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 basic concepts in Category Theory, to create the ability of Mathematical idea and commend, to help to gain the basic categorical 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 category, monomorphism, epimorphism, bimorphism, section, retraction and isomorphism and can give various examples. |
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 | Can determine the initial, final and zero objects of a given category if there exist and can build pullback and pushout diagrams. |
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 category, functor and natural transformation and know the relationships among them. |
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 | ||
| Fundamental Concepts, Definition of Category, Examples, Subcategory, Monomorphism, Epimorphism, Bimorphism, Section, Retraction, Isomorphism, Examples, Initial, Final and Zero Objects, Product and Coproduct, Equalizers, Pullback and Pushout Diagrams, Functors and Properties, Examples, Natural Transformations. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Fundamental Concepts | Lecturing |
| 2 | Definition of Category | Lecturing |
| 3 | Examples | Lecturing |
| 4 | Subcategory | Lecturing |
| 5 | Monomorphism, Epimorphism, Bimorphism | Lecturing |
| 6 | Section, Retraction, Isomorphism | Lecturing |
| 7 | Examples | Lecturing |
| 8 | mid-term exam | |
| 9 | Initial, Final and Zero Objects | Lecturing |
| 10 | Product and Coproduct | Lecturing |
| 11 | Equalizers | Lecturing |
| 12 | Pullback and Pushout Diagrams | Lecturing |
| 13 | Functors and Properties | Lecturing |
| 14 | Examples | Lecturing |
| 15 | Natural Transformations | 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) | 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 | ||