CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

LINEAR ALGEBRA I | MAT203 | FALL | 4+0 | Fac./ Uni. | C | 7 |

Learning Outcomes | 1-To be able to explain fundamentals of matrix theory 2-To be able to solve linear systems in several variables using matrices. 3-To be able to explain fundamentals of real vector spaces 4-To be able to use basic knowledge of the theory of linear transformation |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 6 | 84 | |

Assignments | 10 | 2 | 8 | 16 |

Short-Term Exams (exam + preparation) | 10 | 2 | 8 | 16 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 200 | |||

Total Workload (hours) / 30 (s) | 6,67 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | System of linear equations, solving linear equations by elimination method | |

2 | Matrices, matrix operations and algebraic properties, special types of matrices and echelon form of a matrix | |

3 | Gauss elimination method | |

4 | Elementary matrices, finding the inverse of a matrix, equivalent matrices | |

5 | Vectors in the plane and in 3-space, vector spaces | |

6 | Subspaces | |

7 | Span and linear independence | |

8 | Basis and dimension | |

9 | Coordinates and isomorphisms | |

10 | Basis transformation matrices | |

11 | Homogeneous systems, rank of a matrix | |

12 | Permutation and determinants | |

13 | Determinants and their properties | |

14 | Cofactor expansion, inverse of a matrix, Cramer`s rule |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Faruk KARAASLAN |

Instructors | - |

Assistants | - |

Resources | Elementary Linear Algebra, 8th Edition, B. Kolman, D.R. Hill, Prentice-Hall, New Jersey, 2004 |

Supplementary Book | 1. Basic Linear Algebra, Second Edition, T.S. Blyth, E.F. Robertson, Springer 2002 2. Linear Algebra, 2nd Edition, K. Hoffman, R. Kunze, Prentice-Hall, New Jersey, 1971 |

Document | - |

Goals | The aim of the course is to provide the basic linear algebra background needed by mathematicians. Many concepts in the course will be presented in the familiar setting of the real n-dimensional space. |

Content | Systems of linear equations and finding solutions by elimination method. Matrix algebra. Reducing the augmented matrix to the row-echelon form by Gauss elimination method. Elementary matrices and the inverse of a matrix. Linear span and linear independence. Basis and dimension. Coordinates and isomorphisms. Transformation matrices between the bases. Homogenous systems of linear equations and matrix rank. Permutation and determinant. Properties of the determinant. Cofactor expansion, matrix inversion, Cramer?s rule. |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

2 | To have the ability of abstract thinking | 4 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 3 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 2 |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | 3 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 3 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | - |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | 3 |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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