COLLEGE OF ARTS & SCIENCES
DEPARTMENT OF MATHEMATICS AND INFORMATICS
LINEAR ALGEBRA
SPRING SEMESTER
2023-2024
COURSE SYLLABUS
Course Code:
Math 210 S1
Prerequisites:
None
Number of Credits: 3
Room:
A204
Time:
MW 1:00 to 2:15
Instructor:
Hussein Charafeddine
Instructor Profile:
PhD. Electrical, Computer and Systems Engineering; MS Applied Math
Office:
B202
Office Hours:
MW 9:25-10:40 or (by appointment)
Email:
houssain.charaf@pu.edu.lb
Required Text:
Lay, Lay and McDonald, Linear Algebra and Its Applications, 6th ed, Global Ed, Pearson (2022)
Course Description:
This course is an introduction to linear algebra which includes both theory and application. It covers a variety
of topics such as vector spaces, linear transformations and their matrix representation, linear independence,
bases and dimension, systems of linear equations, orthogonal projection, least-squares approximation,
orthonormal bases, matrices, determinants, and applications.
Learning Outcomes:
By the end of the semester, students are expected to be able to do the following:
-
CLO1: Solve systems of linear equations using multiple methods, including Gaussian
elimination and matrix inversion.
CLO2: Carry out matrix operations, including inverses and determinants and use them to
solve systems of linear equations.
CLO3: Demonstrate an understanding of the concepts of vector space and subspace.
CLO4: Demonstrate an understanding of linear independence, span, and basis.
CLO5: Apply principles of matrix algebra to linear transformations.
CLO6: Demonstrate an understanding of inner products and associated norms.
CLO7: Compute eigenvalues and eigenvectors of a matrix and perform matrix
diagonalization.
Mapping Course Learning Outcomes with Student Outcomes:
SLO1: Understand the value of basic sciences in today’s society and apply acquired knowledge in
solving problems.
SLO2: Function effectively and ethically as global citizens in an increasingly complex and rapidly
changing world.
SLO3: Engage in productive basic and translational research to generate new insights and to
benefit society and foster an enquiring and scientific minds.
CLO/SO
CLO1
CLO2
CLO3
CLO4
CLO5
CLO6
CLO7
SO1
X
X
X
X
X
X
X
SO2
SO3
Students’ Duties:
−
−
−
−
−
−
−
−
Keep an open mind during class sessions
Be sure your books, copybooks and stationery are with you in class
Switch your mobile off
Present a diversity of challenging techniques to grasp the objectives
Share in all activities and participate in all class discussions
Be creative and productive
Learn new methods of researching
Make-up exams are done upon the Department’s approval
Grading Scale:
Letter Grade
A
Quality points
4
%
A ≥ 96
AB+
B
BC+
C
CD+
D
DF
3.82
3.66
3.33
3
2.66
2.33
2
1.66
1.33
1
0
90 ≤ A- < 96
87 ≤ B+ < 90
83 ≤ B < 87
80 ≤ B- < 83
77 ≤ C+ < 80
73 ≤ C < 77
70 ≤ C- < 73
67 ≤ D+ < 70
63 ≤ D < 67
60 ≤ D- < 63
F < 60
Course Policy:
−
−
−
−
−
−
−
−
60 is the minimum passing grade.
Punctuality is also crucial. If you are late more than 10 minutes to class, you are considered absent
Students are required to submit all assignments on time.
Keep a folder for portfolio assessment that includes the course syllabus, handouts, homework
assignments, comments, quizzes, drafts and texts of research and proposal etc.
Avoid plagiarism, redundancy and basic research errors
Write effectively and show proficiency in citation of sources
Behave with academic integrity and maintain a positive attitude
Students must take all scheduled tests. Make-up tests are given only at the instructor’s
discretion if the student presents a valid excuse for his/her absence from the test within one
week of that test
Grading policy:
Your work will be assessed in a variety of ways: participation in class, completion of tasks according to
deadlines, homework and exams.
