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.
Upon successful completion of the course,
you will be able to prove (and occasionally discover) theorems in
linear algebra, at the level of abstraction of linear transformations
and vector spaces. You will know, understand, and be able to apply,
prove, and explain major results in this area. You will be better
able to independently read advanced mathematics.
In contrast to Matrix Algebra (Math 3323), we will be
focusing on proofs and theory instead of applications (though theory
lies closer to applications in linear algebra than it does in, say,
analysis), vector spaces instead of R^n, and linear transformations
instead of matrices. Otherwise, many topics will look familiar.
Linear Algebra Done Right, 2nd ed., Sheldon
Axler, Chs. 1-8.
We will generally spend one class period per
``section'' (see Table of Contents), though parts of Chs.\ 1, 2, and 4
should be review, and we will go a little faster through these.
You will spend a substantial amount of time outside of class reading
the textbook. The course will be structured to encourage and support
you in this endeavor. In-class activities will center around our
making use of what you have read outside of class.
Homework and Participation:
- Advance preparation (20%):
You will read the section
carefully, write responses to reading questions, create some of your
own questions, and reflect. The written part of this assignment will
be due the class period before we discuss the material in class.
- Warmup exercises (10%):
On the day of our class
discussion over the material, we will discuss easier warmup exercises.
You will prepare your answers, in writing, before class, and the class
will share answers in small groups or whole class discussions.
I expect everyone to attend and participate actively in class, in
particular to speak up during class discussion with questions and
ideas, and to work well with others. Your active participation in
class will constitute a substantial part of this part of your grade
for the course.
- Main exercises (30%):
After our class discussion over
the material, you will turn in clearly-written solutions to harder
homework problems. These will generally be due weekly.
Graduate students taking this class will be assigned additional
main exercises, in accordance with university policy.
Written assignments (for all three kinds of homework) will not be
accepted after they are due, except in extenuating circumstances that
you explain to me as soon as possible. Incomplete homeworks will be
accepted, though, so please turn in whatever work you have completed
when homework is due. You are encouraged to work together on your
homework, but you must write up your solutions by yourself.
- Midterm (15%):
The midterm will cover all material we have discussed to that point,
and will be on
Thu., 9 Mar.
- Final (25%)
- The final exam will be comprehensive over all material we discuss in class. The final will be on
Thu., 11 May, 4:00-6:45 p.m.
Makeup tests can be given only in extraordinary and unavoidable
circumstances, and with advance notice.
Due to the course structure, attendance is mandatory. There is no
particular penalty for missing a particular class, but you cannot get
a good participation grade if you miss too many classes. I will
usually "excuse" an absence if you tell me about it in advance, or, in
cases of emergencies, as soon as possible afterwards.
The deadline for student-initiated drops with a W is Fri., 24 Mar. 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.
This course is not likely to be offered again in the near future,
so please exercise the drop option judiciously.