Course Detail
Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| LINEAR ALGEBRA | İM2115789 | Fall Semester | 3+0 | 3 | 4 |
| 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. Damla SÖNMEZ |
| Assistant(s) | |
| Aim | This course aims for students to: solve linear equation systems, perform elementary row operations, interpret the geometric representation of linear equation systems, conduct operations in matrix space, explain the dimensions of spaces, clarify the concept of basis-dimension change, describe matrix transformations, explain eigenvalues and eigenvectors, describe inner product spaces, and elucidate orthogonality. |
| Course Content | This course contains; Introduction to linear equation systems, matrices, and matrix operations,Types and properties of matrices, homogeneous and non-homogeneous linear equation systems and their solution methods, elementary row operations, and the geometric interpretation of linear equation systems,Row echelon matrix, reduced row echelon matrix, and row-reduced matrix,Matrices and linear equation systems (Gauss elimination, Gauss-Jordan reduction method),Powers of matrices, block matrices, finding the inverse of matrices, matrix applications,Determinant of matrices, properties of determinants, applications of determinants,Linear equation systems, the relationship with determinants,Cramer’s method,Vectors in 2-space, 3-space, and n-space; norm in Rn, scalar product and distance, orthogonality, geometry of linear systems, vector product,Space, subspace, linear combinations, linear dependence and independence, coordinates and bases, dimension, basis change,Row space, column space, and zero space; rank, nullity, and fundamental matrix spaces; matrix transformations from Rn to Rm; properties of matrix transformations,The geometry of matrix operators on R2 eigenvalues and eigenvectors, diagonalization,Inner product spaces, angles and orthogonality in inner product spaces, Gram-Schmidt process, QR decomposition,Best approximation, least squares, orthogonal matrices, orthogonal diagonalization. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| Performs operations defined on matrices. | 12, 16, 9 | A |
| Performs elementary row and column operations on a matrix. | 12, 16, 9 | A |
| Explains linear equation systems. | 12, 16, 9 | A |
| Solves systems of equations using the Gauss elimination and Gauss-Jordan methods. | 12, 16, 9 | A |
| Calculates the determinant of a matrix. | 12, 16, 9 | A |
| Explains the relationship between a system of equations and its determinant. | 12, 16, 9 | A |
| Explains the properties of vector spaces and subspaces. | 12, 16, 9 | A |
| Explains the concepts of linear dependence and independence. | 12, 16, 9 | A |
| Explains the fundamental concepts related to 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 | Introduction to linear equation systems, matrices, and matrix operations | [1], [2], [3] |
| 2 | Types and properties of matrices, homogeneous and non-homogeneous linear equation systems and their solution methods, elementary row operations, and the geometric interpretation of linear equation systems | [1], [2], [3] |
| 3 | Row echelon matrix, reduced row echelon matrix, and row-reduced matrix | [1], [2], [3] |
| 4 | Matrices and linear equation systems (Gauss elimination, Gauss-Jordan reduction method) | [1], [2], [3] |
| 5 | Powers of matrices, block matrices, finding the inverse of matrices, matrix applications | [1], [2], [3] |
| 6 | Determinant of matrices, properties of determinants, applications of determinants | [1], [2], [3] |
| 7 | Linear equation systems, the relationship with determinants | [1], [2], [3] |
| 8 | Cramer’s method | [1], [2], [3] |
| 9 | Vectors in 2-space, 3-space, and n-space; norm in Rn, scalar product and distance, orthogonality, geometry of linear systems, vector product | [1], [2], [3] |
| 10 | Space, subspace, linear combinations, linear dependence and independence, coordinates and bases, dimension, basis change | [1], [2], [3] |
| 11 | Row space, column space, and zero space; rank, nullity, and fundamental matrix spaces; matrix transformations from Rn to Rm; properties of matrix transformations | [1], [2], [3] |
| 12 | The geometry of matrix operators on R2 eigenvalues and eigenvectors, diagonalization | [1], [2], [3] |
| 13 | Inner product spaces, angles and orthogonality in inner product spaces, Gram-Schmidt process, QR decomposition | [1], [2], [3] |
| 14 | Best approximation, least squares, orthogonal matrices, orthogonal diagonalization | [1], [2], [3] |
| Resources |
| [1] Anton, H., & Rorres, C. (Last edition). Elementary Linear Algebra. Palme Publishing. [2] Lipschutz, S. (Last edition). Linear Algebra/Schaum's Outlines, Nobel Publishing. [3] Bernard Kolman,B., & David R. Hill, D. R. (Last edition). Applied Linear Algebra. Palme Publishing. |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | It compares the fundamental theoretical frameworks in the field of elementary mathematics education (constructivism, cognitive development theories, models of mathematical thinking) along with their strengths and weaknesses. | X | |||||
