SECTION I: GENERAL INFORMATION ABOUT THE COURSE

Course Code	Course Name	Year	Semester	Theoretical	Practical	Credit	ECTS
CME6112	Linear Algebra	2	Spring	2	1	3	6

Course Type :	Compulsory
Cycle:	Bachelor TQF-HE:6. Master`s Degree QF-EHEA:First Cycle EQF-LLL:6. Master`s Degree
Language of Instruction:	English
Prerequisities and Co-requisities:	N/A
Mode of Delivery:	Face to face
Name of Coordinator:	Dr. Öğr. Üyesi DÜRDANE YILMAZ
Dersin Öğretim Eleman(lar)ı:	Dr. Öğr. Üyesi DÜRDANE YILMAZ
Dersin Kategorisi:	Field Specific

SECTION II: INTRODUCTION TO THE COURSE

Course Objectives & Content

Course Objectives:

The objective of this course is to provide students with a solid foundation in the fundamental concepts and methods of linear algebra, enabling them to solve systems of linear equations, analyze vector and matrix structures, model linear transformations, and interpret eigenvalue problems.

The course aims to develop students’ ability to formulate engineering and scientific problems mathematically, select appropriate solution techniques, and interpret the results in the context of practical applications.

In this respect, the course supports the development of students’ analytical thinking, problem-solving skills, and mathematical modeling competencies, which are essential for engineering practice and advanced studies.

Course Content:

Introduction to linear algebra and its applications in engineering and science

Systems of linear equations and solution methods

Matrix algebra: operations, inverses, and determinants

Gaussian and Gauss–Jordan elimination

Vector spaces and subspaces

Linear independence, basis, and dimension

Linear transformations and matrix representations

Rank and nullity

Eigenvalues and eigenvectors

Diagonalization of matrices

Inner product spaces

Orthogonality, projections, and least squares method

Applications of linear algebra in engineering and data analysis

Course Learning Outcomes (CLOs)

Course Learning Outcomes (CLOs) are those describing the knowledge, skills and competencies that students are expected to achieve upon successful completion of the course. In this context, Course Learning Outcomes defined for this course unit are as follows:



Knowledge *(Described as Theoritical and/or Factual Knowledge.)*
1) Explain the fundamental concepts of linear algebra, including vectors, matrices, and systems of linear equations.
Skills *(Describe as Cognitive and/or Practical Skills.)*
1) Solve systems of linear equations using appropriate analytical methods and interpret the solutions.
2) Analyze vector spaces and linear transformations and represent them using matrix formulations.
3) Compute eigenvalues and eigenvectors and apply them to basic engineering and scientific problems.
Competences *(Described as "Ability of the learner to apply knowledge and skills autonomously with responsibility", "Learning to learn"," Communication and social" and "Field specific" competences.)*
1) Apply linear algebra techniques effectively to solve engineering and scientific problems.

Weekly Course Schedule

Week	Subject	Materials Sharing *
		Related Preparation	Further Study
1)	Introduction to Linear Algebra and Applications in Engineering
2)	Linear equation systems
3)	Matrices and matrix operations
4)	Gauss and Gauss–Jordan elimination methods
5)	Determinant and inverse matix
6)	Vectors and vector spaces
7)	Subspaces, linear dependency and independency
8)	Span, basis and dimension
9)	Linear transformation and matrix demonstration
10)	Rank and nullity
11)	Eigenvalues and eigenvectors
12)	Matrix Diagonalization
13)	Inner Product Spaces
14)	Orthogonal Projections and Least-squares Problem

*These fields provides students with course materials for their pre- and further study before and after the course delivered.

