Spring Semester 2006-2007
MATH 5523: Linear Algebra II
Instructor: Dr. Vu Kim Tuan
Time & Location: Thursdays, 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.
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. Cimmino’s 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 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. You are encouraged to attend these seminars and lectures. Up to 50 bonus points will be given for the attendance (5 bonus points for every seminar or lecture attended).
Important Dates: 2/1 : Test 1 (In-class), 7:00 PM – 8:00 PM
2/22 : Test 2 (Take-home) Due 5 PM, 2/26
3/15 : Test 3 (In-class), 7:00 PM – 8:00 PM
4/12 : Test 4 (Take-home) Due 5 PM, 4/16
5/3 : Final, 5:30 PM – 7:30 PM
Grading: The final letter grade will be determined by the following scale:
A = 450-550, B = 400-<450, C = 350-<400, F = below 350
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 – 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 Georgia’s 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 Graduate Catalog. In short, be responsible and do your own work.