MAT5003 Linear Algebra and Its ApplicationsBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5003 Linear Algebra and Its Applications Fall
Spring
3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. ERTUĞRUL ÖZDAMAR
Recommended Optional Program Components: None
Course Objectives: The purpose of this course is to give the basic concepts of linear algebra with applications to students who intend to study applied mathematics.

Learning Outcomes

The students who have succeeded in this course;
The students who succeeded in this course;
o will be able to describe solution methods for systems of linear equations.
o will be able to apply the fundamental properties of determinants to solve the systems of equations, inverting matrices and also to decide whether a subset is linearly independent or not, spans the space or does not.
o will be able to apply concepts of vector spaces to all relating areas including matrices.
o will be able to formulate the change of basis , to obtain an orthonormal basis and to diagonalize a square matrix, to develop matrix representation of linear mappings.
o will be able to distinguish the subsets that span the space or not , are linear independent or not, and the matrices are orthogonal diagonalizable or not, mappings are linear or not.
o will be able to use determinants to solve the systems of equations, inverting matrices and also to evaluate the eigen vectors , effectively.
o will be able to write equations of Curves and Surfaces passing through given points and apply linear algebra to Leontief economic model applications, Geometric Programming, Cryptography.

Course Content

.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Systems of linear equations, network analysis, Balancing Chemical Equations, Design of Traffic Patterns
2) Matrices, LU decomposition,
3) Vector spaces,subspaces, bases and the dimension
4) Determinants, multilinear functions , Cramer systems
5) Inner product spaces, orthonormal sets, QR decomposition, least squares method
6) Linear mappings, space of linear mappings
7) Matrices and linear mappings
8) Matrix polynomials, characteristic values, characteristic vectors, diagonalization of matrices
9) Applications; genetics, population problems
10) Qudratic forms, geometric applications
11) Special mappings of iner product spaces
12) Equation of curves and surfaces passing through given points, geometric programming
13) Cryptography
14) Leontief economical models

Sources

Course Notes / Textbooks: .
References: .

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 14 % 5
Homework Assignments 2 % 10
Midterms 1 % 35
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Homework Assignments 2 40 80
Midterms 1 30 30
Final 1 40 40
Total Workload 192

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other. 3
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. 4
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. 2
4) Ability to make individual and team work on issues related to working and social life. 4
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. 3
6) Ability to use mathematical knowledge in technology. 5
7) To apply mathematical principles to real world problems. 4
8) Ability to use the approaches and knowledge of other disciplines in Mathematics. 5
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. 4
10) To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. 4
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 3
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, 5