INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
COURSE OUTLINE
Kulliyyah
Science
Department
Computational and Theoretical Sciences
Programme
Mathematical Sciences (BMathSc)
Name of Course / Model
Linear Algebra
Course Code
SMS 1205
Name (s) of Academic staff /
Instructor(s)
Asst. Prof. Dr. Mansoor Saburov
This core course is necessary to provide the fundamental concepts of system of
Rationale for the inclusion of
linear equations, matrices, determinants, the finitne dimensional vector spaces,
the course / module in the
the finite dimensional inner product spaces, eigenvalue and eigenvector
programme
problems.
Proposed Start Date
February 2014
Batch of Student to be
Affected
Batch 131 onwards
Contact Learning Time
42
20
Consultation/PBL/
Seminar
Lecture
Total Student Learning Time
(SLT)
Studentcentered
learning
Practical/tutorial
Teachercentered
14
Independent
Learning Activities
14
8
Formal
assessment
12
5
5
Conversion of SLT into tentative credit (TOTAL ÷ 40)
Credit to be assigned to the course
Credit Value / Hours
3 (3+0)
Pre-requisites (if any)
Nil
Total SLT
Year One Undergraduate
Final exam
Level
Continuous assessment
Core Course
Preparation for assessment
Status
Assignment
Semester 2
Non face-to-face learning
(e.g. : assignment, module,
project)
Semester and Year Offered
120
3.0
3
SMS 1205 - Page 1 of 5
Co-requisites (if any)
Nil
Course Objectives
The objectives of the course are to:
1. Provide a foundation of the theory of matrices, determinants, and
solving of system of equations;.
2. Provide an axiomatic theory of the finite dimensional vector spaces,
inner product spaces, and linear operators acting on them;
3. Expose the spectral theory of matrices (linear operators)
4. Provide an language and a powerful framework for posing and solving
important applied problems encountered in various fields of
mathematical science.
Upon completion of this course, students should be able to:
Learning Outcomes
1. Identify systems of linear equations, matrices, vector spaces, linear
transformations and Solve systems of linear equations (PO1, PO3,
PO4, PO5, PO7, PO9, CTPS3, C1, CS3, C3, P3, A3)
2. Understand properties of matrices and determinants. (PO1, PO3, PO4,
PO5, PO7, PO9, CTPS3, LL2, C3, P3, A3)
3. Formulate axioms and prove theorems on vector spaces. (PO1, PO3,
PO4, PO5, PO7, PO9, CTPS3, LL3, C3, P3, A3)
4. Inner product Space and Orthogonal Basis (PO1, PO3, PO4, PO5,
PO7, PO9, CTPS3, LL3, C3, P3, A3)
5. Apply linear transformations, eigenvalues and eigenvectors. (PO1,
PO3, PO4, PO5, PO7, PO9, CTPS3, CS3, LL2, C3, P3, A3)
Transferable Skills:
Assignment
Tutorial
√
Communication
Critical Thinking /
Problem solving
Creativity /
Inovation
ICT / Information
Management
Teamwork
Teaching-Learning and
assessment strategy
Quiz
Exam
Skill
No.
1
2
3
Presentation
Skills and how they are developed and assessed, project and practical
experience and internship
Assessment
How skills are developed
√
√
Teaching-Learning
Lecture
Tutorial
Practical /Presentation
√
√
√
√
√
√
√
√
Oral presentation, Group
Discussion, Short answer
Group discussion,
Tutorials
Oral presentation,
Tutorials
Collecting data and
information for report
Group presentation,
Laboratory
Assessment
Quiz, Assignment, Exam
Quiz, Q & A
Write-up / Report
SMS 1205 - Page 2 of 5
Course Synopsis
Systems of linear equations. Matrices. Determinants. Vector spaces. Rank and
dimension. Inner product space. Linear transformations. Orthogonality.
Eigenvalues. Diagonalisation of real symmetric matrices. Applications.
Mode of Delivery
Lecture, Tutorial, Practical/Presentation, Quizzes, Assignments
LO
Assessment Methods and
1, 2, 3, 4,5
Type / Course Assessment
State weightage of each type of 1, 2, 3, 4, 5
assessment.
1,2,3
3,4,5
Method
%
20
10
30
40
100
Assignments
Quizzes
Mid-term test
Final examination
Total
Mapping of course / module to the Programme Learning Outcomes
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√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
4. Inner product Space and Orthogonal Basis.
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√
√
√
√
√
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5. Apply linear transformations, eigenvalues and eigenvectors.
