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Information
| Code | MATZ106 |
| Name | Abstract Mathematics |
| Term | 2022-2023 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. PERİHAN ARTUT |
| Course Instructor |
Doç. Dr. DİLEK KAHYALAR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
In this course, it is aimed to give the students the mathematical thinking skills by introducing the abstract structure of mathematics and proof techniques.
Course Content
Sets, propositions, proof methods, relation and function concept.
Course Precondition
None
Resources
H. Hilmi Hacısalihoğlu, Zühtü Özel (2020) Soyut Matematik, Seçkin Yayıncılık, Basri Çelik (2022). Soyut Matematik, Seçkin Yayıncılık
Notes
https://library.cu.edu.tr/cu/e-kaynaklar/veritabanlari
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Makes operations related to set concept, makes definitions about symbolic logic and propositions algebra , solves problems related to propositions. |
| LO02 | Explains the concepts of axiom, theorem, interprets mathematical proof methods, determines which proof methods will be used for the given example, explains the concept of relation. |
| LO03 | Defines the properties of equivalence relation and equivalence relation, constructs numbers with equivalence class concept, explains the concept of functions and types of functions. |
| LO04 | Explains the concept of functions and types of functions. |
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. | |
| 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. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | |
| 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. | |
| 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 | Concepts of set | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Proposition, conjunctions, accuracy tables | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 3 | Tautology and contradiction, equivalent propositions | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | quantifiers | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Axiom, theorem, Introduction to proof methods | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Direct proof method,,proof by contradiction method | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım |
| 7 | Proofs of division | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Preparing to exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Proof by giving contrast examples | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım |
| 10 | Proof through contradiction | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 11 | Proof by induction | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 12 | Concept of relation | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Equivalence relation, | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Equivalence classes | To examine the related section from suggested sources | Öğretim Yöntemleri: Soru-Cevap, Alıştırma ve Uygulama |
| 15 | Fonctions | To examine the related section from suggested sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 16 | Term Exams | Preparing to exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Preparing to exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 10 | 10 |
| Final Exam | 1 | 20 | 20 |
| Total Workload (Hour) | 128 | ||
| Total Workload / 25 (h) | 5,12 | ||
| ECTS | 5 ECTS | ||