| 2 | It compares the national mathematics curriculum (MEB) with international frameworks (NCTM, PISA, TIMSS) in terms of learning objectives and content areas. | X | |||||
| 3 | Explains the principles of assessment and evaluation, research methods, and ethical guidelines relevant to their profession, as well as their practical applications. | X | |||||
| 4 | Applies appropriate pedagogical interventions in connection with the training received regarding the instructional situations and challenges encountered in the field of elementary mathematics education. | X | |||||
| 5 | By analyzing students' misconceptions and learning difficulties in mathematics, they design appropriate teaching strategies and materials to address them. | X | |||||
| 6 | Solves professional problems related to mathematics education independently using scientific methods. | X | |||||
| 7 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 8 | By formulating a research question on a professional topic, they plan the appropriate research method. | X | |||||
| 9 | Distinguishes between situations that fall within the scope of their professional duties and responsibilities and those that do not. | X | |||||
| 10 | Monitors the instructional activities and implementation process aimed at the development of the students under their supervision. | X | |||||
| 11 | Guides the professional development process by integrating this information in line with national and international developments and research findings in mathematics education. | X | |||||
| 12 | By interpreting the results of their own teaching practices, they develop recommendations for professional development. | X | |||||
| 13 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 14 | Ensures compliance with research ethics, professional ethics for teachers, and national education regulations in their professional practice. | X | |||||
| 15 | In the math classroom, we plan for an equitable and inclusive learning environment, activities that support each student’s mathematical potential, and the necessary safety measures regarding workplace safety. | X | |||||
| 16 | In mathematics instruction, they use dynamic software (GeoGebra, Desmos, etc.), learning management systems, and other information and communication technologies at a level equivalent to at least the ECDL Advanced Level. | 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 | 0 | 0 | 0 | |||
| Guided Problem Solving | 0 | 0 | 0 | |||
| Resolution of Homework Problems and Submission as a Report | 0 | 0 | 0 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 0 | 0 | 0 | |||
| General Exam | 0 | 0 | 0 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 0 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(0/30) | 0 | |||||
| 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 | İM2115789 | Fall Semester | 3+0 | 3 | 4 |
| 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. Damla SÖNMEZ |
| Assistant(s) | |
| Aim | This course aims for students to: solve linear equation systems, perform elementary row operations, interpret the geometric representation of linear equation systems, conduct operations in matrix space, explain the dimensions of spaces, clarify the concept of basis-dimension change, describe matrix transformations, explain eigenvalues and eigenvectors, describe inner product spaces, and elucidate orthogonality. |
| Course Content | This course contains; Introduction to linear equation systems, matrices, and matrix operations,Types and properties of matrices, homogeneous and non-homogeneous linear equation systems and their solution methods, elementary row operations, and the geometric interpretation of linear equation systems,Row echelon matrix, reduced row echelon matrix, and row-reduced matrix,Matrices and linear equation systems (Gauss elimination, Gauss-Jordan reduction method),Powers of matrices, block matrices, finding the inverse of matrices, matrix applications,Determinant of matrices, properties of determinants, applications of determinants,Linear equation systems, the relationship with determinants,Cramer’s method,Vectors in 2-space, 3-space, and n-space; norm in Rn, scalar product and distance, orthogonality, geometry of linear systems, vector product,Space, subspace, linear combinations, linear dependence and independence, coordinates and bases, dimension, basis change,Row space, column space, and zero space; rank, nullity, and fundamental matrix spaces; matrix transformations from Rn to Rm; properties of matrix transformations,The geometry of matrix operators on R2 eigenvalues and eigenvectors, diagonalization,Inner product spaces, angles and orthogonality in inner product spaces, Gram-Schmidt process, QR decomposition,Best approximation, least squares, orthogonal matrices, orthogonal diagonalization. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| Performs operations defined on matrices. | 12, 16, 9 | A |
| Performs elementary row and column operations on a matrix. | 12, 16, 9 | A |
| Explains linear equation systems. | 12, 16, 9 | A |
| Solves systems of equations using the Gauss elimination and Gauss-Jordan methods. | 12, 16, 9 | A |
