Modern Algebra - Galois Theory
Instructor: Carl Mautner
Meeting time: TTh 11:10--12:30 in room Sproul 2360.
Office hours: M 1--2:30, W 12--1:30 (or by appointment) in room 255 Surge
TA: Matt O'Dell
TA Office hours: TBA
Course Description: We will study a collection of questions that go back to ancient times and were only answered in 19th century with the creation of modern algebra! Along the way we will turn classical geometric problems into questions about polynomials and their solutions. We will explore connections between polynomials and fields and finally conclude with Galois theory - the crowning jewel of early modern algebra and a powerful tool for studying fields and their extensions.
Text: Galois Theory by David A. Cox, 2nd edition. The book can be accessed from any computer on the UC network. You can find the link in the library catalog.
Supplementary texts: Abstract Algebra: Theory and Applications by Thomas W. Judson and Galois Theory by Ian Stewart, any edition (the 3rd edition is on 2 hour reserve at the library).
Grades: The grade will be based on homework assignments (25%), one in-class exam (30%) tentatively set for Tuesday, May 5, and a final exam (45%) on June 11, 8-11 am. Final letter grade cut-offs will be made at the end of the semester and will be no worse the standard scale (e.g., if you get above 90% you are guaranteed an A or A-).
Homework: Homework will generally be assigned each class meeting and due a week later at the beginning of class. A list of the homework problems will be kept on the webpage. Late homework will not be accepted, but the lowest two homework grades will be dropped.
Collaboration: You are encouraged to discuss homework problems with other students. The final write-up of any solution, however, should be your own. Copying other students' solutions is not allowed.
1) T Mar. 31 (Due T Apr. 7) - pdf.
2) Th Apr. 2 (Due Th Apr. 9) - pdf.
3) T Apr. 7 (Due T Apr. 14) - pdf.
4) Th Apr. 9 (Due Th Apr. 16) - pdf.
5) T Apr. 14 (Due T Apr. 21) - pdf.
6) Th Apr. 16 (Due Th Apr. 23) - short homework! Exer. 1 from Section 3.2.
7) T Apr. 21 (Due T Apr. 28) - Exercises 1, 3, 8 from Section 4.1.
8) Th Apr. 23 (Due Th Apr. 30) - Exercises 2, 4, 6 from Section 4.3.
Midterm review sheet.
9) Midterm corrections (Due T May 12) - please write clean solutions to the problems you missed. There is a typo in Problem 2.b. - it was supposed to ask for the coefficient of the term of degree 5 (not 3!). My sincere apologies for screwing that up!
10) Th May 7 (Due Th May 14) - Exercises 1, 2, 6, 7 from Section 4.4.
11) T May 12 (Due T May 19) - Exercises 3, 6, 7, 9 from Section 5.1.
12) Th May 14 (Due Th May 21) - Exercises 10, 13 from Section 5.1 and exercise 1 from Section 5.2.
13) T May 19 (Due T May 26) - Exercises 3, 4 from Section 5.2 and exercise 3 from Section 5.3.
14) Th May 21 (Due Th May 28) - pdf.
15) T May 26 (Due T June 2) - Exercises 1, 3, 6 from Section 6.1.
16) Th May 28 (Due Th June 4) - Last HW! Exercise 4 of Section 6.2 and exercises 2 and 4 of Section 6.3. (If you have trouble with these, you might first try exercises 2 and 3 from section 6.2 and exercise 1 from Section 6.3 as warm-up problems.)
Final review sheet.