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The primary focus of this course is Galois Theory, including all of the basic theory leading up to the Fundamental Theorem of Galois Theory and the Galois Correspondence. We will begin the course with a very brief review of some of the required material from Math 113 (First Course in Abstract Algebra). As for the bulk of the class, I expect to cover most of the material from Chapters 1-12 of the text. If time permits, we will also discuss some of the material from Chapters 14 and 15, and possibly some other topics in abstract algebra.
Here is a tentative list of topics:
If there’s time:
Final grades will be based on homework, one midterm, and a final exam. Your final grade will be roughly calculated using the following formula:
Important Note: There will be no make-up exams. If you have a legitimate conflict with the scheduled date/time for the midterm (which will be established before the first lecture), you should let me know within the first two weeks of class.
Homework will be assigned on a weekly basis (with the exception of the week of the midterm). Homework assignments will be posted below. Late homework will not be accepted under any circumstances, but your lowest two homework grades will be dropped.
Here are some practice problems from the Math 113 class I taught in the Fall 2013 semester.
Note: Most of these problems are of the same style: Find an example or prove that none exists. Even in cases where the directions ask for an example (e.g. an element in a ring), the problems should still be treated as if “no example” is a possibility, and in such cases you should provide a proof that no example exists.