| Calculates the determinant of a matrix. | 12, 16, 9 | A |
| Explains the relationship between a system of equations and its determinant. | 12, 16, 9 | A |
| Explains the properties of vector spaces and subspaces. | 12, 16, 9 | A |
| Explains the concepts of linear dependence and independence. | 12, 16, 9 | A |
| Explains the fundamental concepts related to 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 | Introduction to linear equation systems, matrices, and matrix operations | [1], [2], [3] |
| 2 | Types and properties of matrices, homogeneous and non-homogeneous linear equation systems and their solution methods, elementary row operations, and the geometric interpretation of linear equation systems | [1], [2], [3] |
| 3 | Row echelon matrix, reduced row echelon matrix, and row-reduced matrix | [1], [2], [3] |
| 4 | Matrices and linear equation systems (Gauss elimination, Gauss-Jordan reduction method) | [1], [2], [3] |
| 5 | Powers of matrices, block matrices, finding the inverse of matrices, matrix applications | [1], [2], [3] |
| 6 | Determinant of matrices, properties of determinants, applications of determinants | [1], [2], [3] |
| 7 | Linear equation systems, the relationship with determinants | [1], [2], [3] |
| 8 | Cramer’s method | [1], [2], [3] |
| 9 | Vectors in 2-space, 3-space, and n-space; norm in Rn, scalar product and distance, orthogonality, geometry of linear systems, vector product | [1], [2], [3] |
| 10 | Space, subspace, linear combinations, linear dependence and independence, coordinates and bases, dimension, basis change | [1], [2], [3] |
| 11 | Row space, column space, and zero space; rank, nullity, and fundamental matrix spaces; matrix transformations from Rn to Rm; properties of matrix transformations | [1], [2], [3] |
| 12 | The geometry of matrix operators on R2 eigenvalues and eigenvectors, diagonalization | [1], [2], [3] |
| 13 | Inner product spaces, angles and orthogonality in inner product spaces, Gram-Schmidt process, QR decomposition | [1], [2], [3] |
| 14 | Best approximation, least squares, orthogonal matrices, orthogonal diagonalization | [1], [2], [3] |
| Resources |
| [1] Anton, H., & Rorres, C. (Last edition). Elementary Linear Algebra. Palme Publishing. [2] Lipschutz, S. (Last edition). Linear Algebra/Schaum's Outlines, Nobel Publishing. [3] Bernard Kolman,B., & David R. Hill, D. R. (Last edition). Applied Linear Algebra. Palme Publishing. |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | It compares the fundamental theoretical frameworks in the field of elementary mathematics education (constructivism, cognitive development theories, models of mathematical thinking) along with their strengths and weaknesses. | X | |||||
| 2 | It compares the national mathematics curriculum (MEB) with international frameworks (NCTM, PISA, TIMSS) in terms of learning objectives and content areas. | X | |||||
| 3 | Explains the principles of assessment and evaluation, research methods, and ethical guidelines relevant to their profession, as well as their practical applications. | X | |||||
| 4 | Applies appropriate pedagogical interventions in connection with the training received regarding the instructional situations and challenges encountered in the field of elementary mathematics education. | X | |||||
| 5 | By analyzing students' misconceptions and learning difficulties in mathematics, they design appropriate teaching strategies and materials to address them. | X | |||||
| 6 | Solves professional problems related to mathematics education independently using scientific methods. | X | |||||
| 7 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 8 | By formulating a research question on a professional topic, they plan the appropriate research method. | X | |||||
| 9 | Distinguishes between situations that fall within the scope of their professional duties and responsibilities and those that do not. | X | |||||
| 10 | Monitors the instructional activities and implementation process aimed at the development of the students under their supervision. | X | |||||
| 11 | Guides the professional development process by integrating this information in line with national and international developments and research findings in mathematics education. | X | |||||
| 12 | By interpreting the results of their own teaching practices, they develop recommendations for professional development. | X | |||||
| 13 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 14 | Ensures compliance with research ethics, professional ethics for teachers, and national education regulations in their professional practice. | X | |||||
| 15 | In the math classroom, we plan for an equitable and inclusive learning environment, activities that support each student’s mathematical potential, and the necessary safety measures regarding workplace safety. | X | |||||
| 16 | In mathematics instruction, they use dynamic software (GeoGebra, Desmos, etc.), learning management systems, and other information and communication technologies at a level equivalent to at least the ECDL Advanced Level. | X | |||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |