Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 2 / Spring 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 | SAMED ÖZKAN (ozkans@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The aim of the course is to teach some basic concepts in Topology, to create the ability of Mathematical idea and commend, to help to gain the basic topological knowledge and ability for their later educations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can define the concepts of product and quotient space. Can build product and quotient topologies. |
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-4 Analytically use the interdisciplinary approach at learning process. |
Examination |
| LO-2 | Can describe the separation axioms and can examine if a given topological space is T0, T1, Hausdorff, regular, completely regular, normal or not. |
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. |
Examination |
| LO-3 | Can define the concepts of compactness and local compactness. |
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. |
Examination |
| LO-4 | Can define the concepts of connectedness and path connectedness. |
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. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Product Spaces, Quotient Spaces, Examples, Countable Spaces, Examples, Separation Axioms, Hausdorff Spaces, Regular, Completely Regular and Normal Spaces, Compact Spaces, Connected Spaces, Path Connectedness and Components. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Product Spaces | Lecturing |
| 2 | Quotient Spaces | Lecturing |
| 3 | Examples | Lecturing |
| 4 | Countable Spaces | Lecturing |
| 5 | Examples | Lecturing |
| 6 | Separation Axioms | Lecturing |
| 7 | Hausdorff Spaces | Lecturing |
| 8 | mid-term exam | |
| 9 | Regular, Completely Regular and Normal Spaces | Lecturing |
| 10 | Compact Spaces | Lecturing |
| 11 | Compact Spaces | Lecturing |
| 12 | Examples | Lecturing |
| 13 | Connected Spaces | Lecturing |
| 14 | Connected Spaces | Lecturing |
| 15 | Connected Spaces Path Connectedness and Components | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 2 | Ş. Yüksel, Genel Topoloji, Selçuk Üniversitesi, Konya, 2002. | |
| 3 | M. Koçak, Genel Topolojiye Giriş ve Çözümlü Alıştırmalar, Kampüs Yayıncılık, Eskişehir, 2011. | |
| 4 | S. Lipschutz, General Topology, Schaum’s Outline Series, New York, 1965. | |
| Required Course instruments and materials | ||
| 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 | 4 | 14 | 56 |
| 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 | 4 | 4 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 5 | 4 | 20 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||