Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 3 / Spring 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 the concepts of compactness and connectedness in metric spaces and to show the relationship between topological spaces and metric spaces. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can define the concepts of continuity and uniform continuity in metric spaces. |
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. |
Examination |
| LO-2 | Can define the concepts of Cauchy sequence, complete metric space and Banach 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-3 | Can define the concepts of compactness, sequentially compactness, connectedness and path connectedness in metric spaces. |
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. |
Examination |
| LO-4 | Can define the concepts of metric topology and metrization. Know the relationship between topological spaces and metric spaces. |
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 |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Continuous Functions, Uniform Continuity, Isometry, Cauchy Sequences, Complete Metric Space and Banach Space, Completion of a Metric Space, Compact Metric Spaces, Sequentially Compactness, Connected Metric Spaces, Local Connectedness, Path Connectedness, Product of Metric Spaces, Topological Spaces, Metric Topology, Metrization. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Continuous Functions | Lecturing |
| 2 | Uniform Continuity | Lecturing |
| 3 | Isometry | Lecturing |
| 4 | Cauchy Sequences, Complete Metric Space and Banach Space | Lecturing |
| 5 | Completion of a Metric Space | Lecturing |
| 6 | Compact Metric Spaces | Lecturing |
| 7 | Sequentially Compactness | Lecturing |
| 8 | mid-term exam | |
| 9 | Connected Metric Spaces | Lecturing |
| 10 | Local Connectedness | Lecturing |
| 11 | Path Connectedness | Lecturing |
| 12 | Product of Metric Spaces | Lecturing |
| 13 | Topological Spaces | Lecturing |
| 14 | Metric Topology | Lecturing |
| 15 | Metrization | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | T. Başkan, O. Bizim, İ. N. Cangül, Metrik Uzaylar ve Genel Topolojiye Giriş, Nobel Yayın, Ankara, 2006. | |
| 2 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 3 | S. A. Kılıç, M. Erdem, Metrik Uzaylar ve Topoloji, Vipaş A.Ş., Bursa, 1999. | |
| 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 | ||