**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.

**Grading Policy:**

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.