Math 386, Spring 2013

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 part 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 focus on advanced topics from Group Theory and their applications to group classifications as well as symmetry.

Instructor: Barry Balof

Office: 236 Olin Hall

Location: 245 Olin Hall Time: Monday 10-10:50, Wednesday, and Friday, 11-11:50 AM

Textbook: We will be using Ian Stewart's Galois Theory for the first part of the course. Throughout the semester, you may find it helpful to refer to Abstract Algebra: Theory and Applications by Tom Judson .

Homework: Homework will be collected weekly, generally on Mondays. I am happy to devote half of each Friday session to homework questions, as well as answering short questions daily in class. I expect that classes will be largely interactive and expect you to ask many questions throughout the semester. There will be occasional assignments that use SAGE.

Tests There will be one midterm and one final exam

Presentations During the last two weeks of the semester, students will present material on a topic of their choosing (in groups of three). Details will be forthcoming early in the semester.

Grading: Grades will be assigned on a rougly 90-80-70 scale, with grades weighted as follows.
Homework and Class Participation 25%
Midterm 25 %
Presentation   15 %
Final Exam 35 %

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! You will receive directions regarding the use of your book and notes on exams. Please SEE ME during office hours or at any other time if you have questions.

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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