Course Description:
An introduction to the theory and applications of linear
operators on finite dimensional vector spaces. Topics include linear systems,
matrix algebra, Euclidean and general vector spaces, subspaces, change of basis
and similarity, the eigenvalue problem, projections, orthogonality, the Spectral
Mapping Theorem, the Jordan Canonical Form, inner product spaces and quadratic
forms.
General Education Goals:
This general education course addresses the following
general education goals:
1. Students will use critical thinking and problem solving in analyzing
information gathered through different media and
from a variety of sources.
2. Students will apply appropriate mathematical and statistical concepts
and operations to interpret data and to solve
problems.
Course Objectives:
Upon successful completion of this course, students will
be able to
1. Understand and utilize the strong interconnection between the geometric
and algebraic properties of vectors and linear
transformations.
2. Gain insight into how diverse problems from many application areas can
be solved in the context of linear algebra .
3. Progress from concrete experiential learning to more abstract
theoretical understanding of concepts.
4. Further develop their analytical ability thorough the precise critical
thinking skills required to understand and do
mathematical proofs.
Methods of Instruction :
Instruction will consist of a combination of lectures ,
presentation of sample problems, clarification of homework
exercises/textbook material, and general class discussion.
Course Requirements:
1. Regular attendance; excessive absences will
negatively affect student understanding and performance.
2. Completing reading and problem solving homework in a timely manner and
contribute to class discussions.
Mathematics cannot be understood without doing a significant amount of outside
study.
3. Participation in a peer study group that meets regularly and maintains
effective member communication links.
4. Taking tests and exams when scheduled. No make-ups will be
permitted. The first missed test will be recorded as a
zero until the end of the semester, at which time the final exam grade will
also be used to replace the missing test grade. Grades from any other missed
tests will be recorded as irreplaceable zeros. The Comprehensive Final
Exam is required and cannot be rescheduled unless some extraordinary
event occurs and prior arrangement is made
with the instructor.
Method of Evaluation:
Final Averages will be computed as follows:
• 3 Tests (dates specified by
the instructor with at least one week advanced notice)
Tests will show evidence of the extent to which students meet course
objectives,
including, but not limited to, identifying and applying concepts,
analyzing and
solving problems, estimating and interpreting results, and stating
appropriate
conclusions using correct terminology . |
60 % of the Final Avg |
• Optional Assignments
e.g., Problems Sets, Research Projects, etc., designed to enhance
understanding
of the Applications Linear Algebra in Business and Economics. |
10% of the Final Avg |
• Final Exam
The comprehensive final exam will examine the extent to which students
have
understood and synthesized all course content and achieved all course
objectives. |
30 % of the Final Avg |
Students may use a scientific or graphing calculator or
laptop computer to enhance understanding during class
or while doing homework, however, no form of technological aid can be used on
tests/exams.
Final Grade Ranges are:
[A 90 – 100] [B+ 85 – 89] [B 80 – 84] [C+ 75 – 79] [C 60 –
74] [D 50 – 59] [F 00 – 49]
|
Chapter 1 Linear Equations and Vectors |
| 1 |
1.1 |
Matrices and Systems of Linear Equations |
| 1.2 |
Gauss- Jordan Elimination |
| 2 |
1.3 |
The Vector Space Vn |
| 3 |
1.4 |
Basis and Dimension |
| 4 |
1.5 |
Dot Product, Norm, Angle, and Distance |
|
Chapter 2 Matrices and Linear Transformations |
| 5 |
2.1 |
Operations of Matrices |
| 2.2 |
Properties of Matrix Operations |
| 6 |
2.3 |
Symmetric Matrices and Seriation in Archaeology |
| 7 |
|
Test 1 |
| 8 – 9 |
2.4 |
The Inverse of a Matrix and Cryptography |
| 10 |
2.5 |
Matrix Transformations, Rotations, and Dilations |
| 11 |
2.6 |
Linear Transformations, Graphics, and Fractals |
|
Chapter 3 Determinants and Eigenvectors |
| 12 |
3.1 |
Introduction to Determinants |
| 13 |
3.2 |
Properties of Determinants |
| 13 |
3.3 |
Determinants, Matrix Inverses, and Systems of Linear Equations |
| 14 |
|
Test 2 |
| 15-16 |
3.4 |
Eigenvalues and Eigenvectors |
|
Chapter 4 General Vector Spaces |
|
17-18 |
4.1 |
General Vector Spaces |
| 4.2 |
Linear Combinations |
| 4.3 |
Linear Dependence and Independence |
| 19 |
4.4 |
Properties of Bases |
| 20 |
4.5 |
Rank |
| 21 |
4.6 |
Orthonormal Vectors and Projections |
| 22 |
|
Test 3 |
| 23 |
4.7 |
Kernal, Range, and the Rank/Nullity Theorem |
| 24 |
4.8 |
One-to-One Transformations and Inverse Transformations |
|
Chapter 5 Coordinate Representations |
| 25 |
5.1 |
Coordinate Representations |
| 5.2 |
Matrix Representation of Linear Tranformations |
| 26 |
5.3 |
Diagonalization of Matrices |
|
Inner Product Spaces |
| 27 |
6.1 |
Inner Product Spaces |
| Final Exam |
