**Spring Semester
2006-2007**

**MATH 4523: Linear
Algebra II**

**Instructor: **Dr. Vu
Kim Tuan** **

**Time & Location: **R,
5:30 PM-8:00 PM, Boyd Building 304

**Office: **Boyd
Building 325

Office Hours: Wednesdays: 11:00 AM-1:00
PM, Tuesdays + Thursdays, 10:00 AM-11:00 AM, 2:30 PM-5:30 PM, or by appointment. Please contact me only through campus MyUWG e-mail or in
person.

**Phone: **678-839-4135** **

**E-mail: **vu@westga.edu

**Hours Credit: **3
hours** **

**Prerequisites: **MATH
4513** **

**Textbook: ***Linear
Algebra and Matrix Theory***, **by
J. Gilbert/ L.Gilbert, Thomson, Brooks/Cole, 2004, ISBN 0-534-40581-9

.

**Course Description: **A
more abstract and advanced treatment of linear algebra including abstract
vector spaces, linear transformations, eigenvalues, and eigenvectors. The
student is supposed to know basic facts on vector spaces, subspaces, linear
transformations, determinants, and elementary canonical forms. We will cover Chapters 4, 5, 7-11. The
student will learn how to find eigenvalues and eigenvectors theoretically and
numerically, functionals, quadratic forms, bilinear and Hermitian forms, spectral decompositions and
the Jordan canonical form, abstract vector spaces, inner products, norms,
calculus over vectors and matrices (sequences, series, and convergence).

**Topics: **Abstract
vector spaces, subspaces, standard bases, and isomorphisms of vector spaces.
Matrices over an arbitrary field and systems of linear equations. Linear
transformations and change of basis. Eigenvalues and eigenvectors. Linear
functionals, real quadratic forms and classification. Bilinear and Hermitian
forms. Inner products, norms and orthogonal bases. Normal and orthogonal
matrices and normal linear operators. Projections and direct sums. Spectral decompositions and the Jordan Canonical
form. Sequences and series of vectors and matrices. The standard method of
iteration and an iterative method for determining eigenvalues. CimminoÕs
method.

**Learning
Outcomes: **the student will be able:

-To work with abstract vector spaces.

-To work with linear transformations in different bases.

-To find eigenvalues and eigenvectors of linear transformations and matrices.

-To be able to classify real quadratic forms.

-To understand the concept of inner products, norms, distances, and convergence in abstract normed vector spaces.

-To find the Jordan canonical form for matrices.

-To solve linear systems of equations iteratively.

-To find numerically engenvalues.

**Tests and Final Exam: **There
will be two in-class one-hour tests and two take-home tests worth 100 points
each. Take-home tests are supposed to be completed *individually*. The
lowest of these test scores will be dropped. You can miss at most one test, and
that test will be considered to be the test with the lowest score to be
dropped. The final counts 200 points. No make-up for missing tests and final
exam.

**Extra Credits: **The
Department** **runs an applied mathematics
seminar on Mondays 4:00 PM-5:00 PM. There will be also a series of lectures
offered by distinguished visitors at the Department throughout the semester.
The Department will organize also a math competition for undergraduates on the
Math Day (March 30^{th}) with money prizes and trophy. You are
encouraged to attend these seminars and lectures, and participate in the
competition. Up to 50 bonus points will be given for the attendance (5 bonus
points for every seminar or lecture attended, and 5 bonus points for
participation in Math Day competition).

** **

**Important Dates: **2/1
: Test 1 (In-class), 7:00 PM Ð 8:00 PM

2/22 : Test 2 (Take-home) Due 5 PM, 2/26

3/15 : Test 3 (In-class), 7:00 PM Ð 8:00 PM

4/12 : Test 4 (Take-home) Due 5 PM, 4/16

5/3 : Final, 5:30 PM Ð 7:30 PM

Grading: The final letter grade
will be determined by the following scale:

A = 450-550, B = 400-<450, C
= 350-<400,
D = 300-<350, F =
below 300

**W Deadline: **March
1st is the last day to withdraw with grade W

** **

**Homework**: This is an
important part of the course. At the end of most classes you will be given a
list of problems Ð these are the minimum that you should work on. These
problems will not be graded. Some of these problems will be gone over in the
next class session and some will be included into the in-class tests. Practice
is important. I encourage you to use my office hours if you have any questions
about them. You should make sure to set aside some time every day to work
problems.

**Disabilities:** Students with
documented disabilities (through West GeorgiaÕs Disability Services) will be
given all reasonable accommodations. Students must take the
responsibility to make their disability known and request academic adjustments
or auxiliary aids. Adjustments needed in relation to test-taking must be
brought to the instructor's attention well in advance of the test (at least one
week prior).

Attendance Policy: You are expected to attend every class. Although absences
are not penalized, if a class is missed, you are responsible for all material
and assignments.

Academic Honesty: You
are expected to achieve and maintain the highest standards of academic honesty
and excellence as described in the Undergraduate Catalog. In short, be
responsible and do your own work.