**MATH 110A Algebra (Honors), Lecture 1**
**Instructor:** Christian Haesemeyer
**Office: MS 6304**
**phone:** 310-825-3364
**Office hours:**M:3-4 W:2-3 F:1-2

**Teaching Assistant:**Justin Shih

**Time and Location:**
MWF 10am, MS 6229 (Lectures)*and* R 10am, MS 6201 (Discussion section).

**Syllabus and assignments:**
Week 1: Preliminaries: Integers, induction, and equivalence relations.
Homework 1, due Friday October 7: Elman Lectures, Exercises 8.5.: 1,2,3,4,7,8,11,13,14,15. Exercises 9.10.: 1,4,5,6.
Week 2: Groups: definition and examples. Subgroups.
Homework 2, due Friday October 14: Elman Lectures, Exercises 10.14: 1,2,3,4,5,6.
Week 3: Homomorphisms. Cosets. Normal subgroups.
Homework 3, due Friday October 21: Elman Lectures, Exercises 11.9: 3,6,14,15,16.
Week 4: The symmetric group (Dummit & Foote 1.3., Elman 18 through 18.8. but you may skip 18.5.). Automorphisms of groups (see Elman, page 60).
Homework 4, due Friday October 28: Elman lectures, Exercises 11.9.: 9,10,11,12 Exercises 12.11.: 1,5,6.
Week 5: Group actions (Dummit & Foote 4.1. through 4.3., Elman 15 and 16).
Homework 5, due Friday November 4: Elman lectures, Exercises 15.9.: 1,2. Exercises 16.26.: 2,6,7,8.
Week 6: Group actions, ctd.
Homework 6, due Monday November 14: Elman lectures, Exercises 16.26.: 5,11,12,13. Exercises 17.11.: 1,2,3.
Week 7: Sylow theorems.
Homework 7, due Monday November 21: Elman lectures, Exercises 17.11.: 4,5,8,11,12. Exercises 14.13.: 1,4.
Week 8: Composition series. (Dummit & Foote 3.4., Elman 14.)
Homework 8, due Monday November 28: Elman lectures, Exercises 17.11.: 9. Dummit & Foote, Exercises 5.2.: 1 (a) and (b) only, 6,9.
Week 9: Abelian groups. (Dummit & Foote 5.2.)
Week 10: Symmetric groups, revisited.

**Midterm Exam:** Friday, October 28 in class.
**Final Exam:** Thursday, December 8, 11:30-2:30. **Take-home part** is here. Due Monday December 5th **by noon**. I will be in my office that Monday 10-12. Late exams will **not be accepted**.

**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. My own notes from another algebra class (as source for the material about finite abelian groups) can be found here.

**Grading Policy:**

There will be 8 homework assignments, to be handed in in class on Fridays. Late homework will not be accepted; the lowest score will be dropped. There will also be one midterm exam,
and a final exam. The total score for the course will be based on the better of the following two: homework will account for 40%, the midterm for 20% and the final will contribute the remaining 40%. Or, homework 20%, and the final 80%. 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.