Math 630  Numerical Linear Algebra
Spring 2014  Matthias K. Gobbert
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@umbc.edu,
office hours: TuTh 03:0003:50 or by appointment
 Classes: SOND 114, TuTh 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 the following books are on reserve in the library.
These books are highly recommended as reference, but are not required.
The intention is to cover the material of the course sufficiently well
by the lectures, possibly complemented by specific reading assignments,
for which you can use the reserve copies in the library.

Recommended textbook:
David S. Watkins,
Fundamentals of Matrix Computations,
third edition, Wiley, 2010.
Webpage of books by the author
including list of errors.
 Also the second edition from 2002 of the textbook is usable.
The third edition inserted a new chapter,
so Chapter 8 in the third edition used to be Chapter 7 in the second one.
A new section was also inserted into that chapter,
but titles clearly identify the sections.

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 and Quizzes
 Participation
 Midterm Exam
 Final Exam
 Project

20%
 10%
 30%
 30%
 10%


The homework is weighted so heavily, because it includes
the computer assignments that are vital to understanding
the course material.
A late assignment accrues a deduction of
up to 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 quizzes will generally be unannounced and brief and
will include the use of learning groups formed by the instructor.
For instance, they may be designed to initiate class discussion
or to give me feedback on your learning.
They may be technical or nontechnical in nature.

The graded participation component rewards
your professional behavior and active involvement
in all aspects of the course.
Examples of expected professional behavior include
attending class regularly,
reading assigned material when requested,
cooperating with formal issues such as
submitting requested material on time, and
participating constructively in class, specifically in group work.

The midterm and final exams are traditional
inclass 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.

The project is designed to give you exposure to the
tasks of creating a professionalgrade report in Mathematics.
The default topic of the project will be a comparison of numerical
methods from various homework during the first half of the semester.
If you want to propose a different topic, contact me.
Additional details or changes will be announced as necessary.
See also general policies and procedures
for more information.

Blackboard
is a course management system that allows for posting
and communicating among registered participants of a course.
We will actively only use the "Course Documents" area
of our course in Blackboard.
I will post class summaries and PDF files of the lecture notes
as well as other material including the homework assignments in this area.
I will also use Blackboard to send email to the class,
which goes to your UMBC account by default.
Therefore, you must either check your UMBC email regularly
or have the mail forwarded to an account that you check frequently.
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.
Learning Goals
By the end of this course, you should:

understand and remember the key ideas, concepts, definitions,
and theorems of the subject.
Examples include computational algorithms, sources of error,
convergence theorems, and implementations of these algorithms.
More broadly, you should also understand the purpose of
numerical linear algebra.
> This information will be discussed in the lecture.
You will apply and use them on homeworks, quizzes, and tests.

have experience using a professional software package,
writing code in it, and understanding how some of its functions work.
We will focus on the package Matlab in this course,
which is the most popular package in mathematics and many application areas.
Writing code in this context includes the requirements to deliver code
in a form required, such as writing code to stated specifications,
using a requested method, complying with a required function header, etc.
The knowledge and skills in this item are valuable job skills,
which justifies the emphasis here.
> This is one of the purposes of the homework and most
learning will take place here.

have some foundational experience in writing professionalgrade reports
in Mathematics.
This is explained more in the syllabus portion on
How to Report on Computer Results.
> This is included in the homeworks and is also
one of the reasons for offering a project option.

have experience working actively with peers in a group,
both on the scale of the class and in a smaller team.
Group work requiring communication for effective collaboration
with peers and supervisors is a vital professional skill,
and the development of professional skills including this networking
is a declared learning goal of this course.
Additionally, getting to know other students as part of learning groups
will prove invaluable for homework and tests.
> The groups will be assigned by the instructor and used
for group quizzes in class. Their formal evaluation is
included in the participation category of the grading policy.
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,
the
UMBC Undergraduate Student Academic Conduct Policy
(PDF)
for undergraduate students,
or the
University of Maryland Graduate School, Baltimore (UMGSB)
Policy and Procedures for Student Academic Misconduct
(PDF)
for graduate students.
Copyright © 19992014 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.1, January 2014.