondence between the structure of field extensions and their groups of automorphisms. The theory has deep and striking applications to geometric constructions and solutions to polynomials. The second half of the course will be split between the study of Algebraic Combinatorics and Advanced Linear Algebra

Instructor: Barry Balof

Office: 236 Olin Hall

Location: 247 Olin Hall Time: Monday, Wednesday, and Friday, 1:00-2:20 PM

Textbook: We will be using Ian Stewart's Introduction to Galois Theory for the first half of the course. In the second half we will be using lecture notes from a course in Algebraic Combinatorics by Guided Discovery and selections from Friedberg, Insel, and Spence's Linear Algebra book. Throughout the semester, you may find it helpful to refer to Contemporary Abstract Algebra, 5th ed. by Joe Gallian .

Class Time: It is my goal to get through two sections of new material per week, one each during the Monday and Wednesday meetings. We will use Friday's time for new material or informal office hours at the discretion of the class. The class will largely be run as a seminar, so there will be no in-class quizzes or exams. Problem sets will challenging and will be due approximately twice every three weeks. You are expected to be an active participant in class daily, supplying answers to questions that arise during the presentation of the material and asking questions of your own for clarification.

Tests: The class will have two take-home exams, one during the week before Spring Break and one during Finals Week.

Grading: Grades will be assigned on a rougly 90-80-70 scale, with grades weighted as follows: 40% homework and class participation, 30% each on the exams.

Academic Honesty: Students are allowed, and in fact, strongly encouraged, to collaborate on homework assignments. However, the work that you turn in must be your own. No copying from any source! On exams, you will be able to use your book and your notes only. Please SEE ME during office hours or at any other time for help.

Special Needs: Any student with a disability for whom special accommodations would be helpful is encouraged to discuss this with the professor as soon as possible.

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