General Syllabus Information

Course Name: Linear Algebra

Semester: Spring 2010

Instructor: Dr. Mariana Montiel

Direct phone: (404) 413-6414

e-mail: internal email (goml)

website for GOML:

Course Description:Theory and application of matrix algebra, vector spaces and linear transformations; topics include characteristic values, the spectral theorem, and orthogonality.

Goals and Objectives:

Students will be able to recognize a linear transformation and to find the kernel and range of a linear transformation.

Students will be able to compute the matrix representation of a linear transformation with respect to given bases.

Students will be able to derive properties of a linear transformation if a matrix representation of it is known.

Students will be able to find the transition matrix from a basis to another basis.

Students will be able to use the similarity between matrices representing the same linear operator from a vector space into itself under difference bases.

Students will be able to show that similar matrices share many common properties.

Students will be able to find the norm of a vector and the angle between two nonzero vectors using an inner product.

Students will be able to state, prove and apply the Cauchy-Schwarz Inequality.

Students will be able to find the distance between a point and a line (or plane) using orthogonal projection.

Students will be able to compute the orthogonal complement of a subspace.

Students will be able to prove and apply the Fundamental Subspace Theorem for matrices.

Students will be able to show and utilize the fact that an inner product space can be written as the direct sum of any subspace and its orthogonal complement.

Students will be able to find the least squares solutions to a linear system by solving the normal equations.

Students will be able to find the best least squares fit by a linear (or quadratic) function to given data.

Students will be able to recall some typical inner product spaces, such as the vector space of real continuous functions on a closed interval and the vector space of all polynomials in x of degree less than a fixed number.

Students will be able to compute various norms that can be defined in a vector space.

Students will be able to demonstrate that every orthogonal set of nonzero vectors is linearly independent.

Students will be able to use properties of orthonormal bases to compute the inner product of two vectors.

Students will be able to establish several conditions on a matrix Q each of which is equivalent to Q being an orthogonal matrix.

Students will be able to compute the orthogonal projection of a vector onto a subspace S if an orthonormal basis for S is known.

Students will be able to find the best least squares approximation to a given function on a closed interval [a, b] by a linear (or quadratic) function.

Students will be able to find the projection matrix onto a subspace of the Euclidean space of dimension n.

Students will be able to apply the Gram-Schmidt orthogonalization process to find an orthonormal basis for (a subspace of) an inner product space.

Students will be able to compute the QR factorization of a matrix

Students will be able to compute the eigenvalues and eigenvectors of a matrix (of small order).

Students will be familiar with some identities involving the product and sum of the eigenvalues of a matrix.

Students will be able to solve certain linear systems of differential equations using eigenvalues and eigenvectors of the coefficient matrix, or using the matrix exponential.

Students will be able to determine if a given matrix is diagonalizable.

Students will be able to find a matrix that diagonalizes a given diagonalizable matrix A and use this to compute a power of A and the matrix exponential of A.

Students will be able to define and compute complex inner products.

Students will be able to prove Schur’s (Upper Triangularization) Theorem.

Students will be able to show that the eigenvalues of a Hermitian matrix H are real and H is unitarily diagonalizable.

Students will be able to demonstrate that a matrix is normal if and only if it is unitarily diagonalizable.

Students will be able to determine if a real symmetric matrix (or a quadratic form) is positive definite, or positive semidefinite.

Students will be able to establish the equivalence of several conditions each of which is equivalent to the matrix A being positive definite.

Textbook Information: Text book: Linear Algebra with Applications, Eigth Edition, by Steven J. Leon 0321690206. It should be bundled with the student’s solution manual and the book of ATLAST exercises for Matlab

For this reason it is important for you to buy the book at the bookstore or make arrangements to have it shipped. If not, you will not have access to many of the Matlab assignments nor will you have the solutions manual. You can also look for information about the book at:

Communication Policies

Since we will be working with one another at a distance, it is important for us to have an efficient and effective means to communicate. I will be monitoring my email and the course site on a daily basis and will respond to questions as soon as possible. Please note the following email and phone meeting guidelines for this course.

Email will be returned within a 24 hour period. Over a weekend, allow 48 hours for a response.

Phone

Phone meetings can be arranged if needed. Contact me by email if you need to arrange a meeting.

Every student should open a v-room in Eluminate. We will have at least 3 group sessions during the semester, on weeks 5, 10 and 14. If the group feels the need for more sessions, we can arrange them.The sessions will be on Thursday at 7 pm each of these weeks, unless this is inconvenient for the majority of the group.

Grading Policy: The final course grade will be calculated from:

1)Three online tests, scheduled for the Saturdays February 13, March 20 and April 19, from 6-9 pm. Each one counts 15%.

2)Matlab assignments: 15%

3)Participation in the forum, posting first or alternate solutions to problems, internet search assignments: 15%

4)Final exam: 25%. The final exam will be proctored. You should make your arrangements for the final as soon as possible. At the end of this syllabus you will find a list of testing sites. Please let me know by the first week of March at which site you will be testing. The final will be comprehensive and the dates are April 28-30. You must pass the final (at least 70%) to pass the course.

