Math 115A Winter 2008 Syllabus

Instructor: Alex Boisvert
Textbook: S. Friedberg, et al, "Linear Algebra", Custom Edition for UCLA
Office: MS 6322
Office Hours: Monday 9:30-10:30
Wednesday 10:30-11:30
Friday 9:30-10:30
Class home page: http://www.math.ucla.edu/~boisvert/115a.3.08w/ or snipurl.com/1vds0

Homework:

Homework will be assigned in class on Monday and will be due in section the following Tuesday. Homework must be written neatly and stapled in the upper left-hand corner. Late homework is never accepted under any circumstances. Your lowest homework score will be dropped; however, I encourage you to turn in all the homework in case for some reason you have to miss a homework later.

Exams:

There will be two midterms: a first on January 30th and a second on February 27th. The final exam will be given on March 19th. There are no make-up exams. You must take the final to pass the class. You must bring your student ID to the final exam.

Grading:

The homework is graded as follows: your TA will select five problems at random to grade, for 10 points each. The remaining 50 points is for completeness. If you have attempted all of the problems (not just writing down the problem number, for instance) you get 50 points, otherwise you get 0. As mentioned above, the lowest homework score is dropped.
There are two grading schema for this class: Note: Even if you get 100% on the first midterm, you are better off taking the second midterm anyway, because the final will probably be harder than the second midterm (i.e. there is no way to beat the system).

The grade for the final exam and the final grade in the class are non-negotiable.

We will be using MyUCLA (http://my.ucla.edu) for grading. All of your grades will be visible there. I recommend you keep your old homeworks and check MyUCLA periodically to make sure there has not been an error.

Course Outline

This outline is preliminary and is subject to change.


Lecture
Section
Topics
1/7
1.2
Vector Spaces over a Field
1/9
1.3
Subspaces
1/11
1.4, 1.5
Linear Combinations and Systems of Linear Equations;
Linear Dependence and Linear Independence
1/14
1.5, 1.6
Linear Dependence and Linear Independence; Bases and Dimensions
1/16
1.6
Bases and Dimensions
1/18
1.6
Bases and Dimensions
1/23
2.1
Linear Transformations, Null Spaces, and Ranges
1/25
2.1
Linear Transformations, Null Spaces, and Ranges
1/28
2.1, 2.2
Linear Transformations, Null Spaces, and Ranges;
The Matrix Representation of a Linear Transformation
1/30
1.2-2.1
Midterm 1
2/1
2.2
The Matrix Representation of a Linear Transformation
2/4
2.3
Composition of Linear Transformations and Matrix Multiplication
2/6
2.4
Invertibility and Isomorphisms
2/8
2.4, 2.5
Invertibility and Isomorphisms; The Change of Coordinate Matrix
2/11
2.5
The Change of Coordinate Matrix
2/13
4.4
Summary - Important Facts about Determinants
2/15
5.1
Eigenvalues and Eigenvectors
2/20
5.1
Eigenvalues and Eigenvectors
2/22
5.2
Diagonalizability
2/25
5.2
Diagonalizability
2/27
2.2-5.1
Midterm 2
2/29
5.2
Diagonalizability
3/3
6.1
Inner Products and Norms
3/5
6.1, 6.2
Inner Products and Norms; The Gram-Schmidt
Orthogonalization Process and Orthogonal Complements
3/7
6.2
The Gram-Schmidt Orthogonalization Process
and Orthogonal Complements
3/10
6.3
The Adjoint of a Linear Operator
3/12
6.4
Normal and Self-Adjoint Operators
3/14
6.4
Normal and Self-Adjoint Operators