Bulletin
Description:
Corequisite: MAT 168 or 179. Vector spaces, systems of linear equations,
linear transformations,
matrices, inner products.
Text
Matrix Analysis and Applied Linear Algebra , Carl D. Myer, SIAM, (2000).
References:
The following is a partial list of supplemental reading:
1. Introduction to Matrices and Linear Transformations , Daniel T. Finkbeiner II,
W.H. Freeman, 3rd ed. (1978).
2. The Maple Handbook, Darren Redfern, Springer-Verlag, (1993).
3. Matrix Computation for Engineers and Scientists, Alan Jennings, Wiley,
(1977).
4. Elementary Linear Algebra 8E, Howard Anton, Prentice Hall , (2000).
Goals: To provide an introduction to the basic
structure of linear vector spaces and an understanding
of the properties and theory of linear transformations. The intent is to
introduce theory and
practice supported by a problem solving approach with foundations in the the
solution of
linear systems of equations and matrix operations . The relationship between a
linear map, its
matrix representations and the theoretical developments needed to categorize its
fundamental
properties are central to the course.
Topics: The intent is to cover chapters 1–7 of the
text. Areas of emphasis
include:
1. Solutions of linear equations and matrix operations, row operations,
reduction and row
equivalence. Fundamentals of matrix algebra.
2. Determinants, including alternating multi-linear maps, permutations and
cofactor expansion.
3. Vector geometry and fundamentals of vector spaces, including linear
independence,
bases and dimension and coordinates with respect to a basis. Rank and nullity.
4. Inner product spaces , orthonormal bases, Gram-Schmidt orthogonalization,
least
squares approximation , and orthogonal matrices.
5. Relating matrices to linear transformations and developing the properties of
linear operators,
coordinate transformations and diagonalizability.
6. Norms and inner products; least squares and orthogonal projection.
7. Eigenvalues and eigenvectors.
Assessment:
The material is presented in a manner which ties these developments to
elementary applications
of interest to the student, including computer error correction coding (Hamming
matrices),
least squares approximation, difference equations , boundary conditions for
hyperbolic
PDEs, and iterated functions. Awareness of computational issues associated with
large linear
systems is developed. Involvement with symbolic algebra using Maple is stressed
at all
levels as a tool to facilitate the study of linear algebra.
The course assessment is based on extensive midterm
assignment (stressing analysis and
theory) 50%, and a comprehensive in-class examination stressing proficiency 50%.
Details
of the grading policy are available online at the web site.
Course Assessment Policy
Basis of the Class Evaluation
Each student is assessed based on a cumulative point score from 0 to 100.
The score is based on examination
papers, bonus points and on class participation (problem solving). The algorithm
is explained under the
topic Scoring and Course Grades. Graduate students have an additional project
grade in mixed undergraduate/
graduate classes which is part of the assessment and some additional rules and
policies apply.
Examination Papers
Typically in a lower level class (100 - 200 level) there are at least four
examinations, one of which consists
of a midterm paper, and one a comprehensive examination. In an upper level class
(300 and above) there is
only the midterm paper and a comprehensive examination paper. Depending on the
syllabus, in a graduate
level class (500 and above) additional projects are assigned. For pre-calculus
classes there is typically one
exam at the end of each chapter.
The midterm paper is intended to provide an extensive
assessment of the student’s ability to work with
the material and to reason in an un-timed environment. The midterm paper is
always a lengthy paper in
upper level classes. and the student is usually given one week to complete the
midterm paper. Because
of this, the level and quality of work is expected to be high. In introductory
classes (e.g., MAT-101), the
midterm is typically a comprehensive, an in-class exam covering the material up
to the date of the exam.
The final exam is a comprehensive evaluation that covers all material which is
discussed in the course and
is usually given in class toward the end of term . Other exams are specific to
topics or chapters, with an
emphasis on the material covered in those chapters.
All in class examinations are closed book, no notes,
unless otherwise specified. The exception to this
rule is for introductory classes (such as MAT-101). The questions are designed
to test reasoning and the
ability to work with the material. Each paper or exam is worth 100 points. The
course grade is based on
the average score obtained on all examination papers, plus bonus points which
are earned for solving more
difficult problems less points deducted for failure to participate in class.
