Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 2nd 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 Category Theory in detail, to create the ability of Mathematical idea and commend, to help to gain the categorical knowledge and ability for their graduate educations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can define the concepts of category, subcategory, initial object and final object, can give examples. Know some special morphisms. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. |
Examination |
| LO-2 | Learn the concepts of source and sink. Perceive the product and coproduct of objects in categories. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. PO-5 Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
Examination |
| LO-3 | Know the concepts of equaliser and limit. Can build pullback and pushout diagrams. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. PO-4 Ability to learn scientific, mathematical perception and the ability to use that information to related areas. PO-5 Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Fundamental Concepts, Definitions of Category and Subcategory, Examples, Initial and Final Objects, Examples, Some Special Morphisms, Examples, Sources and Sinks, Product in Categories, Coroduct in Categories, Equalisers and Coequalisers, Pullback and Pushout Diagrams, Limits and Colimits, General Exercises. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Fundamental Concepts | Lecturing |
| 2 | Definitions of Category and Subcategory | Lecturing |
| 3 | Examples | Lecturing |
| 4 | Initial and Final Objects | Lecturing |
| 5 | Examples | Lecturing |
| 6 | Some Special Morphisms | Lecturing |
| 7 | Examples | Lecturing |
| 8 | mid-term exam | |
| 9 | Sources and Sinks | Lecturing |
| 10 | Product in Categories | Lecturing |
| 11 | Coroduct in Categories | Lecturing |
| 12 | Equalisers and Coequalisers | Lecturing |
| 13 | Pullback and Pushout Diagrams | Lecturing |
| 14 | Limits and Colimits | Lecturing |
| 15 | General Exercises | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 2 | İ. Karaca, Kategori Teorisi, Yüksek Lisans Ders Notları, 2010. | |
| 3 | J. Adamek, H. Herrlich, G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990. | |
| 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 | 5 | 14 | 70 |
| 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 | ||