CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

INTRODUCTION TO TOPOLOGY | MAT305 | FALL | 4+0 | C | 6 |

Learning Outcomes | 1-To comprehend the concept of topological space and related basic notions 2-To comprehend subspace, base and subbase 3-To expalin the generalizations of basic notions encountered in analysis to an arbitrary topological 4-To comprehend the notion of continuity and homeomorphism |

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

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

Classroom study (Pre-study, practice) | 14 | 5 | 70 | |

Assignments | 10 | 2 | 6 | 12 |

Short-Term Exams (exam + preparation) | 10 | 2 | 6 | 12 |

Midterm exams (exam + preparation) | 30 | 1 | 14 | 14 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 14 | 14 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 178 | |||

Total Workload (hours) / 30 (s) | 5,93 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Basic concepts, sets, functions, relations, countable sets, ordered sets | |

2 | Topology definition and examples | |

3 | Subspaces, open and closed sets | |

4 | Metric topology and examples | |

5 | ℝ usual space, open and closed sets | |

6 | Base and subbase for a topology | |

7 | Neighborhood of a point and local base of a set in topological spaces | |

8 | Limit point and closure of a set in topological spaces | |

9 | Interior and isolated point of a set in topological spaces | |

10 | Dense set and boundary of a set | |

11 | Continuity in topological spaces | |

12 | Some real valued functions | |

13 | Open-closed functions | |

14 | Homeomorphisms |

Prerequisites | -- |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Gonca DURMAZ |

Instructors | - |

Assistants | - |

Resources | Genel Topolojiye Giriş ve Çözümlü Alıştırmalar (3. Baskı), Mahmut Koçak, 2011. |

Supplementary Book | [1] Genel Topoloji (7. Baskı), Şaziye Yüksel, Eğitim Akademi Yayınları, 2011 [2] Topolojik uzaylar, Abdugafur Rahimov, Seçkin Yayınları, 2006. [3] Topology (2nd Edition), James R. Munkres, Prentice Hall, Upper Saddle River, 2000 [4] Basic Topology (Undergraduate Texts in Mathematics), M. A. Armstrong, Springer-Verlag, New York, 2010 [5] Elementary Topology Problem Textbook, O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, American Mathematical Society, 2008. [6] General Topology (Schaums`s Outline Series), Seymour Lipschutz, McGraw-Hill, 2011 A General Topology Workbook, Iain T. Adamson, Birkhauser, Boston, 1996. |

Document | Lecture Notes |

Goals | Introducing the concept of topological space, demonstrating that real spaces studied in analysis courses are a topological space example and that many basic concepts and properties in these spaces can be generalized to any topological space |

Content | - |

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 | 5 |

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 | 2 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 3 |

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 | 4 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 4 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | 2 |

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 | 4 |

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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