Math 665 Numerical Linear Algebra (Topics in Grad. Math.)

Spring 2013, UAF

Instructor: Ed Bueler
Office: Chapman 301C.  Office hours online.
Phone: 474-7693
eMail: elbueler@alaska.edu 		Class Time:  MWF 1:00 - 2:00pm,  Reichardt 204
CRN: 39623
Text: Trefethen & Bau, Numerical Linear Algebra, SIAM Press

Course Web Site: www.dms.uaf.edu/~bueler/Math665S13.htm

Course Content and Goals: This course will describe how actual matrices and vectors can be handled in a stable, fast, and accurate manner.  This is key technology for scientific and engineering computation.  We will place these topics in the correct framework, emphasizing the geometry of the action of matrices.  We will cover some famous matrix decompositions, theorems, and algorithms: singular value decomposition (SVD), LU decomposition, spectral theorem, Schur decomposition, the QR method for eigenvalues, and Krylov methods.  Applications of these ideas include solving large linear systems, solving systems of ordinary differential equations, statistical methods, inverse methods in geophysics, and Markov processes.  Numerical linear algebra is key for numerically solving partial differential equations and many large graph problems.

Examples in class will often use Matlab/Octave.  (Or python---scipy/pylab---for students who are already comfortable with python.)  I will help students learn how to use one of these tools, all of which are well-suited to numerical linear algebra.  Student competence with such a language, for scientific computing though not necessarily general programming, is a goal of the course.

Topic list: Outcomes:  At the end of this course you will be able to understand and apply the ideas and algorithms of numerical linear algebra.  You will be very comfortable with Matlab or a similar language.

Assigned Work and Evaluation and Grade:  Weekly homework will include by-hand computations, proofs, and Matlab/Octave computations.  There will be a short project in which you are asked to find and explain/explore an application of numerical linear algebra.  There will be a one hour in-class midterm exam, emphasizing definitions and basic manipulations, and a take-home final exam emphasizing proofs and nontrivial calculations/applications.

Exams/Homework
In class Midterm Exam
Take home Final Exam
Homework
Short Project
 Percent of Grade
15%
25%
55%
5%
 Dates
Monday 25 March, in class
Due in my box 5:00 p.m., Wednesday, May 8.
nearly weekly
due about one week before final; will be announced

Based on your raw homework and exam scores, I guarantee grades according to the following schedule: 90 - 100 % = A, 79 - 89 % = B, 68 - 78 % = C, 57 - 67 % = D, 0 - 56 % = F.  I reserve the right to increase your grade above this schedule based on the actual difficulty of the work and on average class performance.

Policies:   The Dept of Mathematics and Statistics has reasonable policies on incompletes, late withdrawals, early final examinations, etc.; see www.dms.uaf.edu/dms/Policies.html.  You are covered by the UAF Student Code of Conduct.  I will work with the Office of Disabilities Services (208 WHIT, 474-5655) to provide reasonable accommodation to student with disabilities.

Prerequisites:    Undergraduate linear algebra and mathematical maturity.  Concretely, MATH 314 Linear Algebra or equivalent. Recommended: MATH 421 Applied Analysis OR MATH 401 Introduction to Real Analysis OR equivalent post-calculus course in analysis.