**MATH 115A Linear Algebra, Lecture 4**
**Instructor:** Christian Haesemeyer
**Office: MS 6304**
**phone:** 310-825-3364
**Office hours:**M:10:30-11:30 W:3-4 F:9:30-10:30

**Teaching Assistant:**Patrick Allen

**Time and Location:**
MWF 2pm, MS 5117 (Lectures)*and* TR 2pm, MS 5117 (Discussion section).

**Syllabus and assignments:**
Week 1: Fields, vector spaces, subspaces, linear (in)dependence. Sections 1.2 through 1.5 of the textbook.
Week 2: Bases and dimension. Section 1.6 of the textbook.
Homework 1, due **October 10th. Solutions.**
Week 3: Linear transformations. Sections 2.1 and 2.2 of the textbook.
**Friday, October 17:** First midterm exam. Solutions.
Week 4: Matrix representation, composition of linear transformations, isomorphisms. Sections 2.2 through 2.4 of the textbook.
Homework 2, due **October 24th. Solutions.**
Week 5: Change of coordinate, determinants. Sections 2.5 and 4.4. of the textbook.
Week 6: Eigenvalues and Eigenvectors. Section 5.1. of the textbook.
Homework 3, due **November 7th.** **Update**: New version posted October 28: The "right to left" in problem 1 is replaced by "left to right". Also, in problem 4, you may assume V has finite dimension. Solutions.
Week 7: Diagonalization. Section 5.2. of the textbook.
**Friday, November 14:** Second Midterm exam. Solutions.
Week 8: Inner products, norms, orthogonalization. Sections 6.1 and 6.2 of the textbook.
Homework 4, due **November 21st.** **Update:** New version posted November 11. The hint in problem 5 needs to be modified.Solutions.
Weeks 9 and 10: Adjoint operators, normal and self-adjoint operators. Review. Sections 6.3. and 6.4. of the textbook.
Homework 5, due **December 5th.**Solutions.
Review sheet.
**Final Exam:** Wednesday, December 10, 11:30-2:30 in MS 5117.

**Literature:**
We are going to use: Friedberg et al. *Linear Algebra*, 4th (Custom UCLA) Edition.

**Grading Policy:**

There will be 5 homework assignements, to be handed in in class on Fridays. Late homework will not be accepted; the lowest score will be dropped. There will also be two midterm exams, and a final exam. Make-up exams will not be given. The homework will account for 20% of the grade, as will each of the midterms; the final will contribute the remaining 40%. If you should miss a midterm due to documented illness or other emergency, the remaining midterm will count for 25% and the final for 55% of the grade. 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.