Nevşehir Hacı Bektaş Veli University Course Catalogue
|
|||||
| Year/Semester of Study | 1 / Spring 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 the concept of topological group in detail, 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 | Can define the concepts of topological group and topological subgroup, can give examples. Know the concepts of quotient and product in topological groups. |
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 explain the concepts of connectedness, separation axioms, action and covering groups in topological groups. |
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 |
|||
| Course Contents | ||
| Algebraic Concepts, Topological Concepts, Topological Groups and Examples, Topological Subgroups, Right and Left Translations, Some Properties of Topological Groups, Morphisms Between Topological Groups, Topological Quotient Groups, Product of Topological Groups, Fundamental Systems of Neighbourhoods, Connected Topological Groups, Separation Axioms in Topological Groups, Action of Topological Groups, Covering Groups of Topological Groups. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Algebraic Concepts | Lecturing |
| 2 | Topological Concepts | Lecturing |
| 3 | Topological Groups and Examples | Lecturing |
| 4 | Topological Subgroups | Lecturing |
| 5 | Right and Left Translations | Lecturing |
| 6 | Some Properties of Topological Groups | Lecturing |
| 7 | Morphisms Between Topological Groups | Lecturing |
| 8 | mid-term exam | |
| 9 | Topological Quotient Groups | Lecturing |
| 10 | Product of Topological Groups | Lecturing |
| 11 | Fundamental Systems of Neighbourhoods | Lecturing |
| 12 | Connected Topological Groups | Lecturing |
| 13 | Separation Axioms in Topological Groups | Lecturing |
| 14 | Action of Topological Groups | Lecturing |
| 15 | Covering Groups of Topological Groups | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010. | |
| 2 | N. Bourbaki, General Topology, Addison-Wesley Publishing Company, 1966. | |
| 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 | ||