MA210E
Linear Algebra
Spring 2004
Syllabus
Instructor:
Dr. Vladimir Riabov
Associate Professor
MA/CS Department
Office: STH-312
Phone: 603-897-8613
E-mail: vriabov@rivier.edu
Web: http://www.rivier.edu/faculty/vriabov/index.htm
Office
Hours:
Mondays: 9:30 AM – 11:00 AM; Tuesdays: 3:30
PM – 5:30 PM;
Wednesdays: 9:30 AM – 11:00 AM; Thursdays: 4:30
PM – 6:30 PM
Class
Hours:
Thursdays: 6:30 PM – 9:00 PM
Brief Course
Description:
MA210 Linear
Algebra is an introduction to vector spaces and subspaces, linear dependence
and independence, basis and dimension, matrix algebra, solution of equations by
matrix reduction, determinants, matrix inversion, linear transformations,
eigenvalues, and eigenvectors. The course also includes applications of linear
algebra and a proof component in which students learn what is needed in proofs
and develop the ability to read and write proofs. Prerequisite: MA112.
Required Text:
Venit, Stewart & Bishop, Wayne (1996). Elementary Linear Algebra
(4th edition). Boston, MA: PWS Publishing Company.
Course Objectives:
Students will be given an opportunity:
* To develop
understanding of the basic concepts of linear algebra.
* To acquire skills in operations with vectors and matrices.
* To acquire understanding of the nature of mathematical proofs and develop skills
for carrying out proofs.
* To practice problem-solving using the apparatus of linear algebra.
* To develop the ability to read mathematical text and acquire skills for
independent studies.
* To develop the ability to write clearly and concisely about mathematical
ideas.
* To strengthen logical thinking and the ability of operate with mathematical
abstractions.
Teaching & Learning
Strategies:
The part of most class meetings will be lecture, but all students are
encouraged to interact with me by asking questions and contributing ideas.
Examples and hands-on activities will be given in class to illustrate concepts.
Opportunities will be given for individual and collaborative work throughout
the semester.
All new material will be introduced in class first. We will discuss it and work
through a few examples. Your active involvement is crucial: please, participate
in the discussion and contribute ideas.
The next stage will be your work at home with your class notes and the
textbook. Please, read both your notes and the assigned textbook material
making sure you understand everything, study all the examples, and then do the
assigned problems. If something is unclear, formulate it as a question for the
next class. Group work is a great tool to use at this stage.
At the beginning of each class, we will discuss the assignment from the
previous class meeting and address all concerns and uncertainties. Please, do
not leave anything unclear: we can only move forward successfully if we have no
hazy areas left behind. Questions are always welcome before, during and after
class time.
Course Policies & Requirements:
1.You are expected to attend all classes, arrive on time for classes, and come
prepared. Attendance will be taken at the beginning of each class meeting. If
you arrive late, please, make sure your absence has been corrected. In case of
illness, work-schedule conflicts, family commitments, or other emergencies that
require absence from class, you are expected to notify me prior to the class
meeting by sending an e-mail message, a phone message, or placing a written
note in the mailbox next to my office door. If you are absent for two class
meetings, you are required to set up a meeting with me to discuss the
advisability of your remaining in the course.
2. Please, do the assigned reading, study the examples, solve the assigned
problems, and formulate questions to discuss in class.
3. Assignments will be taken from the exercises in the text or given to you on
handouts. Homework assignments are due the class meeting after they are
assigned. Homework has to be handed in on the day for which it was assigned. If
you cannot avoid an absence, please make sure that a friend, roommate, or
classmate will deliver your homework to class, or mail it to me at Rivier
College, 420 S. Main Street, Nashua, NH 03060. Late homework will not be
accepted. All work has to be written neatly and clearly. Illegible work cannot be
graded. Please, staple each home assignment.
4. You are responsible for all material on all handouts whether or not you were
in attendance at the time I distributed them. Please make arrangements for
other students to collect handouts for you.
5. Plan to spend at least five hours per week outside of class learning course
materials. Depending on background and depth of inquiry, more or less time will
be needed by individual students. The estimated time commitment includes
reviewing class notes, reading the textbook, doing and reviewing textbook
examples and assignments, and preparing for quizzes and tests.
