Elementary Mathematics Education  
Bachelor  Length of the Programme: 4  Number of Credits: 240  TRNQFHE: Level 6  QFEHEA: First Cycle  EQF: Level 6 
School/Faculty/Institute  Faculty of Education  
Course Code  MATH 239  
Course Title in English  Linear Algebra  
Course Title in Turkish  Linear Algebra  
Language of Instruction  EN  
Type of Course  Tersyüz öğrenme  
Level of Course  Seçiniz  
Semester  Fall  
Contact Hours per Week 


Estimated Student Workload  145 hours per semester  
Number of Credits  7 ECTS  
Grading Mode  Standard Letter Grade  
Prerequisites 
MATH 139  Introduction to Discrete Mathematics 

Corequisites  None  
Expected Prior Knowledge  None  
Registration Restrictions  Only Undergraduate Students  
Overall Educational Objective  To learn the fundamentals of matrix theory and linear algebra relevant to engineering problems.  
Course Description  This course provides general concepts on linear algebra by covering the following topics: Systems of linear equations and matrices, Gaussian elimination, matrix algebra, inverse of a matrix, elementary matrices, LUfactorization, the determinant of a square matrix, the properties of determinants, Cramer’s rule, vector spaces, subspaces, linear independence, basis and dimension, change of basis, inner product spaces, orthonormal basis, linear transformations, matrix representations of linear transformations, eigenvalues and eigenvectors, diagonalization. 
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) solve the systems of linear equations by using Gauss elimination; 2) compute the inverse of a square matrix and solve the systems of linear equations by using matrix inversion; 3) compute the determinant of a matrix and solve the systems of linear equations by using Cramer's rule; 4) comprehend the concepts span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces; 5) comprehend linear transformations and compute their matrix representations; 6) compute the eigenvalues and the corresponding eigenvectors of a matrix. 
Program Learning Outcomes/Course Learning Outcomes  1  2  3  4  5  6 

1) Apply effective and studentcentered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills.  
2) Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics.  
3) Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics.  
4) Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs.  
5) Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning.  
6) Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness.  
7) Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multidisciplinary as well as take individual responsibility when they work alone.  
8) Have awareness of need for lifelong learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways.  
9) Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources.  
10) Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio.  
11) Have awareness of and sensitivity to different cultures, values and students’ democratic rights.  
12) Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws.  
13) Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities.  
14) Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. 
N None  S Supportive  H Highly Related 
Program Outcomes and Competences  Level  Assessed by  
1)  Apply effective and studentcentered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills.  N  
2)  Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics.  N  
3)  Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics.  H  Exam,Derse Katılım,Proje 
4)  Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs.  H  Proje 
5)  Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning.  N  
6)  Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness.  N  
7)  Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multidisciplinary as well as take individual responsibility when they work alone.  H  Select,Derse Katılım,Proje 
8)  Have awareness of need for lifelong learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways.  S  Select,Derse Katılım,Proje 
9)  Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources.  N  
10)  Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio.  S  Derse Katılım,Proje 
11)  Have awareness of and sensitivity to different cultures, values and students’ democratic rights.  N  
12)  Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws.  N  
13)  Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities.  N  
14)  Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology.  N 
Prepared by and Date  HASAN KÖRÜK , 
Course Coordinator  BENGİ BİRGİLİ 
Semester  Fall 
Name of Instructor  Prof. Dr. MUSTAFA LUTFİ ÖVEÇOĞLU 
Week  Subject 
1)  Matrices and Systems of Equations 
2)  Matrices and Systems of Equations 
3)  Matrices and Systems of Equations 
4)  Matrices and Systems of Equations 
5)  Determinants 
6)  Determinants 
7)  Vector Spaces 
8)  Vector Spaces 
9)  Vector Spaces 
10)  Inner Product Spaces 
11)  Linear Transformations 
12)  Linear Transformations 
13)  Eigenvalues and Eigenvectors 
14)  Eigenvalues and Eigenvectors 
15)  Final Exam/Project/Presentation Period 
16)  Final Exam/Project/Presentation Period 
Required/Recommended Readings  David C. Lay et al., Linear Algebra and Its Applications, Pearson, 5th edition/Global edition, 2016. Elementary Linear Algebra, Ron Larson, Cengage Learning, 7th or 8th edition (ebook or hardcopy).  
Teaching Methods  Lectures using “flipped classroom” as an active learning technique.  
Homework and Projects  Online quizzes/HWs will be assigned.  
Laboratory Work  
Computer Use  
Other Activities  
Assessment Methods 


Course Administration 
korukh@mef.edu.tr Dr. Hasan Körük Instructor’s office and phone number: A Block5th Floor / 0212 3953654 Office hours: Monday 10:0012:00 Email address: korukh@mef.edu.tr Dr. Leyla Parlar Ateş Instructor’s office and phone number: A Block4th Floor / 0212 3953600 Office hours: Wednesday 13:0015:00 Email address: atesl@mef.edu.tr Rules for attendance: Classroom participation contributes to 12% of the final grade. Missing a quiz/HW: No makeup will be given. Missing a midterm: Provided that proper documents of excuse are presented, makeup will be given. A reminder of proper classroom behavior, code of student conduct: YÖK Regulations. Academic dishonesty and plagiarism: YÖK Regulations. 
Activity  No/Weeks  Hours  Calculation  
No/Weeks per Semester  Preparing for the Activity  Spent in the Activity Itself  Completing the Activity Requirements  
Course Hours  14  2  3  1  84  
Homework Assignments  3  2  1  9  
Quiz(zes)  2  2  1  6  
Midterm(s)  2  20  3  46  
Total Workload  145  
Total Workload/25  5.8  
ECTS  7 