| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | 210300401102 | ABSTRACT MATHEMATICS-I | Compulsory | 1 | 1 | 5 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| To improve the mathematical thinking ability by introducing mathematical logic and various proof techniques letting the students' to constitute the mathematical arguments; to formulize and improve the mathematical arguments logically, to be able to make and formulize basic proofs; to introduce the basic concepts such as sets, relations, functions and their characteristics; to prove the corresponding basic theorems using logic and proof techniques. |
| Name of Lecturer(s) |
| Doç. Dr. Alkan ÖZKAN |
| Learning Outcomes |
| 1 | To be able to comprehend different proof techniques | | 2 | Define a function to determine the set of definitions for a function and decide whether the function is individual or overlapping | | 3 | To be able to examine properties of relations and to distinguish them according to their order and equivalence relation | | 4 | To distinguish algebraic structures as groups, rings, bodies according to their properties | | 5 | To evaluate the concepts and theories of mathematics with scientific methods | | 6 | To be able to identify and analyze the problems and issues encountered | | 7 | To have advanced ability in mathematics licenses independently or to be able to discuss jointly with stakeholders | | 8 | Be able to develop suggestions based on potential solutions and research | | 9 | Learn how to translate an expression into mathematical language using correct symbols | | 10 | Having the ability to use basic mathematics-related materials and advanced knowledge equipments built on the qualifications gained in secondary education | | 11 | Having the ability to produce solutions with correct mathematical modeling by looking at current problems from various angles | | 12 | Having professional and scientific ethical values in the stages of collecting, interpreting and sharing data about mathematical science |
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| Mode of Delivery |
| Daytime Class |
| Prerequisites and co-requisities |
| YOK |
| Recommended Optional Programme Components |
| YOK |
| Course Contents |
| Definition of proposition, combined propositions, truth table.
Operations on sets and rules of set theory, endless infinity set definition and examples
Actions on the family and on the family
Overlapping and overlapping of a bunch
Ordered binary Cartesian product, correlation
Properties of the relation, equivalence relation and equivalence classes,
Concepts related to partial order relation, partial order relation Zorn syllabus
Functions, operations and properties, algebraic structures, countability,
Construction of Natural Numbers, Induction Principle |
| Weekly Detailed Course Contents |
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| 1 | Logic and Mathematics | X | X | | 2 | Suggestions Algebra | X | X | | 3 | Clusters Algebra | X | X | | 4 | separation and cover a cluster | X | X | | 5 | Ordered binary Cartesian product, correlation | X | X | | 6 | Properties of the bond | X | X | | 7 | Equality association and equivalence classes | X | X | | 8 | Concepts related to partial order relation, partial order relation Zorn syllabus | X | X | | 9 | Functions | X | X | | 10 | Algebraic structures | X | X | | 11 | Countability | X | X | | 12 | Construction of Natural Numbers | X | X | | 13 | Induction Principle | X | X | | 14 | Axioms and Paradoxes | X | X | | 15 | | | | | 16 | | | |
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| Recommended or Required Reading |
| Sait AKKAŞ, H.Hilm, HACISALİHOĞLU, Zühtü ÖZEL, Arif SABUNCUOĞLU Soyut Matematik Ankara2010
Timur KARAÇAY, Soyut Matematiğe Giriş
Fethi Çallıalp, Örneklerle Soyut Matematik
S.Olgun, Soyut Matematik, ESOGÜ Yayınları, 2004,
Ralph P.Grimaldi, Addison-Wesley, Discrete and Combinatorial Mathematics New York 2000
A. Okay Çelebi- Öner Çakar, |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | | | Language of Instruction | | | Work Placement(s) | | YOK |
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| Workload Calculation |
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| Midterm Examination | 1 | 1 | 1 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 1 | 14 |
| Practice | 14 | 2 | 28 |
| Problem Solving | 14 | 1 | 14 |
| Discussion | 14 | 2 | 28 |
| Question-Answer | 14 | 1 | 14 |
| Brain Storming | 14 | 3 | 42 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 4 | 5 | 5 | 4 | 5 | 5 | 5 | 4 | 4 | 4 | | LO2 | 4 | 5 | 5 | 4 | 5 | 4 | 4 | 4 | 4 | 4 | | LO3 | 4 | 5 | 4 | 5 | 4 | 5 | 4 | 4 | 4 | 4 | | LO4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | | LO5 | 5 | 5 | 4 | 5 | 4 | 4 | 5 | 5 | 4 | 5 | | LO6 | 5 | 5 | 4 | 4 | 4 | 5 | 5 | 5 | 4 | 5 | | LO7 | 4 | 4 | 5 | 5 | 4 | 4 | 4 | 5 | 4 | 5 | | LO8 | 4 | 5 | 5 | 4 | 4 | 4 | 5 | 4 | 5 | 5 | | LO9 | 4 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | | LO10 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | LO11 | 5 | 5 | 4 | 4 | 5 | 5 | 4 | 4 | 5 | 4 | | LO12 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 5 | 4 | 5 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
226 13 14 • e-mail: info@igdir.edu.tr
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