Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course To introduce students with basic concepts and properties related with matrices, linear systems and abstract spaces. To show the use of theoretical knowledge in solving some applied problems. To establish elementary background for more advanced study in linear algebra. To develop problem solving skills and motivate students for doing research and use different literature when learning the course.
Course Content Matrices. Elementary Row Operations. Systems of Linear Equations. Gauss Ellimintaion Method. Matrix Algebra. Square and Invertible Matrices. Techniques for finding matrix inverse. Determinants. Cramer's Rule. LU and Cholesky decompositions. Vector Spaces. Subspaces. Linear independence. Basis and Dimension. Rank-Nullity Theorem. Eigenvalues and Eigenvectors. Diagonalization of Matrices. Similar Matrices. Application to Difference and Differential Equations. Jordan Normal Form.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Şirin ATILGAN BÜYÜKAŞIK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources "Elementary Linear Algebra", Applications Version, H. Anton, C. Rorres, A. Kaul, 12-th Edition, Wiley.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 3 % 10
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 52 52
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 64 64
Exams and Exam Preparations 1 64 64
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 to be able to do basic algebraic operations with matrices
2 to be able to solve systems of linear equations using matrices
3 to be able to recognize vector spaces and their properties
4 to be able to find the eigenvalues and eigenvectors of matrices
5 to be able to solve problems using matrix diagonalization

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction. Linear systems and matrices. Chapter 1.1
2 Elementary Row Operartions. Gaussian Elimination Method. Chapter 1.2
3 Matrix Algebra Chapter 1.3
4 Inverse of a Square Matrix. Techniques for Finding Matrix Inverse. Chapter 1.4, 1.5
5 Determinants. Cramer's Rule. Chapter 2.1, 2.2, 2.3
6 LU and Cholesky decompositions Chapter 9.1
7 Vector Spaces and Subspaces Chapter 3.1, 4.1, 4.2
8 Spanning Sets. Linear Independence. Chapter 4.3 and 4.4
9 Basis and Dimension Chapter 4.5, 4.6, 4.7
10 Row, Column and Null Spaces. Rank-Nullity Theorem Chapter 4.8, 4.9
11 Eigenvalues and Eigenvectors of Matrices Chapter 5.1, 5.2
12 Diagonalization of Matrices Chapter 5.2, 5.3
13 Applications. Difference and Differential Equations Chapter 5.4
14 Jordan Normal Form

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 3 3 4 4
C2 3 3 3 2
C3 3 3 3 4 3 4 2
C4 3 4 3 4 4 3
C5 3 3 4 3 4 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant