Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 3 / Spring 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 fundamental concepts, axioms and theorems in Set Theory, to create the ability of Mathematical idea and commend. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Understand the concepts of finite, infinite, countable and uncountable set. Gain the ability of thinking depending on axioms and rules. |
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 explain the Cantor-Schroder-Bernstein theorem, axiom of choice, Zorn’s lemma and well-ordering theorem. |
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 |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Finite and Infinite Sets, Countability, Uncountable Sets, Cantor-Schroder-Bernstein Theorem, Axiom of Choice, Zorn’s Lemma, Well-Ordering Theorem, Ordinal Numbers, Ordinal Arithmetic, Cardinal Numbers, Cardinal Arithmetic, Russell’s Paradox, ZFC Axioms. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Finite and Infinite Sets | Lecturing |
| 2 | Countability | Lecturing |
| 3 | Uncountable Sets | Lecturing |
| 4 | Cantor-Schroder-Bernstein Theorem | Lecturing |
| 5 | Axiom of Choice | Lecturing |
| 6 | Zorn’s Lemma | Lecturing |
| 7 | Well-Ordering Theorem | Lecturing |
| 8 | mid-term exam | |
| 9 | Ordinal Numbers | Lecturing |
| 10 | Ordinal Arithmetic | Lecturing |
| 11 | Cardinal Numbers | Lecturing |
| 12 | Cardinal Arithmetic | Lecturing |
| 13 | Russell’s Paradox | Lecturing |
| 14 | ZFC Axioms | Lecturing |
| 15 | ZFC Axioms | Lecturing |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | A. Nesin, Sezgisel Kümeler Kuramı, Nesin Yayınevi, 2015. | |
| 2 | N. Ergun, Kümeler Teorisine Giriş, Nobel Yayın, Ankara, 2005. | |
| 3 | A. Nesin, Aksiyomatik Kümeler Kuramı, Ders Notları, 2010. | |
| 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 | ||