98 - 100 = A+

93 - 97 = A

90 - 92 = A-

87 - 90 = B+

83 - 87 = B

80 - 82 = B-

77 - 79 = C+

70 - 76 = C

60 - 69 = D

0 - 59 = F

Activities and Assignments:

On a weekly basis we will have our activities and assignments organized around:

Read and Watch. There will be assigned reading from the textbook. There will also be presentations with the tablet some weeks. The choice of content will be made on past experience of the areas that seem to need reinforcement and detailed explanation.

Assignments.There will be assigned textbook exercises. The textbook exercises will not be graded, but the successful student is one who devotes regular time and effort to working on the assigned problems. The three exams and the final will come from the reading and exercise material, as well as the tablet presentations (although the tablet presentations are just supposed to reinforce the material covered in the reading and exercises, not to introduce new material). Only the problems from the first week’s review will not be explicitly included in the exams, but a working knowledge of the material is necessary for the content of the course.

There will also be assigned Matlab exercises, either from the textbook or from the ATLAST book bundled with your text. These are to be turned in. Ideally they would be turned in the week they are assigned, but they will be accepted up until the review week before each of the three online tests. That is, the first group of Matlab assignments, from weeks 1-4, must be turned in by week 5, the second group, from weeks 6-9, by week 10 and the third group from weeks 11-13, by week 14.

The Matlab assignments are self-contained, and do not require any previous knowledge of Matlab or programming. Matlab is being employed as a learning tool; if the material is understood there should be no procedure problems with Matlab, but if students have a problem with the conceptual content of the course, the Matlab exercises will make this evident and will permit us to work on these aspects.

Forum and Internet Search Assignment. Feel free to share your answers and work together. Those who want to post the first answer to a problem, or an alternative answer to a problem already posted, will have it taken into account for participation credit.

Each week students will also be asked to do a Google search for specific concepts and share with the class at least one definition or explanations, and its source, that complements the material in the book.

Recommended Supplements. This material is not mandatory, but it is recommended as a complement. The material consists, fundamentally, of online textbooks, notes, interactive tutorials and video-lectures (in particular, the MIT series). There are some differences in terminology and notation in the different texts. As this is very common, even amongst high school algebra, geometry, precalculus and calculus textbooks, it is very good practice for real life issues in teaching mathematics at any level, or reading articles on mathematics and mathematics education.

Technical Support for Georgia On My Line Courses

All technical questions should be directed to the GeorgiaVIEW Online Support Center at

GeorgiaState Policy on Academic Honesty: Copied exam papers will not be accepted and will receive a grade of zero. See the University's policy on

Academic Honesty:

Testing Center Information Form for Students

Directions: You will need to contact the nearest USG testing location to schedule a proctored exam for this course. When contacting the testing center, make sure you collect information for ALL of the questions below. Complete this form and email it back to your instructor. It is the student’s responsibility to verify the testing appointment time, location and cost.

1. Please provide the name, address and phone number for the testing center.

2. Please provide the name of the person you spoke with at the testing center.

3. What information does the instructor need to send to the testing center?

4. How can the instructor send this information? Email? Fax? Regular Mail?

5. Does the instructor need to speak with someone at the testing location to confirm the scheduled test? If yes, please include the name and contact information for that person.

6. Will the instructor receive a copy of the completed exam? If so, how?

7. Are there any other policies or procedures specific to this testing center that we need to be aware of?

University System of Georgia Official Test Sites

UNIVERSITIES
Albany
Albany State University
912-430-4667
Americus
Georgia Southwestern State University
912-928-1331
Athens
The University of Georgia
706-542-3183
Atlanta
Georgia Institute of Technology
404-894-2575
Georgia State University
404-651-2217
Augusta
Medical College of Georgia
706-721-2787
(Test Site available for MCG students only.)
Augusta State University
706-737-1471
Carrollton
University of West Georgia
770-836-6435
Columbus
Columbus State University
706-568-2226
Dahlonega
North Ga College and State Univ
706-864-1799
Fort Valley
Fort Valley State University
912-825-6384
Marietta
Kennesaw State University
770-423-6600
Southern Polytechnic State University
No test site
Milledgeville
Georgia College and State University
912-445-5016
Morrow
Clayton State College
770-961-3445
Savannah
Armstrong Atlantic State University
912-927-5271
Savannah State University
912-353-3105
Statesboro
Georgia Southern University
912-681-5415
Valdosta
Valdosta State University 912-245-3878 / TWO-YEAR COLLEGES
Albany
Darton College
912-430-6738
Atlanta
Atlanta Metropolitan College
404-756-4055
Bainbridge
Bainbridge College
912-248-2560
Barnesville
Gordon College
770-358-5021
Brunswick
Coastal Georgia Community College
912-264-7220
Cochran
Middle Georgia College
912-934-3092
Dalton
Dalton College
706-294-3634
Decatur
Georgia Perimeter College
(678) 891-2755
Douglas
South Georgia College
912-383-4244
Dunwoody
Georgia Perimeter College
(770) 274-5440.
Gainesville
Gainesville College
770-718-3863
Macon
Macon State College
912-471-2714
Rome
Floyd College
706-295-6371
Swainsboro
East Georgia College
912-237-7831
Tifton
Abraham Baldwin Agricultural College
912-386-3231
Waycross
Waycross College
912-285-6012