Please feel free to come by my office any time during scheduled
You are welcome to
come at other times, but in that case you might want to make
an appointment, just to make sure that I will be there then. You can
make an appointment simply by talking to me before or after class, by
calling me at
or at home, or by sending
You may also ask any questions directly via phone or e-mail. If I'm
not in when you call, please leave a message on the voice-mail or
answering machine with your name, number, and a good time for me to
call you back. I will try to respond to your phone or e-mail message
as soon as possible.
This course is concerned with matrices and vectors. In one setting,
matrices and vectors merely serve as efficient devices for storing
the coefficients and solutions of systems of linear equations. The
solutions of many such systems, though, are hard to even describe
without the right language. This is the language of vector spaces, where
matrices serve as functions turning vectors into other vectors. We will
then spend most of our time examining vector spaces, and especially
various vector spaces we can naturally assign to a matrix. In this setting,
eigenvalues and eigenvectors of a matrix arise naturally, and we end the
course examining these.
Upon successful completion of this course, you will be able to solve
and analyze systems of linear equations. You will be able to find and
describe the various vector spaces associated to a matrix, and you will be
prepared to study more abstract vector spaces. You will be able to compute
eigenvalues and eigenvectors of a matrix, and know
what they are good for. You will be able to do all of this equally well
with the symbolic/numerical description of matrices and vectors as
arrays of numbers, and with the geometrical description of matrices and
vectors, using the powerful organizing concept of dimension, even in dimensions
higher than 3.
You will improve your skills of investigating and describing mathematical
Introduction to Linear Algebra, 5th ed.,
Johnson, Riess, Arnold, Chs. 1-4.
We will skip some sections, as announced in class.
The textbook is required at all class meetings.
Read each section that we cover in class, both before and after class.
Skim the section before class, even if you don't understand it fully,
to have some idea of what we'll be doing in class. Read it more
carefully after class to clarify and fill in details you missed in
Sometimes, I will not "cover" all the material from a section, but
instead focus on a particular aspect of the section. In such cases, I
will point out in class (and at this
website) which other
parts of the section I expect you to read on your own.
- Quizzes (10%):
Suggested homework problems will be assigned
most class days and will generally be discussed at the next class.
There will be approximately biweekly quizzes, with problems taken from
the homework. Quizzes are closed-book, closed-notes. Missed quizzes
cannot be made up, but your lowest quiz score will be
It is very important that you do your homework before it is discussed
in class. You will only learn the material by doing it yourself, not
by watching others do it for you.
- Investigations (10%):
There will be a series of investigations
available here, where you will get to explore concepts
a little more in depth, using WebMathemtica. Each investigation will
have guiding questions to help you with the computer experiments.
Afterwards, you will write a short report describing your findings. You
will have about 1-2 weeks for each investigation. You are allowed to work
together on investigations (in fact, I encourage you to do so), but the
report you turn in you must write yourself.
- Exams (15% each):
There will be three in-class exams on the following days:
Makeup exams can be given only in extraordinary and unavoidable
circumstances, and with advance notice. (See also "Exception"
- Ch. 1: Thu. 27 Sep.
- Chs. 2, 3: Thu. 8 Nov.
- Ch. 4: Tue. 4 Dec.
- Final (35%)
Thu. 13 Dec., 4:00 p.m.-6:45 p.m.
- Your final exam score will be used in place of your lowest
in-class exam score, if this increases your overall class average. In
particular, if you miss a test, your final exam score will replace it.
I strongly encourage you to attend every class, though there is no
particular grade penalty for absences. My goal is for class meetings and
activities to complement, rather than echo, the textbook, and thus for
every class to be worth attending.
The deadline for student-initiated drops with a W is Fri., 2 Nov. After
this date, you can only drop with the Dean's approval, which is granted
only under extenuating circumstances.
I hope everyone will complete the course successfully, but if you are
having doubts about your progress, I will be happy to discuss your
standing in the course to help you decide whether or not to drop.
You are only allowed three enrollments in this
course, and new freshmen are only allowed six withdrawals in their
entire academic career, so please exercise the drop option judiciously.