DERS ÖĞRENME ÇIKTILARI - PROGRAM ÖĞRENME ÇIKTILARI İLİŞKİSİ

Contribution of The Course Unit To The Programme Learning Outcomes

Ders Öğrenme Çıktıları (DÖÇ)	1	2	3	4	5
Program Öğrenme Çıktıları (PÖÇ)
1) Has sufficient knowledge in mathematics, science and management engineering; use theoretical and applied knowledge in these fields together to solve Management Engineering problems
1) Uses and applies theoretical and applied sciences in the field of basic science subjects for the solution of management engineering problems.
1) Works effectively individually and in multi-disciplinary teams, takes responsibility
1) Acquires the analyzing solving the problems and managing the conflicts.
1) Experiences all processes in business life.
1) Identifies, defines, formulates and solves complex Management Engineering problems; for this purpose selects and applies appropriate analytical and modeling methods
2) Participates as a team member and takes responsibility in the environments that require the solving of the conflicts and acts as a leader when necessary.
2) Takes part in activities related to the field of education in a business operating in the field.
2) Accesses information and for this purpose searches for resources, uses databases and other information resources
2) Analyzes Management Engineering applications, designs and develops models to meet specific requirements under realistic constraints and conditions. For this purpose, it selects and uses appropriate methods, tools and technologies.
2) Designs a complex system, process, device or product to meet certain requirements under realistic constraints and conditions; applies modern design methods for this purpose
3) Selects and uses modern techniques and tools required for engineering applications; uses information technologies and at least one computer software (European Computer Driving License Advanced Level) effectively
3) Owns the competencies required by the constantly developing field of management engineering and the global competitive environment.
3) Has awareness of the necessity of lifelong learning, follows developments in science and technology and renews itself continuously
3) Questions the application with theoretical knowledge.
3) Has awareness for ethical and social responsivity.
4) By supporting the learnt courses with quantitative and qualitative data; and by using verbal and visual communication means, s/he transfers them to the groups within and outside his/her group in a systematical and effective way.
4) Compiles the knowledge and experience gained in the field.
4) Applies the theoretical knowledge in business life during a semester.
4) Designs experiments, conducts experiments, collects data, analyzes and interprets the results for the investigation of engineering problems
4) Communicates effectively in Turkish, both orally and in writing, has at least one foreign language knowledge at the level of European Language Portfolio B1
5) Designs, develops, implements integrated systems for the production of concrete or abstract outputs containing people, materials, information, equipment and energy; controls and improves the operation of these systems
5) S/he acquires the competencies that develop by the expectations of business world and the society defined as the institutional outcomes of our university on the advanced level in relation with his/her field.
5) Evaluates the norms and standards present in the works in which s/he takes responsibility in a critical point of view.
5) Manages projects, has conscious of workplace practices, employee health, environmental and work safety; aware of the legal consequences of engineering applications
6) Develops strategical, innovative and entrepreneurial ideas.
6) Has awareness of the universal and social effects of engineering solutions and applications; has awareness of entrepreneurship and innovativeness and knowledgeable about contemporary issues
7) Acquires competence of managing the change.
7) Has professional and ethical responsibility
8) Shows development personally and socially with and awareness for lifelong learning.
8) Has consciousness of the concept of quality
9) Follows advanced technologies and developments about digital transformation.
9) Has entrepreneurship awareness to undertake the establishment process of a business
10) Has cultural awareness and s/he transfers this to the groups within and outside his/her field.
11) Has awareness about citizenship competency.
12) Acquires communication in a Foreign Language (English) competence defined on the level of at least B1 in European Language Portfolio. (In programs whose medium of instruction is English, on the level of B2/B2+).

SECTION III: RELATIONSHIP BETWEEN COURSE UNIT AND COURSE LEARNING OUTCOMES (CLOs)