6. Have an email account and do check it regularly. I will communicate with you
via email.
7. Keep handouts, class notes, and assignments organized in a three-ring
binder. Submit homework on 8½" by 11" paper. I prefer you use graph
paper. For each section, include a heading with your name, the textbook section
number, the page number, and assigned problems.
8. OPTIONAL: You can obtain and bring to every class meeting a calculator that
performs matrix operations, e.g., a TI-83+. You are expected to read the manual
and figure out how to make it perform all required functions.
9. In every class, we will have a short written quiz. The best 5 quiz grades
will be counted. There are no make-up quizzes.
10. We will have our final exam on May 6. It will be a two-hour written test.
There is no make-up for the final exam.
Grading Method
Written home assignments 40%
Quizzes 30%
Final
exam 30%
Help
There are multiple sources of help that can be used separately or in
conjunction with each other to be successful in this class. Classmates are a
great source of help since they are working on the material at the same time
you are. I am also a source. Do not hesitate to contact me before or after
class, during my office hours, by e-mail (preferably) or by phone. There are
many other possibilities for assistance, such as other Rivier students, friends,
neighbors and relatives. What is important is to seek help at the first
sign of any confusion. Do not postpone asking questions or getting help.
N.B. You are responsible for understanding and complying with the
contents of this syllabus. If you have any questions about this syllabus please
raise them at the beginning of the session.
Bibliography
* Anton, H. (1994). Elementary Linear Algebra. (7th
edition). New York: John Wiley & Sons.
* Anton, H. and Rorres, C. (1991). Elementary Linear Algebra: Applications
Version. (6th edition). New York: John Wiley & Sons.
* Cullen, C. (1997). Linear Algebra with Applications. (2nd edition).
Addison-Wesley.
* Fraleigh, J. and Beauregard, R. (1995). Linear Algebra. (3rd edition).
Reading, MA: Addison-Wesley.
* Lay, D. (1994). Linear Algebra and Its Applications. Reading, MA:
Addison-Wesley.
* Nakos, G. and Joyner, D. (1998). Linear Algebra with Applications.
Brooks/Cole.
* Poole, D. (2003). Linear Algebra: A Modern Introduction. Brooks/Cole.
* Tucker, A. (1993). Linear Algebra: An Introduction to the Theory and Use
of Vectors and Matrices. New York: Macmillan Publishing Company.
|
Dates |
Topics |
Reading Material |
|
January 15 |
Vectors in R^2
and R^3. |
Sections 1.1& 1.2 |
|
January 22 |
Lines and planes. |
Sections 1.3 & 2.1 |
|
January 29 |
Systems of linear
equations. Row-reduction of linear systems. |
Sections 2.2 & 2.3 |
|
February 5 |
Operations on
matrices. |
Sections 3.1 & 3.2 |
|
February 12 |
Theory of linear systems. |
Sections 3.5 & 3.6 |
|
February 19 |
Elementary matrices and
linear systems. Definition of determinants. |
Sections 3.7 & 4.1 |
|
February 26 |
Properties of
determinants. |
Sections 4.2 & 4.3 |
|
March 4 |
Linear dependence and
independence. Subspaces of R^m. |
Sections 5.1 & 5.2 |
|
March 11 |
Spring Break |
NO CLASSES |
|
March 18 |
Basis and dimension. |
Sections 5.3 & 5.4 |
|
March 25 |
Vector spaces and
subspaces. Linear independence, basis, and dimension. |
Sections 6.1 & 6.2 |
|
April 1 |
Definition of a linear
transformation. Algebra of linear independence, basis, and dimension. |
Sections 6.1 &6.2 |
|
April 8 |
EASTER |
NO CLASSES |
|
April 15 |
Kernel and image |
Sections 7.1 & 7.2 |
|
April 22 |
Eigenvalues,
eigenvectors, and their applications. |
Sections 7.3 |
|
April 29 |
Review of the material |
|
|
May 6 |
Final Exam |
Final Exam |