MATZ106 Abstract Mathematics

5 ECTS - 2-0 Duration (T+A)- 2. Semester- 2 National Credit

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

Update Time: 25.01.2023 10:30