Welcome to Math H110A, Honors Linear Algebra! I am designing this course for a look beyond the formal manipulations with matrices to real understanding of the geometry and composition of vector spaces and linear transformations. On this page:
On the first day of class I handed out this survey to get a sense of what the people entering this class already know.
A central goal, permeating this course, will be to develop a sense of
which linear algebra questions should be approached from a highbrow,
coordinate-free manner (almost all), and which should be done down-and-dirty
with matrices (almost none). Is this just mathematical snobbery?
No (at least, not just that); the highbrow proofs, once
understood, are simpler and less prone to error,
and always much much shorter.
In past incarnations (by other professors)
this course has been a mix of some absolutely
obligatory results - I'm thinking Jordan Canonical Form here -
and special topics, such as vector spaces adorned with a finite
group of symmetries, or set-theoretic questions about infinite-dimensional
vector spaces. Here is a list of what I consider essential,
what special topics I fully intend to explore, and more fanciful topics
we may attack if time permits. All page numbers refer to the sixth
printing of Curtis' book, yellow with the ellipse on the cover.
Essential topics, largely in the order we will do them
Less essential topics, still important for much subsequent mathematics,
that I fully expect us to get to
Some other cool advanced linear algebra things,
some of which will fit in somewhere
I would rather assign interesting problems, whose results we will
make use of and generalize in the classes to come. In particular,
many problems will probably become very easy shortly after they are due.
So late homework - later than the beginning of class - is only going
to count 50%. If you know in advance you won't be able to make it to
Thursday's class you can slip your homework under my office door.
The homework will be 50%, the midterm 20%, and the final 30% of your grade.
I have no idea what percentage corresponds to what letter, but will
announce estimations after the midterm.
This being an honors class, I know you're here to really learn some
mathematics, and I will do my best to make sure you learn as much
as is practicable by the end of the course. This is of course subtler
than throwing the maximum amount of material at you -- the hard part
(for me too) is making sure that at the end of the course you
remember and understand everything that has come before.
One thing it does mean is that, if I'm doing my job right, the homeworks
should challenge everyone. Too many people getting perfect grades on
too many homeworks means that the homeworks are lame.
For those of you who haven't taken classes tuned to this sort of
standard, this will be disconcerting for a while, and all I can do
is assure you that I will have it in mind when converting percentages
to letter grades. Those of you who have know how much more can be
gleaned from such a course.
General remarks about this course
"Choosing coordinates on a vector space...is an act of violence"
Things we will definitely do, will probably do,
and might do this term
How the course will be run
Like so many before it, this class will have homework, a midterm, and
a final. Homework will be assigned on Thursdays, due the following
Thursday, and collected in class. Having myself put off many a homework
to the last minute and handed it in at the end of a totally-ignored class,
I will collect homework at the beginning of Thursday's class.
The best time to ask me questions about it is face-to-face in the
couple of minutes before Tuesday's class, such that I can make an
announcement if there's some egregious error or something.
Math class is hard!
-- a swiftly discontinued Talking Barbie