I. Course Course Course
Prefix Number Name Credit Lecture Lab
MAT 260
Linear Algebra 3 3 0
II. Prerequisite:
MAT 251 with a grade of C or better.
III. Course Description:
Course covers matrices and the algebra of linear systems. Content includes equations, vector spaces, real inner product spaces, linear transformations, determinants, eigenvalues, eigenvectors, diagonability, quadratic forms and symmetric matrices. Calculators/computers used when appropriate.
IV. Course
Objectives:
A. Use basic matrix operations and the
algebra of matrices in practical problems.
Possible applications may be drawn from areas such as Kirchoff’s laws, Leontieff model
of an interacting economy, Markov chains, method of least squares, singular
value decomposition and Fourier coefficients of a function.
B. Understand the concepts of vector
spaces, subspaces, basis, independence and dependence, dimension, coordinates,
rank of a matrix, inner product.
C. Use the dependency relationship
algorithm and the Gram-Schmidt orthogonizational
process.
D. Understand linear transformations, range
and null space of a linear transformation, the correspondence principle and
similarity.
E. Understand properties of the
determinant function and the cofactor expansion of determinants.
F. Understand
the concepts of eigenvalues and eigenvectors.
G. Understand
the concepts of quadratic forms.
V. Academic
Integrity:
Students, Faculty and administration at
·
cheating,
·
plagiarism
(turning in work not written by you or lacking proper citation),
·
falsification
and fabrication (lying or distorting the truth),
·
helping
others to cheat,
·
making
unauthorized changes in official documents,
·
pretending
to be someone else or having someone else to pretend to be you,
·
making or
accepting bribes, special favors, or threats, and any other behavior that
violates academic integrity.
There are serious consequences to violations of the academic integrity
policy. Oakton’s policies and procedures provide students with a fair hearing
if a complaint is made. If you are found to have violated the policy, the
minimum penalty is failure on the assignment and a disciplinary record will be
established and kept on file in the office of the Vice President for Student
Affairs for a period of 3 years.
Details of the Code of Academic Conduct can be found in the Student
Handbook.
VI. Outline
of Topics:
A. Systems
of Linear Equations and Matrices
1
Gaussian elimination
2
Homogeneous systems of linear
equations
3
Matrices and matrix arithmetic
4
Matrix invertibility
5 Applications
B. Vector
Spaces
1. Euclidean n-space
2. Linear independence
3. Basis and dimension
4. Rank of a matrix
5. Inner product spaces
6. Orthonormal
bases and projections
C. Linear
Transformations
1. Properties, range and null space
2. Matrix representations, products and
inverses
3. Similarity
D. Determinants
1. The determinant function and evaluation
2. Properties of determinants
3. Cofactor expansion
4. Applications including Cramer's Rule
1. Eigenvalues
and eigenvectors of linear transformations
2. Diagonalization
F. Quadratic
forms
1.
Symmetric
matrices
G. Recommended
Technology
1.
Use
of technology to perform matrix computations
2.
Use
of technology to determine matrix products and inverses
3. Use of technology to evaluate determinants
VII.
Methods of Instruction:
(To be completed by instructor)
Methods of presentation can include lectures, discussion,
experimentation, audio-visual aids, small-group work and regularly assigned
homework. Calculators/computers will be used when appropriate. Mathematica is available for use at the College at no
charge.
VIII. Course
Practices Required:
(To be completed by instructor)
VIII.
Instructional Materials:
Required Textbook:
Linear Algebra: A Modern Introduction by David Poole, 2nd
Edition, Thomson, 2006. 9780534998455
A computer
algebra system is required.
X. Methods
of Evaluating Student Progress:
(To be determined and announced by the instructor)
Evaluation methods can include
grading homework, chapter or major tests, quizzes, individual or group
projects, calculator/computer projects and a final examination.
XI. Other Course
Information:
Individual instructors will establish and announce
specific policies regarding attendance, due dates and make-up work, incomplete
grades, etc.
If you have a documented learning, psychological, or
physical disability you may be entitled to reasonable academic accommodations
or services. To request accommodations
or services, contact the ASSIST office in Instructional Support Services. All students are expected to fulfill
essential course requirements. The
College will not waive any essential skill or requirement of a course or degree
program.
Effective beginning term: ___Fall 2004__________ Ending term: ___________
(term)
(year) (term) (year)
Syllabus prepared by: J. Hasset & R. Sompolski Date:
Reviewed by Dept/program chair: R. Sompolski Date: ____________
Approved by Dean: J. Kotowski Date: ____________