Math 454, Galois Theory
Time: T/TH 1200-115
Location: REC 303
Office hours: 800-1200 T, 100-300 W, 800-1200 Th
Book: I do not plan to have an official textbook for the class. We will use the class notes that will be updated throughout the term. I will have links to web pages (mostly wikipedia) that give lengthier discussions of the various topics we cover. You should utilize the free information that abounds. The hyperlinks in the class notes are meant to make that easier.
Problem sets: I will post weekly problem sets here in .pdf format. The problem sets will be due on Thursdays. I will try to post the problem sets a week before they are due.
Grades: To be discussed.
Class announcements:
The lecture schedule with topic is below (this is tentative):
- Lecture 0. January 10. Class Overview.
- Lecture 1. January 12. Groups, I (1.1 in class notes).
- Lecture 2. January 17. Groups, II (1.2 in class notes).
- Lecture 3. January 19. Groups, III (1.3 in class notes). Problem Set 1 Due.
- Lecture 4. January 24. Rings (2.1 in class notes).
- Lecture 5. January 26. Fields, I (2.2 in class notes). Problem Set 2 Due.
- Lecture 6. January 31. Matrix Groups and Fields (2.3 in class notes).
- Lecture 7. February 2. Maximal Ideals and Fields (2.4 in class notes). Problem Set 3 Due.
- Lecture 8. February 7. Polynomial Rings, I (2.5 in class notes).
- Lecture 9. February 9. Polynomial Rings, II (2.5 in class notes). Problem Set 4 Due.
- Lecture 10. February 14. Polynomial Rings, III (2.5 in class notes).
- Lecture 11. February 16. Polynomials and Splitting Fields (2.6 in class notes). Problem Set 5 Due.
- Lecture 12. February 21. Extension Fields and Automorphisms (3.1 in class notes).
- Lecture 13. February 23. Automorphisms of Splitting Fields (3.2 in class notes). Problem Set 6 Due.
- Lecture 14. February 28. Galois Connections, I (3.3 in class notes).
- March 2. No class (3.4 in class notes).
- March 7. No class. (3.5 in class notes).
- March 9. No class. Take home exam due.
- March 14. No class. Spring Break.
- March 16. No class. Spring Break
- March 21. Hand back exams.
- March 23. No class (Ben is away)
- Lecture 15. March 28. Galois Connections I,II (3.3 and 3.4 in the class notes)
- Lecture 16. March 30. Galois Connections III (3.5 in the class notes) Problem Set 7 Due.
- Lecture 17 April 4. Galois Extensions (3.6 in class notes)
- Lecture 18. April 6. Primitive Element Theorem and Loose ends (3.7 in class notes). Problem Set 8 Due.
- Lecture 19. April 11. Finite Fields.
- Lecture 20. April 13. Number Fields. Problem Set 9 Due.
- April 18. Review.
- April 20. Final Exam.
- April 25. Hand back exams and give final grades.
- April 27. No Class.