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Information
| Unit | FACULTY OF EDUCATION |
| ELEMENTARY MATHEMATICS EDUCATION PR. | |
| Code | MATZ113 |
| Name | Abstract Mathematics |
| Term | 2025-2026 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | FE Field Education Courses C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. KAMURAN TARIM |
| Course Instructor |
Dr. Öğr. Üyesi Emrah KORKMAZ
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to equip students with skills in mathematical thinking and logical reasoning. By working on topics such as logic, sets, proof techniques, and relations, students strengthen their ability to engage with abstract concepts and become well-prepared for advanced mathematics courses.
Course Content
The content of this course consists of four main sections: Logic, Sets, Proof Techniques, and Relations.
Course Precondition
There are no prerequisites.
Resources
Ahmet Arıkan, Sait Halıcıoğlu, Abstract Mathematics, 6th Edition, Palme Publishing, 2021.
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Accurately defines and uses the propositions, logical connectives, and quantifiers that form the foundation of mathematical logic |
| LO02 | Can test the truth or validity of mathematical arguments using rules of logic and principles of inference. |
| LO03 | Can comprehend the fundamental principles of set theory and set operations (such as union, intersection, etc.) and apply these concepts to solve mathematical problems. |
| LO04 | Can analyze a mathematical proposition and apply fundamental proof techniques such as direct proof, proof by contradiction, and contrapositive proof. |
| LO05 | Recognizes special proof techniques (such as proof by cases, existence and uniqueness proofs) and can apply them in appropriate situations. |
| LO06 | Recognizes the properties of relations (reflexivity, symmetry, antisymmetry, transitivity) and can distinguish equivalence relations in different contexts |
| LO07 | Understands the concepts of equivalence classes and partitioning of sets, and can establish the relationship between these concepts. |
| LO08 | Can establish logical connections between abstract mathematical concepts and transfer this knowledge to solve new problems. |
| LO09 | Can read and comprehend mathematical texts and proofs, and express their own arguments in a clear and coherent manner. |
| LO10 | Develops a solid logical and conceptual foundation necessary for advanced mathematics courses such as algebra, analysis, and topology. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has enough knowledge about mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has pedagogical knowledge about teaching profession and field. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Implements classroom management approaches to be used in educational environments effectively. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Uses Turkish properly and effectively according to the rules. | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Selects and designs appropriate materials, in mathematics teaching. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Monitors students' progress using different assessment and evaluation methods and techniques. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Takes responsibility as an individual and as a team member to solve problems related to the field. | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people. | 2 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses information and communication technologies and other related materials for an effective mathematics teaching. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Has enough foreign language knowledge to follow foreign resources related to the field. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Has the knowledge of the purpose, structure and functioning of the Turkish education system. | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes a teacher who adheres to Atatürk's principles and revolutions. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | propositions | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 2 | Logical Equivalence: Rules of Logic | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Logical Implication, Rules of Inference | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Use of Quantifiers and Quantified Propositions | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Definition of a Set, Subsets | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Set Operations | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Families of Sets | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Repetition of the topics covered in lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Concept of Proof, Trivial and Vacuous Proofs, Direct Proof | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Proof by Contrapositive, Proof by Cases | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Proof by Contradiction, Existence and Uniqueness Proof | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Relations, Properties of Relations | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Equivalence Relations | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Partitions of Sets and Equivalence Classes | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Order Relations | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 16 | Term Exams | Repetition of the topics covered in lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Repetition of the topics covered in lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
Assessment (Exam) Methods and Criteria
Current term shares have not yet been determined. Shares of the previous term are shown.
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 128 | ||
| Total Workload / 25 (h) | 5,12 | ||
| ECTS | 5 ECTS | ||