•
•
•
•
Attendance and Classwork
Homework
2 Exams (possilbly out of 3)
Final Exam
15%
10%
35%
40%
Course Topics / Schedule
Week
Week 1:
Week 2:
Topic
1.1 Systems of linear equations
1.2 Row reduction and echelon form
1.3 Vector equations
1.4 Matrix equations
1.5 Solutions sets of linear systems
Reading
Assessment
Exam 1
Text by Lay
Sections: 1.1, 1.2, 1.3
Sections 1.4, 1.5, 1.7
Exam 1
1.7 Linear independence
Week 3:
1.8 Introduction to linear transformations
1.9 The matrix of a linear transformation
2.1 Matrix operations
Week 4:
2.2 The inverse of a matrix
2.3 Characterizations of invertible matrices
2.4 Partitioned matrices
Exam 1
Sections 1.8, 1.9, 1.10
Exam 1
Sections 2.2, 2.3, 2.4
Week 5:
Week 6:
Week 7:
Week 8:
2.5 Matrix factorizations
3.1 Introduction to determinants
3.2 Properties of determinants
4.1 Vector Spaces
4.2 Null spaces, column spaces, linear
transformations
4.3 Linearly independent sets; bases
4.4 Coordinate systems
Week 10:
Week 11:
Exam 2
Sections 4.1, 4.2, 4.3
Section 4.4
4.5 The dimension of a vector space and Matrix
Rank
4.6 Change of basis
Week 9:
Exam 2
Sections 2.3, 3.1, 3.2
Exam 2
Exam 2
Sections 4.5, 4.6, 4.7
Applications Revision/catch up
Exam 3 / Final
5.1 Eigenvectors and eigenvalues
5.2 The characteristic equation
5.3 Diagonalization
Sections 5.1, 5.2, 5.3
5.4 Eigenvectors and linear transformations
6.1 Inner products
6.2 Orthogonal sets
Section 5.4, 6.1, 6.2
Week 12:
Mid-term 2 (on Chapters 4 – 5)
6.3 Orthogonal projections
Week 13:
6.4 Gram-Schmidt process
6.5 Least squares problem
Exam 3 / Final
Section 6.3
Exam 3 / Final
Exam 3 / Final
Sections 6.4, 6.5, 7.1
7.1 Diagonalization of symmetric
matrices
Week 14:
7.2 Quadratic forms Catchup/Revision
Section 7.2
Exam 3 / Final
Note: Alterations to the above literature may occur through the semester and additional handouts or
films/slides may be utilized.
Class Rules & Discipline
Classroom Etiquette
Cellular phones must be turned off during instruction in the classrooms and laboratories. The first
failure to respect this rule results in a warning. If a student chooses to disregard the warning the
student will be dismissed from class.
Students are also required to use proper social and professional etiquette when using e-mail. Use of the
Phoenicia University network implies consent for monitoring of traffic, which is necessary for smooth
administration of the resource. Phoenicia University does not overlook the use of inappropriate
language when writing messages to instructors, staff, or students. Student initiated messages to mass
audiences that are not part of the normal instructional process are prohibited.
ACADEMIC INTEGRITY
CHEATING
Cheating on exams or other work submitted in fulfillment of course requirements will result in
disciplinary action. Cheating discovered during an exam will result in the exam being collected and
the student being dismissed with instructions for a meeting with the faculty member.
PLAGIARISM
Plagiarism is the presentation of someone else’s ideas or words as your own. Paraphrasing or extensive
rewriting of another’s work is still plagiarism if credit is not given to the author and a citation of where
the information can be found is not listed. This also applies to ideas or words borrowed from the
Internet.
A student who presents a plagiarized work is subject to disciplinary action. A faculty member who
discovers that plagiarized work has been submitted in fulfillment of course requirements will
immediately inform the student and will give the student an opportunity to explain. Students guilty of
plagiarism will be severely penalized. Penalties range from a failing grade to suspension.
SABOTAGE
Students destroying, damaging, or stealing another’s work or working materials (including laboratory
experiments, computer programs, and term papers etc..) are subject to appropriate disciplinary
measures.
FALSIFICATION
Students who misrepresent material or fabricate information in an academic exercise or assignment
(e.g., false or misleading citations, falsification of experiments or computer data) will be held
accountable.
STUDENT ATTENDANCE
Student Attendance is Mandatory. Students are expected to attend all classes, laboratories, or required
fieldwork. Adequate measures will be taken concerning unjustified attendance as per the University’s
rules and regulations.
No student is allowed to attend a class if his/her name does not appear on the class roster.
If a student is absent for more than 25% of the class sessions, he/she will be withdrawn from the class
and will receive a ‘W (Withdraw)’ grade for the course. If a student misses 25% percent of class
sessions after the withdrawal deadline, he/she will receive an ‘F (Failed)’ grade for the course.
The Academic Progress Committee (APC) has the sole discretion to grant exceptions for students
whose attendance has been significantly impacted by exceptional circumstances. The Office of the
Registrar will require supporting and credible evidence before any exceptions can be considered.