Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Compulsory | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | HATİCE TOPCU (hatice.kamit@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | HATİCE TOPCU, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To teach the students the basic concepts of linear algebra , such as, sets, relations, algebraic structures, matrices, matrce operations determinants and system of linear equations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Learn the definition of matrices and doing operations on matrices. Find the tranpose of a matrix, recognize special matrices and know the relationships between them. Learn the definition and properties of a trace of a matrix. Learn the concepts of inverse matrix and zero divisor matrix. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| LO-2 | Can do elementary matrix operations, learn elementary matrix concept. By applying elementary operations, transform a matrix into reduced echelon form. Tell matrix rank by finding the reduced form. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| LO-3 | Learn the concept and properties of the determinant. Find the determinant with minors. Find the determinant of the product. Find the adjoint matix of a matrix. Use adjoint matrix to find inverse. Find the inverses of the some special matrices by splitting into blocks |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| LO-4 | Represent linear equation systems with matrices, investigate the existence and uniqueness of solutions. Know the solution methods of linear equation systems and find solutions by applying them. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. PO-3 Define the some models of mathematical problems, evaluate with a critical approach, analyze with theoretical and applied knowledge. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Basic concepts of Matrix Algebra, Operations with matrices, Matrix product by splitting into blocks, Hadamard product, Kronecker product, Transpose of a matrix, some special matrices,some relations including special matrices, Trace of a matrix and properties of trace, inverse matrices, zero divisor matrices, Elementer operations and elementer matrices, Reduced echelon form of matices, rank of a matrix, equivalance of matrices, Basic properties of determinant concept, Determinant with minors, Determinant of the product, Adjoint matrix, inverse matrix by splitting into blocks, Linear equation systems and matrices, Existence criteria of the solutions of the linear equation systems and solution methods | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Basic concepts of Matrix Algebra | Problems and solutions |
| 2 | Operations with matrices | Problems and solutions |
| 3 | Matrix product by splitting into blocks, Hadamard product, Kronecker product | Problems and solutions |
| 4 | Transpose of a matrix, some special matrices,some relations including special matrices | Problems and solutions |
| 5 | Trace of a matrix and properties of trace, inverse matrices, zero divisor matrices | Problems and solutions |
| 6 | Elementer operations and elementer matrices | Problems and solutions |
| 7 | Reduced echelon form of matices, rank of a matrix, equivalance of matrices | Problems and solutions |
| 8 | mid-term exam | |
| 9 | Basic properties of determinant concept | Problems and solutions |
| 10 | Determinant with minors | Problems and solutions |
| 11 | Determinant of the product | Problems and solutions |
| 12 | Adjoint matrix, inverse matrix by splitting into blocks | Problems and solutions |
| 13 | Linear equation systems and matrices | Problems and solutions |
| 14 | Existence criteria of the solutions of the linear equation systems and solution methods | Problems and solutions |
| 15 | Preparation for the final exam | Problems and solutions |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Lineer Cebir, Prof. Dr. Dursun Taşçı | |
| 2 | Kenneth Hoffman/Ray Kunze, Linear AlgebraPrentice Hall | |
| Required Course instruments and materials | ||
| Text books and lecture notes. | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 4 | 14 | 56 |
| Outside Class | |||
| a) Reading | 2 | 14 | 28 |
| b) Search in internet/Library | 2 | 14 | 28 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 2 | 8 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 2 | 15 | 30 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 162 | ||