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
set theory.
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.
HOMEWORK(revised policy):
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.
COURSE OUTLINE:
1-Vector spaces
2- Linear independence, basis, dimension
3-Linear maps
Chapter 4 is a reading assignment
5-Eigenvalues and eigenvectors
EXAM 1
8-Operators on complex vector spaces
9-Operators on Real Vector spaces
EXAM 2
6-Inner-product spaces
7-Operators on inner product spaces
X-The classical matrix groups
EXAM 3
Other topics ( Differential equations, stochastic matrices
and linear
dynamical systems) will be included depending on the
time available.