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 basic concepts of algebraic topology, to create the ability of Mathematical idea and commend, to help to gain the basic knowledge and ability for their graduate educations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Learn the concepts of homotopy, convexity, contractibility and path connectedness, can give examples. |
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-2 | Can define the concepts of fundamental group, free group, covering space and universal covering space. |
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 | ||
| Some Basic Algebraic and Topological Concepts, Quotient Spaces and Examples, Identification Spaces, Homotopies, Convexity and Contractibility, Paths and Path Connectedness, Fundamental Groups, Free Groups, Covering Spaces, Universal Covering Spaces, The Fundamental Group of Covering Spaces, The Existence Theorem for Covering Spaces, Homotopy Groups. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Some Basic Algebraic Concepts | Lecturing |
| 2 | Some Basic Topological Concepts | Lecturing |
| 3 | Quotient Spaces and Examples | Lecturing |
| 4 | Identification Spaces | Lecturing |
| 5 | Homotopies | Lecturing |
| 6 | Convexity and Contractibility | Lecturing |
| 7 | Paths and Path Connectedness | Lecturing |
| 8 | mid-term exam | |
| 9 | Fundamental Groups | Lecturing |
| 10 | Free Groups | Lecturing |
| 11 | Covering Spaces | Lecturing |
| 12 | Universal Covering Spaces | Lecturing |
| 13 | The Fundamental Group of Covering Spaces | Lecturing |
| 14 | The Existence Theorem for Covering Spaces | Lecturing |
| 15 | Homotopy Groups | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 2 | J. J. Rotman, An Introduction to Algebraic Topology, Springer-Verlag, 1988. | |
| 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 | ||