MATH 110C Algebra, Lecture 1
Instructor: Christian Haesemeyer
Office: MS 6304
Office hours:M:10 W:2 F:10
Teaching Assistant:Geunho Gim
Time and Location:
MWF 9am, MS 6201 (Lectures)and R 9am, MS 6201 (Discussion section).
Syllabus and assignments:
Week 1: Field extensions.
Homework 1, due friday April 13: Elman notes, exercises 40.23.: 1,2,3,4,5,6.
Week 2: Splitting fields and normal extensions. Algebraic closure.
Homework 2, due Friday April 20: Read section 41 of the Elman notes and do problems 1-3 listed under "Examples 41.5.". Also Exercises 42.18.: 3,5,6.
Weeks 3: Separable and purely inseparable extensions. Perfect fields.
Homework 3, due Monday April 30: Elman notes, exercises 45.10: 2,3,4,5,7.
Week 4: finite fields and their automorphisms.
Homework 4, due Monday May 7: Elman notes, exercises 42.18: 7,11,14. And, exercises 45.10: 8
Weeks 5 and 6: Galois theory.
Homework 5, due Monday May 14: Elman notes, exercises 48.21:6,9,10,11,12.
Week 6: Norm and trace.
Homework 6, due Monday May 21: Exercises 52.23: 1,2,4 and 6 (meaning: complete the proof sketch from class describing norm and trace in terms of the linear operator),7.
Week 7: Cyclic extensions. Solvable extensions.
Homework 7, due Wednesday May 28 (due to holiday): Elman notes, exercises 49.11.: 1,2,4,5,6.
Weeks 8: Solving equations by radicals.
Homework 8, due Wednesday June 6: File.
Weeks 9 and 10: Rings of integers in number fields.
Midterm Exam: Friday, April 27 in class.
Final Exam: Take home, available here. Due June 8th in class at the latest. Note I am leaving the country for 6 months the next day, so NO late submissions can be accepted under any circumstances.
We are going to use: Dummit and Foote, Abstract Algebra (3rd ed.), Wiley 2003; and Prof. R. Elman's Lectures in Abstract Agebra available for download here. And here are the very incomplete notes of mine that I am following.
There will be 8 homework assignments, to be handed in in class on Fridays. Late homework will not be accepted. There will also be one midterm exam,
and a final exam. The total score for the course will be based on the following: homework will account for 30%, the midterm for 30% and the final will contribute the remaining 40%. This class will use the myUCLA gradebook facility.
Requests for a regrading will only be considered within 14 calendar days of the due date of the original assignment, and no later than the day before the final. All such requests must be directed to the instructor; the TA is not allowed to make changes to grades.