Monday through Friday, 8:00-9:30, Ayres 129
First class: May 30 Last class: July 3
GOAL: second course in linear algebra for
mathematicians, scientists and engineers.
Structure of linear operators on finite-dimensional vector spaces, including
the spectral theorem and the Jordan canonical form. Students will be expected to
study and understand proofs, and to provide complete proofs of simple statements.
This is not a `computational' course.
PREREQUISITE: Math 251 or 257. Familiarity with
the language of elementary
TEXT: Linear Algebra Done Right, by Sheldon Axler. 2nd. edition, Springer-Verlag 1997
ATTENDANCE to every class is expected. On occasion
I will introduce material not
found in the text; such material is an integral part of the course. If you have to miss a
class, you must find out what was covered. (Check the course log . ) It is probably a good
idea to take notes. I encourage students to ask questions during class. Some sections in
the text won't be covered in class- there will be reading assignments.
GRADING will be based on three exams, or two exams
and homework (see below).
The first exam will follow chapter 5, the second will be given after chapter 7 and the
last one after chapter 9. (At least two days between conclusion of a chapter and
the corresponding exam) Expected grading scale:A=80 and above, B=65-79, C=50-65,
less than 50 ave: F (D's in borderline cases).
Deadline to drop the class with WP: June 25- you must bring a form for me to sign.
A list of problems from the text will be posted on
the `course log' page after each class. Turn in two of those at the beginning of the
following class. The homework grade will count as one exam. (Of the four grades-
three exams and one homework grade- only three will be used for the final average.)
OFFICE HOURS for this course will be the one-hour
period following each class.
I will also answer questions by e-mail.
2- Linear independence, basis, dimension
Chapter 4 is a reading assignment
5-Eigenvalues and eigenvectors
8-Operators on complex vector spaces
9-Operators on Real Vector spaces
7-Operators on inner product spaces
X-The classical matrix groups
Other topics ( Differential equations, stochastic matrices
dynamical systems) will be included depending on the time available.