Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 3rd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS (DOCTORATE DEGREE) | ||||
| 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 concept of topological category in detail, to create the ability of Mathematical idea and commend, to help to gain the basic knowledge and ability for their postgraduate educations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Learn the important topological categories. Know the definition of discre and indiscre structure, can give examples. |
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field. PO-5 Be able to access to information, make research on resources for this purpose and be able to use databases and other information resources. PO-10 Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
Examination |
| LO-2 | Know the wedge product and maps. Can express local and general separation axioms in topological categories. |
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field. PO-5 Be able to access to information, make research on resources for this purpose and be able to use databases and other information resources. |
Examination |
| LO-3 | Learn the infinite wedge product. Can define the concepts of closedness, connectedness and compactness in topological categories. |
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field. PO-5 Be able to access to information, make research on resources for this purpose and be able to use databases and other information resources. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Well-known Topological Categories, Stack Convergence and Filter Convergence Spaces, Discre and Indiscre Structures, Theorems, Examples, Wedge Product and Maps at p, Local Separation Axioms, Theorems, Examples, Maps, General Separation Axioms, Theorems, Examples, Infinite Wedge Product, Closedness in Topological Categories, Theorems, Examples, Connectedness and Compactness. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Well-known Topological Categories | Lecturing |
| 2 | Stack Convergence and Filter Convergence Spaces | Lecturing |
| 3 | Discre and Indiscre Structures | Lecturing |
| 4 | Theorems, Examples | Lecturing |
| 5 | Wedge Product and Maps at p | Lecturing |
| 6 | Local Separation Axioms | Lecturing |
| 7 | Theorems, Examples | Lecturing |
| 8 | mid-term exam | |
| 9 | Maps | Lecturing |
| 10 | General Separation Axioms | Lecturing |
| 11 | Theorems, Examples | Lecturing |
| 12 | Infinite Wedge Product | Lecturing |
| 13 | Closedness in Topological Categories | Lecturing |
| 14 | Theorems, Examples | Lecturing |
| 15 | Connectedness and Compactness | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | J. Adamek, H. Herrlich, G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990. | |
| 2 | H. Herrlich, G.E. Strecker, Category Theory, Allyn and Bacon Inc., Boston, 1973. | |
| 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) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 4 | 14 | 56 |
| b) Search in internet/Library | 3 | 14 | 42 |
| 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 | ||