MATH 706

 

Numerical Linear Algebra

Spring 2009

 

 

Meeting times: MWF  1:25 - 2:15 PM  at  LeConte (LC) 303B.

 

Instructor: Dr. Peter G. Binev        http://www.math.sc.edu/~binev/

e-mail:    binev@math.sc.edu)

phones:   576-6269 (at LC 425)   or   576-6304 (at SUM 206H)

Office hours:  MWF  11:00 - 12:00 AM  and MW  2:20 - 2:50 PM  at LeConte 425/Sumwalt 206, or by appointment.

 

 

Text: Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, Sixth Edition, Paperback - SIAM, 1997. The course will cover the entire material considered in the book.

 

Description: Numerical Linear Algebra studies the practical algorithmic ideas which every mathematical scientist needs to work effectively with vectors and matrices. Its knowledge is a step towards achieving the necessary qualification for the best profession (according to JobRated.com and Wall Street Journal from January 6, 2009,) which is described as follows: Applies mathematical theories and formulas to teach or solve problems in a business, educational, or industrial climate. The course will give an introduction to general ideas in Numerical Linear Algebra and will discuss different aspects of the performance of the numerical procedures involved. In addition to the theoretical material, some numerical implementations in MATLAB will be considered on an elementary level. Topics include (not necessarily in the order they will be considered): orthogonality, norms, orthogonal and affine projections, Singular Value Decomposition (SVD), matrix factorizations, finite precision arithmetic, stability, least squares, systems of equations, direct and iterative methods, pre-conditioning, eigenvalue/eigenvector problems, and conjugate gradient methods. Both theoretical development of concepts and constructive methods realized in terms of practical algorithm implementation are considered.

 

Prerequisites: MATH 700.

 

Learning Outcomes: At the end of this course students will be able to read, interpret, and use vocabulary, symbolism, and basic definitions from Numerical Linear Algebra. The students will be able to develop and/or use facts, formulas, and techniques learned in this course to apply algorithms and theorems to find numerical solutions, analyze stability and theoretically bound their errors to various types of problems including singular value decomposition, matrix factorizations, direct and iterative methods, pre-conditioning, eigenvalue / eigenvector problems, and conjugate gradient methods.

 

Attendance: Regular class attendance is important. A grade penalty will be applied to any student missing five or more classes (10%) during the semester. The "10 percent rule" stated above applies to both excused and unexcused absences. Students who anticipate potential excessive absences due to participation in permissible events as described in the USC Academic Bulletins (http://www.sc.edu/bulletin/ugrad/acadregs.html#class atten.) should receive prior approval from the instructor to potentially avoid such penalty.

 

Cell Phones: All cell phones must be turned off during the class.

 

Homework: A few homework problems will be assigned each class. Be sure to solve and write these problems before the next class. Some solutions will be collected (with or without preliminary notice).

 

Projects: Every student has to choose a project motivated by the computational or theoretical problems discussed in the course. Several possible themes for the projects will be suggested by the instructor in the length of the course. The project in a form of a poster, slides, or a short paper should be submitted on or before April 20, 2009.

 

Presentations: The students should also prepare a 15-minute oral presentation about their projects during the class on April 22, 2009.

 

Discussions: The homework and the projects will be discussed in class. The participation in the discussions will be taken into account as part of the homework grade.

 

Midterm Exam: There will be a midterm exam in a form of a test. The tentative date of the exam is February 16, 2009. The problems on the test will be similar to the ones from the homework and the discussions in class.

 

Final Exam: The final exam in a form of a test will take place on Monday, May 4 at 2:00 PM.

 

Grading: The final grade will be determined from the homework (30%), the midterm exam (20%), the project (20%), and the final (30%).

 

Academic Dishonesty: Cheating and plagiarism will not be allowed. The University of South Carolina has clearly articulated its policy governing academic integrity and students are encouraged to carefully review the policy on the Honor Code in the Carolina Community (see http://www.jour.sc.edu/pages/academicintegrity/policies.html).

 

ADA: If you have special needs as addressed by the Americans with Disabilities Act and need any assistance, please notify the instructor immediately.

 

Important Dates:

                                    January 16 Last  day to drop without W

                                    February 16 Midterm Exam

                                    February 23 Last  day to drop without WF

                                    April 4/5 33rd SIAM Southeastern-Atlantic Section Conference

                                    April 20 Deadline to submit the projects

                                    April 22 Project Presentations

                                    May 4 Final Exam at 2:00 PM