SYLLABUS
Course: MATH 344
Linear Algebra Term: Winter 2010-11 Meets: MWF 9:20-10:30
Instructor: Craig Kalicki Office: H-284 E-mail:
craig.kalicki@briarcliff.edu
Phone: 279-5541
Text: Kolman and Hill, Introductory
Linear Algebra: An Applied First Course , Eighth Edition,
Pearson Prentice Hall, c.2005 ISBN
0-13-143740-2
Prerequisites:
Students
in this course should have passed MATH 218 Calculus II or an equivalent course.
Goals of course:
This course is a survey of topics in linear algebra intended for
students majoring in mathematics, physical
sciences, and pre-engineering. Students
in this course should expect to
1) become familiar with the basic concepts,
theorems, and computational procedures of linear algebra.
2) gain an appreciation of linear algebra as a
tool fundamental to many applications in mathematics and
the sciences.
3) develop skills in the investigation and
discovery of mathematical truths and in the construction of valid
mathematical arguments.
4) achieve a degree of mathematical maturity
necessary for success in other advanced mathematics
courses.
Grading:
|
Two
exams @ 25% |
50% |
|
A = 100 - 90 |
C+
= 73 - 70 |
|
Final
exam |
30% |
|
A- = 89
- 87 |
C =
69 - 64 |
|
Assignments
|
20% |
|
B+
= 86 - 83 |
C- = 63
- 61 |
|
|
|
|
B =
82 - 77 |
D+
= 60 - 57 |
|
Total |
100% |
|
B- = 76
- 74 |
D =
56 - 50 |
Grading rubric:
The
grading rubric below will be used to assess written work, including text
assignments and exam
questions.
|
Level |
Characteristics |
|
4 |
Solution
is correct and clearly presented. |
|
3 Good |
Method
of solution is substantially correct and clearly presented. |
|
2 Adequate |
Method
of solution is flawed but mostly correct. |
|
1 Minimal |
Solution
is attempted but significant errors occur. |
|
0
Unacceptable |
Solution
is omitted or an answer is given with no supporting evidence. |
Expectations of students:
Exams and assignments will require that students demonstrate the
ability to
state precisely important
definitions and theorems;
supply illustrative
examples of the concepts discussed;
perform basic
computational procedures;
use the procedures to solve applied
problems;
use technology as a
problem solving tool;
verify elementary results
involving the concepts discussed.
Clarity of expression is essential in presenting mathematics
well. Students are expected to observe
the
standard rules of grammar and punctuation in all work that is handed in.
Some suggestions:
1) Attendance at all class
meetings is expected. You will need to
take some notes in class, but the basic
lecture notes will be posted on
BCU Online as the term progresses. You
may want to bring hard
copy of the notes to class.
2) Come to class
prepared. Read the text, paying
particular attention to definitions of terms and
examples.
Be prepared to discuss and present solutions of assigned problems. Not all material that
you are responsible for will be
covered in class.
3) Make reasonable attempts
to solve most of the assigned problems.
Credit will be given for
assignments handed in and selected
problems will be graded. Solutions of
more difficult problems
can be posted online if requested. Assignments are to be handed in at the
beginning of class on the
date due. No
late work will be accepted except in cases of serious illness or family emergency.
4) Make use of your
instructor’s office hours. Time
constraints do not permit solution of all problems in
class, so seeking
help outside of class is encouraged.
5) Use computing resources
whenever appropriate as problem solving tools.
Have a graphing calculator
available for use in
class and on exams. Many of the assigned
problems may be done with the aid of
graphing calculators
or computer software.
Learning
outcomes:
Expected learning outcomes for this course are listed below. Assessment of the degrees to which these
outcomes have been achieved will be done via written exams and graded
homework assignments.
Students who have completed MATH 344 will be able to
1) perform standard operations involving
matrices.
2) solve linear systems using matrix methods
and technology.
3) solve applied problems involving linear
systems.
4) compute and apply determinants.
5) perform and apply vector operations in n-space.
6) understand and apply linear transformations
on n-space.
7) describe the effects of matrix operators on
the plane.
8) compute and apply cross products in
3-space.
9) solve problems involving lines and planes
in 3-space.
10) demonstrate understanding of
the concepts of real vector space and subspace.
11) solve problems involving span, linear
independence, basis, and dimension.
12)
use matrices to do least-squares estimation.
13) compute eigenvalues and eigenvectors of a
square matrix.
14) verify basic results involving eigenvalues
and eigenvectors.
15) identify and analyze linear transformations
on real vector spaces.
16) use matrices to analyze and apply linear
transformations.
Course material:
Linear systems / matrices /
Gaussian and Gauss-Jordan elimination /
matrix operations / properties of
matrix operations / inverse of a matrix.
Ch 2 Applications of Linear
Equations and Matrices [2 classes]
Selected topics.
Ch 3 Determinants [2 classes]
Determinants / cofactor
expansions / applications / adjoint of a matrix.
Ch 4 Vectors in Rn
[3 classes]
Vectors in the plane
/ vectors in n-space / length and angle
/ dot products / linear transformations.
Ch 5 Applications of
Vectors in R2 and R3 [2 classes]
Cross products / lines and planes.
Ch 6 Real Vector
Spaces [6 classes]
Real vector spaces / subspaces /
linear independence / basis and
dimension / rank of a matrix /
coordinates and change of
basis / orthonormal bases.
Ch 8 Eigenvalues,
Eigenvectors, and Diagonalization [2
classes]
Eigenvalues of a square
matrix / eigenvectors / diagonalization / orthogonal matrices.
Ch 9 Applications of
Eigenvalues and Eigenvectors [2
classes]
Selected topics.
Ch 10 Linear
Transformations and Matrices [3
classes]
Linear transformations
/ kernel and range / matrix of a linear transformation / affine transformations /
fractals.
c.2010 by
Craig Kalicki PhD