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Course Detail

Course Description

CourseCodeSemesterT+P (Hour)CreditECTS
LINEAR ALGEBRA II-Spring Semester2+022
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of CourseTurkish
Course LevelFirst Cycle (Bachelor's Degree)
Course TypeRequired
Course CoordinatorAssist.Prof. Damla SÖNMEZ
Name of Lecturer(s)Assist.Prof. Alaattin PUSMAZ
Assistant(s)
AimWith this course, it is aimed that students will be able to explain dimensions of spaces; explain base-dimension change; explain matrix transformations; explain eigenvalues and eigenvectors; explain inner product space; explain orthogonality.
Course ContentThis course contains; 2-Space, 3-Space and Vectors in n-Space,Norm, Scalar Product and Distance in Rn,Orthogonality,Geometry of Linear Systems, Vector Product,Space, Subspace, Linear Unions, linear dependence and independence,Coordinates and bases, Dimension, Base Change,Row Space, Column Space and Zero Space, Rank Zero and Basic Matrix Spaces,Matrix Transformations from Rn to Rm, Properties of Matrix Transformations,Geometry of Matrix Operators on R2,Eigenvalues and Eigenvectors, Diagonalization,Inner Product Spaces, Angle and Orthogonality in Inner Product Spaces,Gram-Schmidt Method, QR-Separation,Best Approximation, Least Squares,Orthogonal Matrices, Orthogonal Diagonalization.
Dersin Öğrenme KazanımlarıTeaching MethodsAssessment Methods
Explains the properties of vector space and subspace.12, 16, 9A
Explains the concepts of linear dependence, independence and solves related problems.12, 16, 9A
Explains the basic concepts of inner product spaces.12, 16, 9A
Solves problems related to eigenvalues and eigenvectors.12, 16, 9A
Solves problems related to linear transformations.12, 16, 9A
Teaching Methods:12: Problem Solving Method, 16: Question - Answer Technique, 9: Lecture Method
Assessment Methods:A: Traditional Written Exam

Course Outline

OrderSubjectsPreliminary Work
12-Space, 3-Space and Vectors in n-Space[1], [2], [3]
2Norm, Scalar Product and Distance in Rn[1], [2], [3]
3Orthogonality[1], [2], [3]
4Geometry of Linear Systems, Vector Product[1], [2], [3]
5Space, Subspace, Linear Unions, linear dependence and independence[1], [2], [3]
6Coordinates and bases, Dimension, Base Change[1], [2], [3]
7Row Space, Column Space and Zero Space, Rank Zero and Basic Matrix Spaces[1], [2], [3]
8Matrix Transformations from Rn to Rm, Properties of Matrix Transformations[1], [2], [3]
9Geometry of Matrix Operators on R2[1], [2], [3]
10Eigenvalues and Eigenvectors, Diagonalization[1], [2], [3]
11Inner Product Spaces, Angle and Orthogonality in Inner Product Spaces[1], [2], [3]
12Gram-Schmidt Method, QR-Separation[1], [2], [3]
13Best Approximation, Least Squares[1], [2], [3]
14Orthogonal Matrices, Orthogonal Diagonalization[1], [2], [3]
Resources
[1] Elementer Lineer Cebir. Howard Anton, Chris Rorres, Palme Yayıncılık. (Last Edition) [2] Lineer Cebir/Schaum's Outlines. Seymour Lipschutz, Nobel Yayin Dağıtım-Teknik Kitaplar. (Last Edition) [3] Uygulamalı Lineer Cebir. Bernard Kolman, David R. Hill (Editör: Ömer Akın), Palme Yayıncılık. (Last Edition)

Course Contribution to Program Qualifications

Course Contribution to Program Qualifications
NoProgram QualificationContribution Level
12345
1
It verbally refers to the meanings of professional terms and concepts within the scope of primary mathematics teaching. It verbally refers to the basic concepts, principles and techniques of theories in the field of primary mathematics teaching. It compares the theories in its field and lists the strengths and weaknesses of each theory verbally.
X
2
In the field of primary mathematics teaching, he applies the necessary intervention in connection with the education he receives regarding the situations or problems he encounters professionally.
X
3
A problem he faces professionally, he analyzes and solves it based on scientific methods. He solves a problem he faces professionally on his own. It makes necessary interventions by distinguishing between situations that are within the scope of their duties and responsibilities from a professional point of view and situations that are not.
X
4
Follows new developments related to the profession in line with the principle of lifelong learning from a professional point of view.
X
5
In the process of resolving a problem from a professional point of view, he consults with his colleagues when necessary. When he encounters a problem, he formulates it in writing or verbally. He has a sense of social responsibility and uses his professional gains to solve problems in his immediate and distant environment. He speaks at least B1 level English to monitor international professional developments.
X
6
He knows the basic concepts of his profession. Applies basic skills related to his profession. It applies measurement and evaluation tools in accordance with its purpose and in line with ethical principles. In a professional subject, it conducts research by choosing the appropriate research method.
X

Assessment Methods

Contribution LevelAbsolute Evaluation
Rate of Midterm Exam to Success 40
Rate of Final Exam to Success 60
Total 100
ECTS / Workload Table
ActivitiesNumber ofDuration(Hour)Total Workload(Hour)
Course Hours14228
Guided Problem Solving000
Resolution of Homework Problems and Submission as a Report14114
Term Project000
Presentation of Project / Seminar000
Quiz000
Midterm Exam11010
General Exam11010
Performance Task, Maintenance Plan000
Total Workload(Hour)62
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(62/30)2
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.