√
√
√
√
√
√
√
√
PO 10
PO 7
√
3. Formulate axioms and prove theorems on vector spaces.
PO 9
PO 6
PO 8
PO 5
linear transformations and Solve systems of linear equations.
2. Understand properties of matrices and determinants.
PO 4
1. Identify systems of linear equations, matrices, vector spaces,
PO 3
PO 1
Learning Outcome of the course
PO 2
Programme Outcomes
√
Content outline of the course / module and the SLT per topic
1
2
System of linear equations
Introduction to Systems of Linear
Equations, System of linear
equations, Gaussian Elimination
Matrices:
Operation with Matrices and
Properties. The Inverse of the
matrices, Elementary Matrices
3
3
1
1
2
2
1
1
1
1
Review for
test/quiz
Assessment
(quizzes/mid
sem/final
Assignment
Self Study
Practical/
Others
Tutorial
Topics
Lecture
Weeks
Learning Hours
0
0
0
0
Task/Reading
Chapter 1
Lay D.C. or
Larson&Falvo
Chapter 2
Lay D.C. or
Larson&Falvo
SMS 1205 - Page 3 of 5
3
4
5
6
7-8
9
10
11
12-13
14
Determinants:
Determinants and Properties of
Determinant. Evaluating the
Inverse of the Matrices, Solving
System of Equation
Vector spaces:
Definition of Vector Space,
Subspace, Examples
Linear dependence and
independence
Spanning sets, Linear dependence
and independence, Basis and
Dimension
Rank of Matrices
Rank of Matrices, System of
Equations, Kronecker –Capelli
theorem
Inner product spaces
Inner product space, Angle
between vectors, Cauchy-Schwarz
inequality, Pythagorean theorem
Gram-Schmidt Process
Orthonormal basis, Gram-Schmidt
Process
Linear Transformations:
Linear transformations, null space
and range, the relation between
null space and range
Matrix of Linear
Transformation
Matrix of Linear Transformation,
Matrix of changing bases,
Similarity
Eigenvalues and eigenvectors
Eigenvalues and eigenvectors,
Characteristic Equation,
Diagonalization
Symmetric Matrices
Symmetric Matrix, Orthogonal
Matrix, Orthogonal
Diagonalization
TOTAL
Chapter 3
Lay D.C. or
Larson&Falvo
3
3
1
1
1
1
1
1
0
0
1
1
1
1
Chapter 4
Lay D.C. or
Larson&Falvo
Chapter 4
Lay D.C. or
Larson&Falvo
3
3
1
1
2
2
1
1
1
1
0
0
0
0
6
2
2
2
0
2
2
3
1
2
1
1
0
0
3
1
2
1
1
0
0
Chapter 4
Lay D.C. or
Larson&Falvo
Chapter 6
Lay D.C. or
Chapter 5
Larson&Falvo
Chapter 6
Lay D.C. or
Chapter 5
Larson&Falvo
Chapter 6
Larson&Falvo
Chapter 6
Larson&Falvo
3
6
1
2
1
2
1
2
0
0
1
2
1
2
3
1
1
1
0
1
1
42
14
20
14
6
8
8
Required Learning Duration
Chapter 5
Lay D.C. or
Chapter 7
Larson&Falvo
Chapter 7
Lay D.C. or
Larson&Falvo
112
Main references supporting the course
Required
Lay D.C. (2012). Linear Algebra and Its Applications (2nd Ed.), Addison Wesley
Larson R. & Falvo D. (2009) Elementary Linear Algebra (6th Ed.), Houghton Mifflin Harcourt.
Springer-Verlag Berlin Heidelberg.
SMS 1205 - Page 4 of 5
Additional references supporting the course
Recommended
Thomas S. Shores (2007) Applied Linear Algebra and Matrix Analysis (6th Ed.) Springer.
Johnson L.W., Riess R.D. & Arnold J.T. (1997). Introduction to Linear Algebra (4th Ed.), AddisonWesley.
Prepared by:
Checked by:
Approved by:
Dr. Mansoor Saburov
Lecturer, CTS
Kulliyyah of Science
Dr. Pah Chin Hee
Head of CTS
Kulliyyah of Science
Prof. Dr. Kamaruzzaman Yunus
Dean
Kulliyyah of Science
SMS 1205 - Page 5 of 5