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Information
| Code | MATZ116 |
| Name | Abstract Mathematics II |
| Term | 2024-2025 Academic Year |
| Semester | 2. 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 |
Arş.Gör.Dr. Emrah KORKMAZ
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to examine the basic number systems of mathematics: natural numbers, integers, rational numbers, real numbers, and complex numbers.
Course Content
Quotient rings. the construction of natural numbers. The construction of integers. The construction of rational numbers. Cauchy sequences in an ordered field. The construction of real numbers. The construction of complex numbers.
Course Precondition
none
Resources
1-) Bhattacharya, P. B., Jain, S. K., & Nagpaul, S. R. (1986). Basic abstract algebra. Cambridge University Press. 2-) Mendelson, E. (2008). Number systems and the foundations of analysis. Dover Publications. SUPPLEMENTARY BOOKS: 1-) Çallıalp, F. (2009). Soyut Matematik. Birsen Yayınevi. 2-) Nesin, A. (2010). Aksiyomatik Kümeler Kuramı I. Nesin Yayınevi.
Notes
Related digital resources.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands the algebraic structure of residue class rings, ring homomorphisms, and the First Isomorphism Theorem for rings, and can explain them with examples. |
| LO02 | State the Peano axioms and construct the natural numbers axiomatically using the Recursion Theorem, and understand their algebraic structure. |
| LO03 | Can use relations in the construction of integers, rational numbers, and complex numbers, and understands the algebraic structures of these number systems. |
| LO04 | Understand how the real numbers are constructed using Cauchy sequences and understand the completeness property of the real numbers. |
| LO05 | Defines ordering relations on the sets of natural numbers, integers, and rational numbers, and understands the properties of these ordering relations. |
| LO06 | Defines the ordering relation on the set of real numbers and understands the relation between the completeness property and ordering in the real numbers. |
| LO07 | Recognizes number sets as abstract objects. |
| LO08 | Can compare the algebraic structures of number systems and analyze the properties of these structures. |
| LO09 | Can use appropriate mappings to move between number systems. |
| LO10 | Can solve mathematical problems involving number sets by using their relevant properties. |
| LO11 | Can understand abstract mathematical concepts and express them accurately. |
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. | 2 |
| 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. | 2 |
| 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. | 2 |
| 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 | Quotient ring, ring homomorphisms. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | The First Isomorphism Theorem for Rings. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Peano axioms, defining binary operations on natural numbers using the Recursion Theorem. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | The algebraic structure of natural numbers. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | The ordering of natural numbers | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | The construction of the integers and the definition of binary operations. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | The algebraic structure and ordering of integers | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Source 1,2 | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The construction of rational numbers and the definition of binary operations. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | The algebraic structure of rational numbers and ordering of rational numbers. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Cauchy sequences in an ordered field. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | The construction of real numbers and the definition of binary operations. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | The algebraic structure of real numbers and ordering of real numbers. | Source 1 | Öğretim Yöntemleri: Soru-Cevap, Anlatım |
| 14 | The construction of complex numbers, the definition of binary operations, and the algebraic structure of complex numbers. | Source 1 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | The polar form and geometric interpretations of complex numbers. | Sorce 2 | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams. | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams. | Term Exams | 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.) | 3 | 8 | 24 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 126 | ||
| Total Workload / 25 (h) | 5,04 | ||
| ECTS | 5 ECTS | ||