Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 4 / Fall Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| 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 concepts in Topology in detail, to create the ability of Mathematical idea and commend, to help to gain the 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 countable set, topological space, continuous function and homeomorphism. |
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-2 | Learn the concepts of initial and final topology. Can obtain finite and infinite product 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-3 | Can define the concepts of first-countable, second-countable, separable and Lindelöf space. |
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 describe the separation axioms. Learn Urysohn lemma. |
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 | ||
| Countable Sets, Topological Spaces, Continuity and Homeomorphisms, Initial Topology, Final Topology, Finite Product Spaces, Infinite Product Spaces, First-countable and Second-countable Spaces, Separable Spaces, Lindelöf Spaces, T0 ve T1 Separation Axioms, Hausdorff Spaces, Regular and Completely Regular Spaces, Normal Spaces and Urysohn Lemma. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Countable Sets | Lecturing |
| 2 | Topological Spaces | Lecturing |
| 3 | Continuity and Homeomorphisms | Lecturing |
| 4 | Initial Topology | Lecturing |
| 5 | Final Topology | Lecturing |
| 6 | Finite Product Spaces | Lecturing |
| 7 | Infinite Product Spaces | Lecturing |
| 8 | mid-term exam | |
| 9 | First-countable and Second-countable Spaces | Lecturing |
| 10 | Separable Spaces | Lecturing |
| 11 | Lindelöf Spaces | Lecturing |
| 12 | T0 ve T1 Separation Axioms | Lecturing |
| 13 | Hausdorff Spaces | Lecturing |
| 14 | Regular and Completely Regular Spaces | Lecturing |
| 15 | Normal Spaces and Urysohn Lemma | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 2 | S. Lipschutz, General Topology, Schaum’s Outline Series, New York, 1965. | |
| 3 | Ş. Yüksel, Genel Topoloji, Selçuk Üniversitesi, Konya, 2002. | |
| 4 | M. Koçak, Genel Topolojiye Giriş ve Çözümlü Alıştırmalar, Kampüs Yayıncılık, Eskişehir, 2011. | |
| 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 | ||