MATZ113 Abstract Mathematics

5 ECTS - 3-0 Duration (T+A)- 1. Semester- 3 National Credit

Information

Code MATZ113
Name Abstract Mathematics
Term 2024-2025 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 Belirsiz
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. KAMURAN TARIM
Course Instructor Prof. Dr. PERİHAN ARTUT (A Group) (Ins. in Charge)


Course Goal / Objective

The aim of the course is to gain the ability to think abstractly, to gain the ability to make proofs and to introduce the basic concepts of analysis and algebra.

Course Content

The content of this course includes the development of abstract thinking skills, the learning of proof techniques and the basic concepts of calculus and algebra. In this course, students will deepen their mathematical thinking and develop their ability to work with abstract concepts, reason logically and construct valid proofs. In addition, the basic building blocks of analysis and algebra will be introduced and the importance of abstract thinking and proof processes in mathematics will be emphasized.

Course Precondition

There are no prerequisites.

Resources

S. Akkas, H. H. Hacısalihoğlu, Abstract Mathematics, Gazi University publication No:43, Ankara, 1984. A. Dönmez., Set Theory and Abstract Mathematics, Atatürk University publications No. 638, Erzurum, 1987.

Notes

F. Çallıalp, Abstract Mathematics, Istanbul Technical University. Istanbul, 1995.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Explains the concept of deduction from proof techniques of theorems.
LO02 Proves theorems about sets with the concept of set.
LO03 Knows the concept of relation and properties of equivalence relation.
LO04 Explains the order relation and the concepts of exact ordering and good ordering.
LO05 It defines that the function is a special relation and functions of a special type.
LO06 Defines the concept of operation, unary and binary operations.


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 propositions Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
2 Basic proof techniques Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
3 clusters Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
4 Cluster operations Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
5 Relationship and properties Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
6 Equivalence relation and fragmentation. Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
7 Ranking relation and its properties Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Repetition of the topics covered in lecture notes and resources Ölçme Yöntemleri:
Yazılı Sınav
9 functions Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
10 Operation, unary, binary, and n-fold operations Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
11 Internal and external transactions Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
12 Algebraic structures, Group and basic properties Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
13 Ring and Body structure Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
14 Module structure Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
15 Problem solution Reading the relevant parts of the course materials Öğretim Yöntemleri:
Anlatım
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


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 3 42
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) 114
Total Workload / 25 (h) 4,56
ECTS 5 ECTS

Update Time: 14.11.2024 07:31