Detail Informations of the Course

Course Description

CourseCodeSemesterT+P (Hour)CreditECTS
LINEAR ALGEBRA II-Spring Semester2+022
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of CourseTurkish
Course LevelFirst Cycle (Bachelor's Degree)
Course TypeRequired
Course CoordinatorAssist.Prof. Damla SÖNMEZ
Name of Lecturer(s)Assist.Prof. Alaattin PUSMAZ
Assistant(s)
AimWith this course, it is aimed that students will be able to explain dimensions of spaces; explain base-dimension change; explain matrix transformations; explain eigenvalues and eigenvectors; explain inner product space; explain orthogonality.
Course ContentThis course contains; 2-Space, 3-Space and Vectors in n-Space,Norm, Scalar Product and Distance in Rn,Orthogonality,Geometry of Linear Systems, Vector Product,Space, Subspace, Linear Unions, linear dependence and independence,Coordinates and bases, Dimension, Base Change,Row Space, Column Space and Zero Space, Rank Zero and Basic Matrix Spaces,Matrix Transformations from Rn to Rm, Properties of Matrix Transformations,Geometry of Matrix Operators on R2,Eigenvalues and Eigenvectors, Diagonalization,Inner Product Spaces, Angle and Orthogonality in Inner Product Spaces,Gram-Schmidt Method, QR-Separation,Best Approximation, Least Squares,Orthogonal Matrices, Orthogonal Diagonalization.
Dersin Öğrenme KazanımlarıTeaching MethodsAssessment Methods
Explains the properties of vector space and subspace.12, 16, 9A
Explains the concepts of linear dependence, independence and solves related problems.12, 16, 9A
Explains the basic concepts of inner product spaces.12, 16, 9A
Solves problems related to eigenvalues and eigenvectors.12, 16, 9A
Solves problems related to linear transformations.12, 16, 9A
Teaching Methods:12: Problem Solving Method, 16: Question - Answer Technique, 9: Lecture Method
Assessment Methods:A: Traditional Written Exam

Course Outline

OrderSubjectsPreliminary Work
12-Space, 3-Space and Vectors in n-Space[1], [2], [3]
2Norm, Scalar Product and Distance in Rn[1], [2], [3]
3Orthogonality[1], [2], [3]
4Geometry of Linear Systems, Vector Product[1], [2], [3]
5Space, Subspace, Linear Unions, linear dependence and independence[1], [2], [3]
6Coordinates and bases, Dimension, Base Change[1], [2], [3]
7Row Space, Column Space and Zero Space, Rank Zero and Basic Matrix Spaces[1], [2], [3]
8Matrix Transformations from Rn to Rm, Properties of Matrix Transformations[1], [2], [3]
9Geometry of Matrix Operators on R2[1], [2], [3]
10Eigenvalues and Eigenvectors, Diagonalization[1], [2], [3]
11Inner Product Spaces, Angle and Orthogonality in Inner Product Spaces[1], [2], [3]
12Gram-Schmidt Method, QR-Separation[1], [2], [3]
13Best Approximation, Least Squares[1], [2], [3]
14Orthogonal Matrices, Orthogonal Diagonalization[1], [2], [3]
Resources
[1] Elementer Lineer Cebir. Howard Anton, Chris Rorres, Palme Yayıncılık. (Last Edition) [2] Lineer Cebir/Schaum's Outlines. Seymour Lipschutz, Nobel Yayin Dağıtım-Teknik Kitaplar. (Last Edition) [3] Uygulamalı Lineer Cebir. Bernard Kolman, David R. Hill (Editör: Ömer Akın), Palme Yayıncılık. (Last Edition)

Course Contribution to Program Qualifications

Course Contribution to Program Qualifications
NoProgram QualificationContribution Level
12345
1
It verbally refers to the meanings of professional terms and concepts within the scope of primary mathematics teaching. It verbally refers to the basic concepts, principles and techniques of theories in the field of primary mathematics teaching. It compares the theories in its field and lists the strengths and weaknesses of each theory verbally.
X
2
In the field of primary mathematics teaching, he applies the necessary intervention in connection with the education he receives regarding the situations or problems he encounters professionally.
X
3
A problem he faces professionally, he analyzes and solves it based on scientific methods. He solves a problem he faces professionally on his own. It makes necessary interventions by distinguishing between situations that are within the scope of their duties and responsibilities from a professional point of view and situations that are not.
X
4
Follows new developments related to the profession in line with the principle of lifelong learning from a professional point of view.
X
5
In the process of resolving a problem from a professional point of view, he consults with his colleagues when necessary. When he encounters a problem, he formulates it in writing or verbally. He has a sense of social responsibility and uses his professional gains to solve problems in his immediate and distant environment. He speaks at least B1 level English to monitor international professional developments.
X
6
He knows the basic concepts of his profession. Applies basic skills related to his profession. It applies measurement and evaluation tools in accordance with its purpose and in line with ethical principles. In a professional subject, it conducts research by choosing the appropriate research method.
X

Assessment Methods

Contribution LevelAbsolute Evaluation
Rate of Midterm Exam to Success 40
Rate of Final Exam to Success 60
Total 100

Numerical Data

Student Success

Ekleme Tarihi: 04/10/2023 - 14:59Son Güncelleme Tarihi: 04/10/2023 - 14:59