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 related with the abstract spaces and linear operators. To teach the spectral properties of some special matrices. To show the use of theoretical knowledge in solving some applied problems. To give elementary background for more advanced study in linear algebra. To motivate students to do research and use different literature when learning the course
Course Content Inner Product Spaces. Orthınormal Bases. Orthogonal Projections. Gram-Shmidt Process. Best Approximation. Least Squares. Orthogonal Matrices. Orthogonal Diagonalization. Real Quadratic Forms. Optimization Using Quadratic Forms. Hermitian, Normal, and Unitary Matrices. Unitary Diagonalization. General Linear Transformations. Matrix Representation of Linear Transformations. Singular Value Decomposition. Polar Decomposition. Linear Programming. Selected Applications.
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 have knowledge about inner product spaces
2 to be able to fing orthogonal basis and use it in problem solving
3 to be able to solve problems related to special matrices
4 to have knowledge about linear transformations
5 to be able to use theoretical knowledge for solving problems

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Inner Product Spaces, Orthonormal Basis. Chapter 6.1 and 6.2
2 Orthogonal Projections. Gram-Schmidt Process. Chapter 6.3
3 Best Approximation. Least Squares Chapter 6.4
4 Orthogonal Matrices. Orthogonal Diagonalization. Chapter 7.1 and 7.2
5 Real Quadratic Forms Chapter 7.3
6 Optimization Using Quadratic Forms Chapter 7.4
7 Hermitian, Normal and Unitary Matrices. Unitary Diagonalization. Chapter 7.5
8 General Linear Transformations Chapter 8.1 and 8.2
9 Matrix Representation of Linear Transformations Chapter 8.3, 8.4, 8.5
10 Singular Value Decomposition Chapter 9.4 ve 9.5
11 Polar Decomposition Chapter 9.4 ve 9.5
12 Linear Programming
13 Simplex Method
14 Applications
15 Final 1st week
16 Final 2nd week

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

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