MATH 110C Algebra, Lecture 1
Instructor: Christian Haesemeyer
Office: MS 6304
phone: 310-825-3364
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.

• Literature:
• 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.