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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 | Lisans Dersi |
| 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 Kenneth H. Rosen, Discrete Mathematics and Its Applications, 7th Edition, McGraw-Hill Companies, Inc. 2012. L.Gilbert, J. Gilbert, Elements of Modern Algebra, 7th Edition, Brooks/Cole, Cengage Learning, 2009. Fethi Çallıalp, Soyut Matematik, 1.Baskı, Birsen Yayınevi, 2012. Hüseyin Bilgiç, Soyut Matematik Ders Notları, Kahramanmaraş Sütçü İmam Üniversitesi, 2014. https://acikders.ankara.edu.tr/course/view.php?id=25 Timur Karaçay, Soyut Matematik, 1. Baskı, Seçkin Yayıncılık, 2014 Okay Çelebi, Öner Çakar, Soyut Matematik, 6. Baskı, Ankara Üniversitesi Fen Fakültesi Yayınları, Ankara, 2009. Sait AKKAŞ, H. Hilmi HACISALİHOĞLU, Zühtü ÖZEL, Arif SABUNCUOĞLU, Soyut Matematik, 3. Baskı, Gazi Üniversitesi, Fen-Ede. Fak. yayıları, ANKARA, 1998.
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 | Explain 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 | Solves relations and functions problems |
| LO07 | Solves problems related to the concept of operations and 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. | 3 |
| 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. | 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 | Basic proof techniques | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | clusters | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Cluster operations | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Relationship and properties | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Equivalence relation and fragmentation. | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Ranking relation and its properties | 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 | functions | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Operation, unary, binary, and n-fold operations | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Internal and external transactions | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Algebraic structures, Group and basic properties | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Ring and Body structure | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Module structure | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Problem solution | Reading the relevant parts of the course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 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 | ||