Math 630 - Numerical Linear Algebra
Spring 2021 - Syllabus - Matthias K. Gobbert
This page can be reached via my homepage at
http://www.umbc.edu/~gobbert.
Basic Information
- Instructor: Matthias K. Gobbert, gobbert@umbc.edu,
office hours by e-mail and online appointment.
Dr. Gobbert has accumulated extensive experience in teaching
with state-of-the-art technology.
Since participating in the
first cohort in the Alternative Delivery Program (ADP) in 2006,
he uses hand-writing on tablet laptops for all lectures.
These lectures are taped and hosted online for streaming,
with the added benefits of allowing for pausing, rewinding, and reviewing.
Using the taped lectures for contents delivery,
Dr. Gobbert uses a team-based active-learning teaching model,
in which students work on problems in learning groups during class.
Since 2019, his classes use online comprehension quizzes on the lectures
and fully online submission of all assignments, complete with online grading.
Since starting online teaching full-time in 2020,
the synchronous class meetings are used additionally for
student presentations to maximize active student engagement.
In 2010, Dr. Gobbert received the
University System of Maryland Board of Regents'
Faculty Award for Excellence in Mentoring.
- This syllabus consists of this frontpage and the sub-pages
- Classes: online, TuTh 04:00-05:15;
please see the detailed schedule
for more information.
This course will be taught in a flipped classroom format. This means
that the contents is delivered asynchronously online by taped videos of
my lectures that you study before our synchronous online class meetings.
The synchronous online class meetings will
use a team-based active-learning teaching model, in which
students work on problems in learning groups formed by the instructor
with the help of the instructor.
Learning groups:
I will form learning groups of two to four students.
These groups will be set up in Blackboard to facilitate the
submission of the in-class group quizzes.
These groups are strongly encouraged
to also communicate outside of class.
Synchronous class meetings:
Our synchronous class meetings are an opportunity for
active teamwork with your learning group,
while the instructor is available immediately for questions.
These meetings will take place in Blackboard Collaborate,
which is included with Blackboard, see below and note on recordings.
We will also have presentations by students on their homework solutions
in the synchronous class meetings.
This and the other strategies above are designed to
foster student engagement as well as give you chances
to participate more actively, get to know each other better,
have a demonstrated record of using the tools of online learning,
and more.
If you have any concerns about any of these items,
such as concerns about adequate internet connection,
about team work, or special needs related to learning styles,
please reach out to me as soon as possible,
so I can clarify questions and/or
we can work out alternate appropriate approaches and metrics.
My goal is definitely that anyone can participate successfully
in this course, even if you might need to do it completely
asynchronously, but we need to communicate about this.
- Prerequisites: a grade of C or better in Math 221, Math 301,
familiarity with a high-level programming language,
or permission of instructor.
Math 430 recommended.
- 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,
that I will post online.
-
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/Octave:
Desmond J. Higham and Nicholas J. Higham,
Matlab Guide, third edition, SIAM, 2017.
Associated webpage:
http://www.maths.manchester.ac.uk/~higham/mg/index.php
including list of errors.
Matlab's documentation is excellent, but along with its functionality
has reached a scale that requires a lot of sophistication to fully
understand. Moreover, there is a definite role for a book that
is organized by chapter on topics such as all types of functions
(inline, anonymous, etc.), efficient Matlab programming
(vectorization, pre-allocation, etc.), Tips and Tricks, and more.
- Grading rule:
Quizzes
| Homeworks
| Midterm Exam
| Final Exam
| Project Report
|
20%
| 20%
| 20%
| 20%
| 20%
|
-
The online quizzes
are administered in the course management system Blackboard,
see below, and are due before class.
The detailed schedule indicates
the planned due dates of these online quizzes,
but the Blackboard assignments list the official due dates and times.
There will also be in-class quizzes
using 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 non-technical in nature.
An individual Quiz 0 will be given before the first day
of the semester on some material that is critical to
your success in this class.
The overall quiz score will eventually be appended by components
that score the complete watching of the taped lectures,
the active participation in team work,
the participation in synchronous class meetings,
and
adequate professional behavior in all aspects of the course,
such as communicating with the instructor, team mates,
respectful behavior in communications,
and timely submission of work, for instance.