Level of Contribution of the Course to PLOs

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Programme Learning Outcomes	Contribution Level (from 1 to 5)
1)	Has sufficient knowledge in mathematics, science and management engineering; use theoretical and applied knowledge in these fields together to solve Management Engineering problems	2
1)	Uses and applies theoretical and applied sciences in the field of basic science subjects for the solution of management engineering problems.	3
1)	Works effectively individually and in multi-disciplinary teams, takes responsibility	1
1)	Acquires the analyzing solving the problems and managing the conflicts.	2
1)	Experiences all processes in business life.
1)	Identifies, defines, formulates and solves complex Management Engineering problems; for this purpose selects and applies appropriate analytical and modeling methods	3
2)	Participates as a team member and takes responsibility in the environments that require the solving of the conflicts and acts as a leader when necessary.
2)	Takes part in activities related to the field of education in a business operating in the field.
2)	Accesses information and for this purpose searches for resources, uses databases and other information resources	2
2)	Analyzes Management Engineering applications, designs and develops models to meet specific requirements under realistic constraints and conditions. For this purpose, it selects and uses appropriate methods, tools and technologies.	2
2)	Designs a complex system, process, device or product to meet certain requirements under realistic constraints and conditions; applies modern design methods for this purpose	3
3)	Selects and uses modern techniques and tools required for engineering applications; uses information technologies and at least one computer software (European Computer Driving License Advanced Level) effectively	1
3)	Owns the competencies required by the constantly developing field of management engineering and the global competitive environment.
3)	Has awareness of the necessity of lifelong learning, follows developments in science and technology and renews itself continuously
3)	Questions the application with theoretical knowledge.	1
3)	Has awareness for ethical and social responsivity.
4)	By supporting the learnt courses with quantitative and qualitative data; and by using verbal and visual communication means, s/he transfers them to the groups within and outside his/her group in a systematical and effective way.
4)	Compiles the knowledge and experience gained in the field.
4)	Applies the theoretical knowledge in business life during a semester.
4)	Designs experiments, conducts experiments, collects data, analyzes and interprets the results for the investigation of engineering problems	2
4)	Communicates effectively in Turkish, both orally and in writing, has at least one foreign language knowledge at the level of European Language Portfolio B1
5)	Designs, develops, implements integrated systems for the production of concrete or abstract outputs containing people, materials, information, equipment and energy; controls and improves the operation of these systems
5)	S/he acquires the competencies that develop by the expectations of business world and the society defined as the institutional outcomes of our university on the advanced level in relation with his/her field.
5)	Evaluates the norms and standards present in the works in which s/he takes responsibility in a critical point of view.
5)	Manages projects, has conscious of workplace practices, employee health, environmental and work safety; aware of the legal consequences of engineering applications
6)	Develops strategical, innovative and entrepreneurial ideas.
6)	Has awareness of the universal and social effects of engineering solutions and applications; has awareness of entrepreneurship and innovativeness and knowledgeable about contemporary issues
7)	Acquires competence of managing the change.
7)	Has professional and ethical responsibility
8)	Shows development personally and socially with and awareness for lifelong learning.
8)	Has consciousness of the concept of quality
9)	Follows advanced technologies and developments about digital transformation.
9)	Has entrepreneurship awareness to undertake the establishment process of a business
10)	Has cultural awareness and s/he transfers this to the groups within and outside his/her field.
11)	Has awareness about citizenship competency.
12)	Acquires communication in a Foreign Language (English) competence defined on the level of at least B1 in European Language Portfolio. (In programs whose medium of instruction is English, on the level of B2/B2+).

SECTION IV: TEACHING-LEARNING & ASSESMENT-EVALUATION METHODS OF THE COURSE

Teaching & Learning Methods of the Course

(All teaching and learning methods used at the university are managed systematically. Upon proposals of the programme units, they are assessed by the relevant academic boards and, if found appropriate, they are included among the university list. Programmes, then, choose the appropriate methods in line with their programme design from this list. Likewise, appropriate methods to be used for the course units can be chosen among those defined for the programme.)

Teaching and Learning Methods defined at the Programme Level	Teaching and Learning Methods Defined for the Course
Problem Solving

Assessment & Evaluation Methods of the Course

(All assessment and evaluation methods used at the university are managed systematically. Upon proposals of the programme units, they are assessed by the relevant academic boards and, if found appropriate, they are included among the university list. Programmes, then, choose the appropriate methods in line with their programme design from this list. Likewise, appropriate methods to be used for the course units can be chosen among those defined for the programme.)

Aassessment and evaluation Methods defined at the Programme Level	Assessment and Evaluation Methods defined for the Course
Midterm
Final Exam
Quiz

Contribution of Assesment & Evalution Activities to Final Grade of the Course

Measurement and Evaluation Methods	# of practice per semester	Level of Contribution
Quizzes	2	% 15.00
Midterms	1	% 35.00
Semester Final Exam	1	% 50.00
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
Total		% 100

SECTION V: WORKLOAD & ECTS CREDITS ALLOCATED FOR THE COURSE

WORKLOAD OF TEACHING & LEARNING ACTIVITIES
Teaching & Learning Activities	# of Activities per semester	Duration (hour)	Total Workload
Course	14	3	42
Laboratory	0	0	0
Application	0	0	0
Special Course Internship (Work Placement)	0	0	0
Field Work	0	0	0
Study Hours Out of Class	14	2	28
Presentations / Seminar	0	0	0
Project	0	0	0
Homework Assignments	0	0	0
Total Workload of Teaching & Learning Activities	-	-	70
WORKLOAD OF ASSESMENT & EVALUATION ACTIVITIES
Assesment & Evaluation Activities	# of Activities per semester	Duration (hour)	Total Workload
Quizzes	2	12	24
Midterms	1	20	20
Semester Final Exam	1	30	30
Total Workload of Assesment & Evaluation Activities	-	-	74
TOTAL WORKLOAD (Teaching & Learning + Assesment & Evaluation Activities)			144
ECTS CREDITS OF THE COURSE (Total Workload/25.5 h)			6

Course Notes / Textbooks:	Linear Algebra With Applications by Steven J. Leon 8th Edition
References: