Course Detail
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|
LINEAR ALGEBRA II | - | Spring Semester | 2+0 | 2 | 2 |
Course Program |
Prerequisites Courses | |
Recommended Elective Courses |
Language of Course | Turkish |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Required |
Course Coordinator | Assist.Prof. Damla SÖNMEZ |
Name of Lecturer(s) | Assist.Prof. Alaattin PUSMAZ |
Assistant(s) | |
Aim | With 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 Content | This 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 Kazanımları | Teaching Methods | Assessment Methods |
Explains the properties of vector space and subspace. | 12, 16, 9 | A |
Explains the concepts of linear dependence, independence and solves related problems. | 12, 16, 9 | A |
Explains the basic concepts of inner product spaces. | 12, 16, 9 | A |
Solves problems related to eigenvalues and eigenvectors. | 12, 16, 9 | A |
Solves problems related to linear transformations. | 12, 16, 9 | A |
Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam |
Course Outline
Order | Subjects | Preliminary Work |
---|---|---|
1 | 2-Space, 3-Space and Vectors in n-Space | [1], [2], [3] |
2 | Norm, Scalar Product and Distance in Rn | [1], [2], [3] |
3 | Orthogonality | [1], [2], [3] |
4 | Geometry of Linear Systems, Vector Product | [1], [2], [3] |
5 | Space, Subspace, Linear Unions, linear dependence and independence | [1], [2], [3] |
6 | Coordinates and bases, Dimension, Base Change | [1], [2], [3] |
7 | Row Space, Column Space and Zero Space, Rank Zero and Basic Matrix Spaces | [1], [2], [3] |
8 | Matrix Transformations from Rn to Rm, Properties of Matrix Transformations | [1], [2], [3] |
9 | Geometry of Matrix Operators on R2 | [1], [2], [3] |
10 | Eigenvalues and Eigenvectors, Diagonalization | [1], [2], [3] |
11 | Inner Product Spaces, Angle and Orthogonality in Inner Product Spaces | [1], [2], [3] |
12 | Gram-Schmidt Method, QR-Separation | [1], [2], [3] |
13 | Best Approximation, Least Squares | [1], [2], [3] |
14 | Orthogonal 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 | |||||||
No | Program Qualification | Contribution Level | |||||
1 | 2 | 3 | 4 | 5 | |||
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 Level | Absolute Evaluation | |
Rate of Midterm Exam to Success | 40 | |
Rate of Final Exam to Success | 60 | |
Total | 100 |
ECTS / Workload Table | ||||||
Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
Course Hours | 14 | 2 | 28 | |||
Guided Problem Solving | 0 | 0 | 0 | |||
Resolution of Homework Problems and Submission as a Report | 14 | 1 | 14 | |||
Term Project | 0 | 0 | 0 | |||
Presentation of Project / Seminar | 0 | 0 | 0 | |||
Quiz | 0 | 0 | 0 | |||
Midterm Exam | 1 | 10 | 10 | |||
General Exam | 1 | 10 | 10 | |||
Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
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
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|
LINEAR ALGEBRA II | - | Spring Semester | 2+0 | 2 | 2 |
Course Program |
Prerequisites Courses | |
Recommended Elective Courses |
Language of Course | Turkish |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Required |
Course Coordinator | Assist.Prof. Damla SÖNMEZ |
Name of Lecturer(s) | Assist.Prof. Alaattin PUSMAZ |
Assistant(s) | |
Aim | With 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 Content | This 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 Kazanımları | Teaching Methods | Assessment Methods |
Explains the properties of vector space and subspace. | 12, 16, 9 | A |
Explains the concepts of linear dependence, independence and solves related problems. | 12, 16, 9 | A |
Explains the basic concepts of inner product spaces. | 12, 16, 9 | A |
Solves problems related to eigenvalues and eigenvectors. | 12, 16, 9 | A |
Solves problems related to linear transformations. | 12, 16, 9 | A |
Teaching Methods: | 12: Problem Solving Method, 16: Question - Answer Technique, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam |
Course Outline
Order | Subjects | Preliminary Work |
---|---|---|
1 | 2-Space, 3-Space and Vectors in n-Space | [1], [2], [3] |
2 | Norm, Scalar Product and Distance in Rn | [1], [2], [3] |
3 | Orthogonality | [1], [2], [3] |
4 | Geometry of Linear Systems, Vector Product | [1], [2], [3] |
5 | Space, Subspace, Linear Unions, linear dependence and independence | [1], [2], [3] |
6 | Coordinates and bases, Dimension, Base Change | [1], [2], [3] |
7 | Row Space, Column Space and Zero Space, Rank Zero and Basic Matrix Spaces | [1], [2], [3] |
8 | Matrix Transformations from Rn to Rm, Properties of Matrix Transformations | [1], [2], [3] |
9 | Geometry of Matrix Operators on R2 | [1], [2], [3] |
10 | Eigenvalues and Eigenvectors, Diagonalization | [1], [2], [3] |
11 | Inner Product Spaces, Angle and Orthogonality in Inner Product Spaces | [1], [2], [3] |
12 | Gram-Schmidt Method, QR-Separation | [1], [2], [3] |
13 | Best Approximation, Least Squares | [1], [2], [3] |
14 | Orthogonal 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 | |||||||
No | Program Qualification | Contribution Level | |||||
1 | 2 | 3 | 4 | 5 | |||
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 Level | Absolute Evaluation | |
Rate of Midterm Exam to Success | 40 | |
Rate of Final Exam to Success | 60 | |
Total | 100 |