CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ANALYTIC GEOMETRY I | MAT105 | FALL | 3+0 | Fac./ Uni. | C | 4 |

Learning Outcomes | 1-To be able to explain the relationship between a line in plane and its equation 2-To be able to determine linear dependence by using matrices 3-To be able to determine the image of geometric objects in the plane under affine transformations 4-To be able to explain properties of geometric objects do not change under affine transformations 5-To be able to classify types of conics 6-To be able to classify types of curves 7-To be able to classify second degree plane algebraic curves by using transformations |

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

Course Duration (Weeks x Course Hours) | 14 | 3 | 42 | |

Classroom study (Pre-study, practice) | 14 | 3 | 42 | |

Assignments | 10 | 2 | 4 | 8 |

Short-Term Exams (exam + preparation) | 10 | 2 | 4 | 8 |

Midterm exams (exam + preparation) | 30 | 1 | 6 | 6 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 8 | 8 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 114 | |||

Total Workload (hours) / 30 (s) | 3,8 ---- (4) | |||

ECTS Credit | 4 |

Week | Topics | Study Metarials |

1 | Systems of linear equations, algebra of matrices, row operations | |

2 | Determinant and its properties | |

3 | Rectangular coordinates in plane and space, polar coordinates | |

4 | The definition of a vector and algebra of vectors | |

5 | Linear dependence, dot product, angle | |

6 | Cross product and mixed product | |

7 | Line in plane and line equations, distance in plane | |

8 | Symmetry and translation in plane | |

9 | Rotation in plane | |

10 | The notion of a curve and its examples, algebraic and transcandental curves in plane | |

11 | Specifying conics as geometric loci | |

12 | Circle, the power of a point with respect to a circle, ellipse | |

13 | Parabola, hyperbola and their asymptotes | |

14 | The classification of second degree plane algebraic curves |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Celalettin KAYA |

Instructors | - |

Assistants | - |

Resources | Analitik Geometri (9. Baskı), Rüstem Kaya, Bilim Teknik Yayınevi, 2009 |

Supplementary Book | 1. Analitik Geometri (7. Baskı), Arif Sabuncuoğlu, Nobel Akademik Yayıncılık, Ankara, 2012 2. Analitik Geometri (8. Baskı), H.Hilmi Hacısalihoğlu, Hacısalihoğlu Yayıncılık, Anakara, 2013 3. Çözümlü Analitik Geometri Problemleri (3.Baskı), H.Hilmi Hacısalihoğlu, Ömer Tarakçı, Hacısalihoğlu Yayıncılık, Anakara, 2012 4. Analytic Geometry, H. İbrahim Karakaş, METU Department of Mathematics, Ankara,1994 5. Analytic Geometry (Schaum`s Outline Series in Mathematics), J. H. Kindle, McGraw-Hill, 1990 |

Document | - |

Goals | To introduce fundamental concepts of plane geometry and to teach the relation between algebra and geometry |

Content | Systems of linear equations, algebra of matrices, row operations; Determinant and its properties; Rectangular coordinates in plane and space, polar coordinates; The definition of a vector and algebra of vectors; Linear dependence, dot product, angle between two vectors; Cross product and mixed product; Line in plane and line equations, distance in plane; Symetry and translation in plane; Rotation in plane; The notion of a curve and its examples, algebraic and transcandental curves in plane; Specifying conics as geometric loci; Circle, the power of a point with respect to a circle, ellipse; Parabola, hyperbola and their asymptotes; The classification of second degree plane algebraic curves |

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 | 2 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 2 |

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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