Spring 2007
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: Tuesdays:
3:30PM–5:30PM; Wednesdays: 4:00PM–6:30PM; Thursdays: 5:15PM–7:45PM
Class Hours: Wednesdays: 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.
Optional Text: Poole, David. (2003). Linear
Algebra: A Modern Introduction. Brooks/Cole.
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.
·
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.
·
The
MATLAB computing tool will be introduced. You may use this tool for matrix
calculations in your homework and quiz assignments.
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 (see The Rivier College Statement of Attendance in Appendix 1).
2.
Please,
do the assigned readings, 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 e-mail account with Rivier College
and do check it regularly. I will communicate with you via e-mail.
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.
OPTIONAL: You are encouraged to use the MATLAB computing tool for matrix
calculations in your homework and quiz assignments. The brief MATLAB tutorials
will be offered during the class sessions. (MATLAB is available in all Computer
Labs on campus).
10. In every class, we will have a short
written quiz. The best 5 quiz grades will be counted.
There are no make-up quizzes.
11. We will have our final exam on May 2. 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.
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.
Tucker, A. (1993). Linear
Algebra: An Introduction to the Theory and Use of Vectors and Matrices. New
York: Macmillan Publishing Company.
Williams, G. (2005). Linear Algebra with Applications. (5th
edition). Boston: Jones and Bartlett Publishers.
MATLAB Books and Manuals:
Poole, David. (2003). Linear
Algebra: A Modern Introduction. Brooks/Cole.
Palm, W. J. III. (2005). Introduction
to MATLAB 7 for Engineers. (2nd edition). Boston, MA: McGraw-Hill.
Chapra, S. C. (2005). Applied
Numerical Methods with MATLAB. (2nd edition). Boston, MA: McGraw-Hill.
|
Dates |
Topics |
Reading Material |
|
January 17 |
Vectors
in R^2 and R^3. Dot and cross products. |
Sections 1.1& 1.2 |
|
January 24 |
Lines and
planes. Euclidean m-space. |
Sections 1.3 & 2.1 |
|
January 31 |
Systems of
linear equations. Row-reduction of linear systems. |
Sections 2.2 & 2.3 |
|
February 7 |
Operations
on matrices. Matrix equations and inverses. |
Sections 3.1 & 3.2 |
|
February 14 |
Theory of
linear systems. LU Decompositions. |
Sections 3.5 & 3.6 |
|
February 21 |
Elementary
matrices and linear systems. Definition of determinants. |
Sections 3.7 & 4.1 |
|
February 28 |
Properties
of determinants. Cramer's rule. |
Sections 4.2 & 4.3 |
|
March 7 |
Spring
Break |
NO CLASSES |
|
March 14 |
Linear
dependence and independence. Subspaces of R^m. |
Sections 5.1 & 5.2 |
|
March 21 |
Basis and
dimension. Rank of a matrix. |
Sections 5.3 & 5.4 |
|
March 28 |
Vector
spaces and subspaces. Linear independence, basis, and dimension. |
Sections 6.1 & 6.2 |
|
April 4 |
Definition
of a linear transformation. Algebra of linear independence, basis, and
dimension. |
Sections 6.3 & 6.4 |
|
April 11 |
Kernel
and image. |
Sections 7.1 & 7.2 |
|
April 18 |
Eigenvalues,
eigenvectors, and their applications. |
Sections 7.3 & 8.1 |
|
April 25 |
Review of
the course material. |
|
|
May 2 |
Final
Exam |
Final Exam |
APPENDIX 1: The Statement
of Attendance
The classroom is the heart of the educational experience at
Rivier College because it provides, uniquely, a formal setting for the
important exchanges among faculty and students. Regular and punctual attendance
at all classes, essential for maximum academic achievement, is a major
responsibility of Rivier College students. Failure to attend and contribute to
the classroom environment significantly and demonstrably reduces the quality of
the educational experience for everyone in the classroom. As a result, absences
almost always impact the quality of performance.
As part of its commitment to a quality educational
experience for all members of the Rivier community, the College formally
requires specific attendance policies to be developed by its professors and
reviewed by the Division Head and Academic Dean. Any attendance policy used by
an individual professor as a criterion for evaluation must be specified in the
course syllabus and presented to students during the first week of classes.
These policies can be found in respective course syllabi, and may include
reasonable penalties and sanctions for excessive absences.
In the event of prolonged illness, accident, or similar
emergency, it is the responsibility of the student to notify both the professor
and the Office of the Academic Dean. Students must remember that it is always
their responsibility to make up the work they may have missed during an absence
from class. Students are directed to confer with their professors when their
absences jeopardize satisfactory progress. Whenever a professor is absent
without notification, students are expected to wait fifteen minutes before
leaving and to sign an Attendance List, which a class member delivers to the
Office of the Academic Dean.
Instructors are required to record attendance and alert the
Registrar when a student fails to attend the equivalent of two weeks of courses
(2 absences for a course meeting once a week, 4 absences for a course meeting
twice a week, 6 absences for a course meeting three times a week). The student
will then be alerted that he/she is in danger of falling under the 'habitual
non-attendance policy" (see below).
Habitual Non-Attendance Policy:
Habitual non-attendance is defined as an absence in any
course (for any reason whatsoever) equating to three full weeks of missed class
sessions (3 absences for a course meeting once a week, 6 absences for a course
meeting twice a week, 9 absences for a course meeting three times a week).
It is the responsibility of the student to notify the
College of any intention to withdraw from a course or withdraw from the
College. The College will attempt to resolve the issue of habitual
non-attendance with the student; however, the College reserves the right to
withdraw students who are no longer attending classes. Habitual non-attendance
in one or more classes may result in administrative withdrawal from the class
or classes affected, withdrawal from the College or, in cases with extenuating
circumstances, an administrative leave of absence. In such cases a grade of W
of NF
will be assigned to the classes affected according to the appropriate date
published in the academic calendar.
Students who have attended no class sessions of a course or
courses from which they are registered by the end of the drop/add period will
be dropped from each class not attended. If a student never attended any courses
during the drop/add period, the student will be withdrawn from his/her full
schedule of courses.
APPENDIX 2: Honesty Policy
Plagiarism
and cheating are serious breaches of academic honesty. In general, plagiarism
is defined as the presentation of someone else’s work in whatever form:
copyrighted material, notes, film, art work, reports, statistics,
bibliographies, and the like, as one’s own, and failing to acknowledge the true
source. Quoting word-for-word, or almost so, or using the argumentation of another
source without acknowledging this dependence also constitutes plagiarism.
Cheating is defined as the giving or attempting to give or to receive
unauthorized information or assistance during an examination or in completing
an assigned project. Submission of a single work for two separate courses
without the permission of the instructors involved is also a form of cheating.
APPENDIX 3: Americans with Disabilities Act (ADA)
Rivier
College wants to provide reasonable accommodations to students with disabilities.
To accomplish this goal effectively and to ensure the best use of our
resources, timely notice of a disability must be provided to the Office of
Special Services for verification and for evaluation of available options. Any
student whose disabilities fall within ADA should inform the instructor within
the first two weeks of the term of any special needs or equipment necessary to
accomplish the requirements for the course. To obtain current information on
this procedure, contact the Office of Special Services at phone extension 8497.
APPENDIX 4: 24/7 Blackboard Technical Support
All
students have the ability to access Blackboard technical support on a 24/7
basis. Students have many different options for obtaining support, including
phone, online technical library, or Live Chat with a customer service
representative. The support can be accessed by following this link: http://supportcenteronline.com/ics/support/default.asp?deptID=3250