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Text: Algebra, Lang, Springer (GTM 211).

Prerequisite:Ma120a, an equivalent course, or permission of the instructor.

Course Objectives: This is the second quarter of the graduate algebra sequence.

This quarter will focus on the structure of field extensions, and especially Galois extensions. We will cover the fundamental theorem of Galois theory for (finite or infinite) algebraic extensions and will investigate some well-known classical applications such as the "insolvability of the quintic". We will also study some of the basic properties of transcendental extensions.

Grading and Homework Policy: There will be weekly homework worth 50% of the grade, and a final worth 50%. The final may be a written examination or a presentation given to the class. Collaboration on the homework is allowed, but you must write up your solutions on your own and in your own words. You may hand in one homework assignment up to a week late. Except in unusual circumstances no other late homework will be accepted.