-
The homework assignments will be posted in
the Blackboard site of our course, see below.
The detailed schedule indicates
the planned due date of each homework,
but the Blackboard assignments list the official due dates and times.
Working the homework is vital to understanding the course material,
and you are expected to work all problems.
In the flipped classroom format of this course,
we will work on the homework
about the associated taped lectures on that topic in class.
You should then complete the homework afterwards,
and it is then due before the start of the next topic.
The homeworks are weighted so heavily,
because they include the computer assignments
that are vital to the computational focus of this course.
Homework submission is online as one PDF file
in the Assignments area of our Blackboard site.
Late submission of homeworks, except Homework 0,
cannot be accepted under any circumstances.
If homework is accepted late, it 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.
Homework 0 is required of all students and is accepted late.
-
The midterm and final exams
will be held in Blackboard with online submission
as one PDF file, just like homework.
To help you focus on what is relevant,
they are closed-book and closed-notes, but
you should have a scientific calculator.
See the detailed schedule for the dates
of the exams.
-
It is increasingly important
at this point in your education to learn
how to work on a larger project on your own
(with guidance by the instructor)
and to present your results in the form of a
professional-grade type-set report.
To allow interested students to develop the necessary skills,
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 rules and procedures
for more information.
Announcements may be made in class, by e-mail, or in Blackboard.
You are responsible for checking
your UMBC e-mail address sufficiently frequently.
-
We will use the course management system
Blackboard Ultra
for posting of all material
(including homework, lesson plans, PDF transcripts, handouts),
for links (to tapings of lectures),
for submission of homeworks, quizzes, and exams,
and
for the synchronous online class meetings using Blackboard Collaborate.
All meetings will be taped and will be available in Blackboard;
see full note on recordings below.
Notice that Blackboard Ultra is the new version of Blackboard
that is more mobile friendly.
The main navigation buttons are arranged along the top of the screen,
with Course Content, Gradebook, and Messages the ones we will use.
The link to Blackboard Collaborate is on the left of the screen,
and its recordings will appear a while after class
by following the three dots "..." to View all recordings.
I will also use Blackboard to send messages and e-mails to the class,
which goes to your UMBC account by default.
Therefore, you must either check your UMBC e-mail regularly
or have the mail forwarded to an account that you check frequently.
Do not use Blackboard to message me,
since I may not find it in a timely fashion;
rather use conventional e-mail to my UMBC address listed above.
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 hand-calculations 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
least-squares 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.
This course will also include computational work to gain practical
experience with the numerical methods discussed.
I recommend the professional software package
Matlab or
equivalently the free and nearly fully compatible package
Octave
as platform of choice, because they are very popular packages
and knowing them thoroughly is itself a marketable skill.
For both packages,
you can read its expansive and well-written documentation or
you may consider the book recommended above.
For hands-on training in Matlab and Octave,
you can consider the 2-credit class Math 426 on Matlab or
for a brief initial overview the software workshops
offered by CIRC.
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 analysis.
--> 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 professional-grade reports
in Mathematics.
This is explained more in the syllabus portion on
How to Report on Computer Results.
--> This is included in the homeworks.
-
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.
--> Group discussions and quizzes will contribute to this goal.
Other Information
Note on Recordings and Their Publication
This class is being audio-visually recorded so students who cannot attend
a particular session and wish to review material can access the full content.
This recording will include students' images, profile images, and
spoken words, if their camera is engaged and their microphone is live.
Students who do not consent to have their profile or video image recorded
should keep their camera off and not use a profile image.
Likewise, students who do not consent to have their voice recorded should
keep their mute button activated and participate exclusively through
alternative formats such as email or the chat feature (where available).
UMBC Statement of Values for Academic Integrity
Academic integrity is an important value at UMBC.
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.
Consult the the UMBC webpage on Academic Integtrity at
academicconduct.umbc.edu
for the
UMBC Undergraduate Student Academic Conduct Policy
for undergraduate students
and the
UMBC Graduate School's Policy and Procedures for Student Academic Misconduct
for graduate students.
Copyright © 1999-2021 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.0, December 2020.