Bonus Problems
Bonus problems are typically given as extra problems on examination papers, or
else are given during
the course of the semester, to be turned in at the required time. Bonus problems
are more difficult and
challenging problems which are available for students to gain experience beyond
the requirements of the
course. These problems usually have point values from 1 to 10. Students are not
required to do these
problems, but it is to the student’s benefit to attempt them since they are
counted after the examination
results are averaged.
In classes with a mixed graduate and undergraduate
component the bonus points are worth only half as
much for the graduate students taking the course.
Class Participation (Assignments and Homework)
There is no credit given for homework assignments in any class, except an
introductory class (e.g., MAT-
101), however since examination papers are based on the material and problems
which are to be found in the
homework assignments, it is beneficial to attempt all of the problems. In an
introductory class, homework
assignments will be handed in each week for credit (typically 1/2 bonus point,
if there was a substantial
attempt to obtain the required solutions, and 0 points otherwise). All students
are required to be able to
solve or attempt to solve homework problems in class. Failure to participate in
this activity will result in the
loss of up to 5 points from your final score.
The use of Technology
The use of technology is strongly encouraged, particularly in classes where
there there a strong linkage
between computers and mathematics, e.g., in numerical or computational classes,
or in those where symbolic
algebraic computation is required. In contrast, the use of calculators or other
technology which serves to
mask deficiencies in being able to work with arithmetic or algebra is strongly
discouraged. Often students
use technology to avoid working with concepts and abstraction and this is also
discouraged. Thus the correct
use of technology, and policies regarding its use are set strictly for each
class, and each examination.
Scoring and Course Grades
The class grade is based on the student’s earned point score for the
semester. This earned point score is
computed using the average of all points earned on papers to which the bonus
points are then added. From
this score, up to 5 points may be lost for failure to participate in class work.
Determination of Class Grade
The class grade is assigned based on
• 90 – 100 : A
• 80 – 90 : B
• 70 – 80 : C
• 60 – 70 : D
• 00 – 60 : F
Grades which fall on a grade boundary, for example a score
of 90, are decided at the discretion of the
instructor based on the participation of the student in class.
Further Considerations and Rules
Late Papers
Any material handed in late without having obtained prior approval or without
having a valid university
excused absence (e.g., a signed medical excuse) results in a 50% factor being
applied to the students score
on that paper. Material handed in over one week late without prior approval is
not accepted, resulting in a
score of 0 for that paper. Please note:
It is the student’s responsibility to contact the
instructor concerning any scheduling conflicts
which may result in late papers or result in a failure to attend scheduled in
class
exam.
Considerations for the Student
Because of the importance attached to solving bonus problems and because no
examination results are
curved or normalized, it is strongly emphasized to the student that they attempt
as many bonus problems as
possible. These provide a mechanism for improving performance; however, unlike
‘curving’ exam results,
they require that the students take the initiative to improve their scores. The
examinations are structured
so that without attempting to solve any of the bonus problems the average grade
that can be expected by a
student is a high C or low B. If there is a need for better grade, it is
important to attempt bonus problems.
In a lower level class the first exam will always be
before the drop date. This allows students to assess
without penalty whether they desire to continue with the class. In an upper
level class, self-assessment is
the responsibility of the student.
Plagiarism/Cheating Statement
Students are expected to adhere to the highest standards of academic honesty
as outlined in the USM Student
Handbook. Any information that is copied from another source must be noted as
such in student materials.
Page number or Internet reference must appear in the text ad full bibliographic
references must appear
in the reference section of the paper/assignment. Sources must be in quotes, and
include author(s), year of
publication or other reference notes as required by the college department
format (e.g. APA, Chicago). Other
forms of academic dishonesty include, but are not limited to buying papers,
copying paragraphs/pages of
text/whole papers off the Internet, copying another student’s answers, etc.
Academic dishonesty will result
in the grade of a ”0” on the assignment and/or in the course and/or the student
may be reported to the Vice
President for Academic Affairs for further action.
