This page, and all homework assignments, are available at
http://www.math.colostate.edu/~achter/469
Introduction
This is an advanced course in linear algebra. While the emphasis of
the prerequisite course Math
369 is on the relationship between linear algebraic structures
and the solution sets to systems of linear equations, the emphasis
of 469 is on the structures themselves.
On one hand, this abstract theory of vector spaces and the linear maps
between them is at the heart of much of modern mathematics. On the
other hand, it also provides a coherent explanation for certain
phenomena observed in a first linear algebra course.
For the most part, the course will follow the plan of the textbook,
albeit with (even) less emphasis on the mechanical solution of systems
of equations:
- Vector spaces, linear transformations and matrices;
- Duality, functionals, adjoints;
- Determinants;
- Invariant subspaces;
- Inner product spaces;
- Structure theorems
with additional topics as time allows.
Logistics
Requirements and other expectations
As in any other 400-level class, you will need to work both diligently
and creatively.
- Homework and class participation -- 35% The work you do in
class and for homework is by far the most important
component of the course. Homework will be assigned weekly,
and is due at the beginning of class on Wednesdays.
No late homework will ever be accepted. Your work must be
neat, and pages stapled, in order to be graded.
- Midterm -- 30% There will be a midterm on Friday,
March 13, in class.
- Final -- 35% The final is on Wednesday, May 13, 7am-9am.
You must take the exams during the scheduled
time; no make-ups will be given. You must pass the final in
order to pass the course.
Help
This is challenging material, and you may need a little help every now
and then.
- Questions directed to j.achter@colostate.edu will
be answered swiftly.
- Office hours will be posted, or you can schedule an appointment.