Math 630  Matrix Analysis
Spring 2007  Matthias K. Gobbert
Section 0101  Schedule Number 3826
This page can be reached via my homepage at
http://www.math.umbc.edu/~gobbert.
Basic Information
 Matthias K. Gobbert,
Math/Psyc 416, (410) 4552404, gobbert@math.umbc.edu,
office hours: MW 03:0004:00 or by appointment
 Classes: ITE 241, MW 04:0005:15;
see the detailed schedule for more information
 Prerequisites: a grade of C or better in Math 221, Math 301,
familiarity with a highlevel programming language,
or permission of instructor.
Math 430 recommended.
 Copies of all following books are on reserve in the library.

Required textbook:
David S. Watkins,
Fundamentals of Matrix Computations,
second edition, Wiley, 2002.
Webpage of the book
including list of errors.

Recommended book on Matlab:
Desmond J. Higham and Nicholas J. Higham,
Matlab Guide, second edition, SIAM, 2005.
Webpage of the book
including list of errors.
 Grading policy:
Homework
 Group quizzes
 Participation
 Midterm
 Project
 Final

30%
 5%
 5%
 20%
 10%
 30%

In addition to any formally graded course components,
your professional behavior and active participation in all aspects
of the course are required.
In particular, you are required to read assigned sections
in the textbook ahead of their coverage in class.
See the learning goals
for more information on how all the components of the course
are integrated.

The homework includes the computer assignments that are
vital to understanding the course material.
A late assignment accrues a deduction of 10% of the possible score
for each day late until my receiving it;
I reserve the right to exclude any problem from scoring
on late homework, for instance, if we discuss it in class.

The group quizzes are administered in class and take
the form of group discussions; these learning groups will be
assigned by the instructor at the beginning of the semester.

The participation score acknowledges your
professional behavior and your active participation
in all aspects of the course,
in particular in components of the course that are not otherwise graded,
such as the work in your learning group, active participation in class,
timely submission of the class summaries,
and posting on the Blackboard Discussion Board.

The project is designed to give you exposure to the
tasks of creating a professionalgrade report in Mathematics,
the process of editing, and
working with others to give and receive feedback.
The default topic of the project will be a comparison of numerical methods
from various homework during the first half of the semester.

The midterm and final
are traditional inclass exams and designed to help prepare you
for the comprehensive exams.
To help you focus on what is relevant,
they are closedbook and closednotes, but
you should bring a scientific calculator.
See the detailed schedule for the dates
of the exams.
Additional details or changes will be announced as necessary.
Announcements may be made in class or by email.
You are responsible for checking your UMBC email address
sufficiently frequently to stay abreast of announcements.

Blackboard
is a course management system that allows for posting
and communicating among registered participants of a course.
To log in, I suggest to go to myUMBC
and then use the Blackboard link on the left.
Then look for this course under "My Courses".
We will actively only use the following areas in Blackboard:
 Under "Course Documents", I will post the class summaries,
taped lectures and workedout examples, and any other material as needed.
 Under "Communication", we will use the Discussion Board for
online discussions of questions on homework or any other class material.
I will check the Board normally at least once a day,
but to increase the speed to get answers, I encourage all of
you to answer each others' questions, too.
Participation in the Discussion Board is part of the participation score.
In particular, the Discussion Board will be available and I will
check it very frequently on the day preceeding each test.
 I may also use Blackboard to send email to the class.
Therefore, you must either check your UMBC email regularly
or have the mail forwarded to an account that you check frequently.
We will demonstrate and discuss the use of Blackboard
during the first class.
Course Description
This course encompasses basic theory of matrices and
numerical methods for computations with matrices
including both their theory and implementation in a computer.
One prototypical example of a problem in linear algebra concerns
the solution of a system of simultaneous linear equations.
Gaussian elimination (also known as reduction to row echelon form)
is the traditional computational technique
for its solution, both in handcalculations and in a computer.
Using it as an example, we will learn what might be necessary
to make a computational technique reliable and efficient in a computer
and what analytical results can be developed for a numerical method.
To analyze the problems and numerical methods,
we will introduce basic tools including vector and matrix norms.
Gaussian elimination is an example of a direct method
(that produces the solution in a predetermined number of steps).
We will also consider iterative methods
(that find successively better approximations to solution
as more steps are taken) and their advantages and drawbacks.
In addition to system of linear equations, we will study
leastsquares and eigenvalue problems,
and various numerical methods to solve them.
Their analysis will require a review of various facts about matrices
including the theory of eigenvalues and the singular value decomposition
as well as the development of a number of other computational techniques.
We will involve the professional software package
Matlab in several ways:
We will use it to extend handcalculations to larger examples,
its scripting language will serve as a programming environment for our own code,
and we will spend time understanding how some of the numerical methods
discussed in class are implemented in Matlab's functions.
Other Information
UMBC Academic Integrity Policy
By enrolling in this course, each student assumes the responsibilities of
an active participant in UMBC's scholarly community in which everyone's
academic work and behavior are held to the highest standards of honesty.
Cheating, fabrication, plagiarism, and helping others to commit these acts
are all forms of academic dishonesty, and they are wrong.
Academic misconduct could result in disciplinary action that may include,
but is not limited to, suspension or dismissal.
To read the full Student Academic Conduct Policy, consult the
UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity
webpage www.umbc.edu/integrity,
or the Graduate School website
www.umbc.edu/gradschool.
Copyright © 19992007 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.0, January 2007.